Six Sigma is a data-driven methodology for improving processes by reducing variation. It was developed by Motorola in the 1980s to help address quality issues that were causing them to lose market share to Japanese competitors. Motorola found that the Japanese companies had much lower variation in their production processes, allowing them to produce higher quality products at a lower cost. By implementing Six Sigma, Motorola was able to improve their processes, lower defects, and increase customer satisfaction, leading to billions of dollars in savings over time. The core of Six Sigma is reducing defects to 3.4 per million opportunities through the DMAIC process of Define, Measure, Analyze, Improve, and Control. It has now been adopted by many major companies
DMAIC, which stands for Define, Measure, Analyze, Improve and Control, has provided a structure for process improvement for almost four decades. It’s an easy-to-follow five-step method that works in any industry and on any process. Tune in to this 1-hour Introductory webinar to get a primer on this how this handy model can help you in your quest to improve the world around you.
https://goleansixsigma.com/webinar-introduction-dmaic/
DMAIC is a methodology for improving existing processes. DMAIC stands for Define, Measure, Analyze, Improve, and Control.
https://goleansixsigma.com/lean-six-sigma-step-by-step/
DMAIC, which stands for Define, Measure, Analyze, Improve and Control, has provided a structure for process improvement for almost four decades. It’s an easy-to-follow five-step method that works in any industry and on any process. Tune in to this 1-hour Introductory webinar to get a primer on this how this handy model can help you in your quest to improve the world around you.
https://goleansixsigma.com/webinar-introduction-dmaic/
DMAIC is a methodology for improving existing processes. DMAIC stands for Define, Measure, Analyze, Improve, and Control.
https://goleansixsigma.com/lean-six-sigma-step-by-step/
Learn about the DMAIC method that is used in Six Sigma. This Overview will walk you through Define, Measure, Analyze, Improve and Control in under 5 minutes. Learn more about the DMAIC method and other six sigma techniques on Lean Strategies International LLC's website: www.leanstrategiesinternational.com
I've been asked to put together a basic (and therefore relatively quick) introduction to Lean Six Sigma & DMAIC. While it’s not yet finished, I thought I would put it out there for people to comment on. Since the presentation is supposed to be training material there’s more text on the slides than I would prefer, but there are a few exercises and games to get the trainees involved.
I've put the PowerPoint version on my blog:
http://alesandrab.wordpress.com/2013/06/07/introduction-to-lean-six-sigma-dmaic/
Basic understanding of lean six sigma approach for improvementViral Jain
Before we start working on a project for process improvement.
It is very important to create awareness.
I made this presentation to provide basic understanding of Lean and six sigma.
Usually audience used to be SME, process owner and Higher management people.
After this training ,audience gets a roadmap/ strategy for improvement and how I will help them to improve.
I take their inputs after training and than we start with VOC, VOB and identification of problems and this is how I prefer to start.
This presentation is for the personnel who are going to be a part of Six Sigma project as process owner or team member & need to know the basics.
The scope of this presentation is “Overview” & “Define” of Six Sigma.
Lean six sigma explained: Beginners trainingQualsys Ltd
A free online introduction to Lean six sigma principles.
Includes lean six sigma tools, philosophy, disciplines, history overview of lean six sigma, applying DMAIC for complex decision making, using Qualsys EQMS software for Lean Six Sigma.
six sigma DMAIC approach for reducing quality defects of camshaft binding pro...Niranjana B
Data collection for 11 months revealed that 26% of the defects are due to improper camshaft binding. The six sigma approach involves DMAIC approach with statistical tools involved in each stage. The main root are identified and improvements are implemented. The quality is improved by reducing the number of defects
Learn about the DMAIC method that is used in Six Sigma. This Overview will walk you through Define, Measure, Analyze, Improve and Control in under 5 minutes. Learn more about the DMAIC method and other six sigma techniques on Lean Strategies International LLC's website: www.leanstrategiesinternational.com
I've been asked to put together a basic (and therefore relatively quick) introduction to Lean Six Sigma & DMAIC. While it’s not yet finished, I thought I would put it out there for people to comment on. Since the presentation is supposed to be training material there’s more text on the slides than I would prefer, but there are a few exercises and games to get the trainees involved.
I've put the PowerPoint version on my blog:
http://alesandrab.wordpress.com/2013/06/07/introduction-to-lean-six-sigma-dmaic/
Basic understanding of lean six sigma approach for improvementViral Jain
Before we start working on a project for process improvement.
It is very important to create awareness.
I made this presentation to provide basic understanding of Lean and six sigma.
Usually audience used to be SME, process owner and Higher management people.
After this training ,audience gets a roadmap/ strategy for improvement and how I will help them to improve.
I take their inputs after training and than we start with VOC, VOB and identification of problems and this is how I prefer to start.
This presentation is for the personnel who are going to be a part of Six Sigma project as process owner or team member & need to know the basics.
The scope of this presentation is “Overview” & “Define” of Six Sigma.
Lean six sigma explained: Beginners trainingQualsys Ltd
A free online introduction to Lean six sigma principles.
Includes lean six sigma tools, philosophy, disciplines, history overview of lean six sigma, applying DMAIC for complex decision making, using Qualsys EQMS software for Lean Six Sigma.
six sigma DMAIC approach for reducing quality defects of camshaft binding pro...Niranjana B
Data collection for 11 months revealed that 26% of the defects are due to improper camshaft binding. The six sigma approach involves DMAIC approach with statistical tools involved in each stage. The main root are identified and improvements are implemented. The quality is improved by reducing the number of defects
A Gyrocopter, Gyroplane, or Gyro for short, can be considered a cross between a helicopter and a fixed wing airplane. A Gyro uses rotor blades like a helicopter, but uses a propeller for power, as does a fixed wing airplane.
The rotor blades on top of a Gyro are mounted on a free spinning bearing and teetering system. These blades get their lifting power from the air moving up through them. As they move through the air they spin like a windmill. This spinning produces lift.
The forward motion of the Gyro provides the air moving up through the rotor, and a propeller provides the forward motion. As with a fixed wing airplane, in the absence of engine power, gravity must provide this forward motion.
To differentiate a helicopter from a gyro is simple. In a helicopter the rotor blades are powered. This power to the rotor blades creates an equal and opposite torque on the helicopter fuselage. A tail rotor is required to counteract this torque. A Gyro does not create this torque and therefore does not need a tail rotor
An autogyro is a flying machine. Like a helicopter, it is a rotary wing aircraft- which means that it has a rotor to provide lift instead of wings like conventional airplanes. Unlike a helicopter, the rotor is not powered by the engine. It is made to spin by aerodynamic forces, through a phenomenon called autorotation. Since the rotor is not powered, an autogyro needs a separate source for propulsion, like an airplane. Conventionally, these have been propellers, but it's possible to use jet engines as well.
Our solution to Marvel\'s increasing market power and expanding product portfolio centered around acquiring human and physical capital to vertically integrate the movie production process.
This is an introduction for six sigma green belt program , it briefly describes the its history, adoption , and various component and tools . This presentation also include the current ASQ examination pattern .
Description of various types of clutches and gear boxes has been given in the following sections of this unit. The term ‘Transmission’ is used for a device which is located between clutch and propeller shaft. It may be a gear box, an over drive or a torque converter, etc.
For Video on Transmission System Click The Link Below:-
https://www.youtube.com/watch?v=_EPsdRP2nXI
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#An Introduction to Lean Six Sigma (6σ)# By SN Panigrahi, SN Panigrahi, PMP
#An Introduction to Lean Six Sigma (6σ)# By SN Panigrahi,
Essenpee Business Solutions,
Lean - Six Sigma,
Six Sigma - Introduction,
Six Sigma – Methodology - DMAIC,
Six Sigma – Tools & Techniques,
Lean Defined – 5 Principles of Lean,
Lean – 7 / 8 Wates,
Implementing Lean Six Sigma
This slide deck will help you appreciate the application of statistics (and now data science) in the field of Quality Management and Process Improvement. And why is there a need to produce a consistent "in spec" product at 99.9997% of the time.
In the early and mid-1980s, Motorola engineers decided that the traditional quality levels — measuring defects in thousands of opportunities – didn’t provide enough granularity. Instead, they wanted to measure the defects per million opportunities. Motorola developed this new standard and made a cultural change associated with it. Six Sigma helped Motorola realize powerful bottom-line results in their organization – in fact, they documented more than $16 Billion in savings as a result of our Six Sigma efforts.
Six Sigma has evolved over time. It’s more than just a quality system like TQM or ISO. It’s a way of doing business.
Six Sigma at many organizations simply means a measure of quality that strives for near perfection. Six Sigma is a disciplined, data-driven approach and methodology for eliminating defects (driving toward six standard deviations between the mean and the nearest specification limit) in any process – from manufacturing to transactional and from product to service. A Six Sigma defect is defined as anything outside of customer specifications.
A Six Sigma opportunity is then the total quantity of chances for a defect.
Total Quality Management (TQM) is a comprehensive and structured approach to organizational management that seeks to improve the quality of products and services through ongoing refinements in response to continuous feedback. Six Sigma is a disciplined, data-driven approach and methodology for eliminating defects (driving toward six standard deviations between the mean and the nearest specification limit) in any process – from manufacturing to transactional and from product to service.
Democratizing Fuzzing at Scale by Abhishek Aryaabh.arya
Presented at NUS: Fuzzing and Software Security Summer School 2024
This keynote talks about the democratization of fuzzing at scale, highlighting the collaboration between open source communities, academia, and industry to advance the field of fuzzing. It delves into the history of fuzzing, the development of scalable fuzzing platforms, and the empowerment of community-driven research. The talk will further discuss recent advancements leveraging AI/ML and offer insights into the future evolution of the fuzzing landscape.
Student information management system project report ii.pdfKamal Acharya
Our project explains about the student management. This project mainly explains the various actions related to student details. This project shows some ease in adding, editing and deleting the student details. It also provides a less time consuming process for viewing, adding, editing and deleting the marks of the students.
Forklift Classes Overview by Intella PartsIntella Parts
Discover the different forklift classes and their specific applications. Learn how to choose the right forklift for your needs to ensure safety, efficiency, and compliance in your operations.
For more technical information, visit our website https://intellaparts.com
Sachpazis:Terzaghi Bearing Capacity Estimation in simple terms with Calculati...Dr.Costas Sachpazis
Terzaghi's soil bearing capacity theory, developed by Karl Terzaghi, is a fundamental principle in geotechnical engineering used to determine the bearing capacity of shallow foundations. This theory provides a method to calculate the ultimate bearing capacity of soil, which is the maximum load per unit area that the soil can support without undergoing shear failure. The Calculation HTML Code included.
Vaccine management system project report documentation..pdfKamal Acharya
The Division of Vaccine and Immunization is facing increasing difficulty monitoring vaccines and other commodities distribution once they have been distributed from the national stores. With the introduction of new vaccines, more challenges have been anticipated with this additions posing serious threat to the already over strained vaccine supply chain system in Kenya.
Event Management System Vb Net Project Report.pdfKamal Acharya
In present era, the scopes of information technology growing with a very fast .We do not see any are untouched from this industry. The scope of information technology has become wider includes: Business and industry. Household Business, Communication, Education, Entertainment, Science, Medicine, Engineering, Distance Learning, Weather Forecasting. Carrier Searching and so on.
My project named “Event Management System” is software that store and maintained all events coordinated in college. It also helpful to print related reports. My project will help to record the events coordinated by faculties with their Name, Event subject, date & details in an efficient & effective ways.
In my system we have to make a system by which a user can record all events coordinated by a particular faculty. In our proposed system some more featured are added which differs it from the existing system such as security.
COLLEGE BUS MANAGEMENT SYSTEM PROJECT REPORT.pdfKamal Acharya
The College Bus Management system is completely developed by Visual Basic .NET Version. The application is connect with most secured database language MS SQL Server. The application is develop by using best combination of front-end and back-end languages. The application is totally design like flat user interface. This flat user interface is more attractive user interface in 2017. The application is gives more important to the system functionality. The application is to manage the student’s details, driver’s details, bus details, bus route details, bus fees details and more. The application has only one unit for admin. The admin can manage the entire application. The admin can login into the application by using username and password of the admin. The application is develop for big and small colleges. It is more user friendly for non-computer person. Even they can easily learn how to manage the application within hours. The application is more secure by the admin. The system will give an effective output for the VB.Net and SQL Server given as input to the system. The compiled java program given as input to the system, after scanning the program will generate different reports. The application generates the report for users. The admin can view and download the report of the data. The application deliver the excel format reports. Because, excel formatted reports is very easy to understand the income and expense of the college bus. This application is mainly develop for windows operating system users. In 2017, 73% of people enterprises are using windows operating system. So the application will easily install for all the windows operating system users. The application-developed size is very low. The application consumes very low space in disk. Therefore, the user can allocate very minimum local disk space for this application.
Explore the innovative world of trenchless pipe repair with our comprehensive guide, "The Benefits and Techniques of Trenchless Pipe Repair." This document delves into the modern methods of repairing underground pipes without the need for extensive excavation, highlighting the numerous advantages and the latest techniques used in the industry.
Learn about the cost savings, reduced environmental impact, and minimal disruption associated with trenchless technology. Discover detailed explanations of popular techniques such as pipe bursting, cured-in-place pipe (CIPP) lining, and directional drilling. Understand how these methods can be applied to various types of infrastructure, from residential plumbing to large-scale municipal systems.
Ideal for homeowners, contractors, engineers, and anyone interested in modern plumbing solutions, this guide provides valuable insights into why trenchless pipe repair is becoming the preferred choice for pipe rehabilitation. Stay informed about the latest advancements and best practices in the field.
Courier management system project report.pdfKamal Acharya
It is now-a-days very important for the people to send or receive articles like imported furniture, electronic items, gifts, business goods and the like. People depend vastly on different transport systems which mostly use the manual way of receiving and delivering the articles. There is no way to track the articles till they are received and there is no way to let the customer know what happened in transit, once he booked some articles. In such a situation, we need a system which completely computerizes the cargo activities including time to time tracking of the articles sent. This need is fulfilled by Courier Management System software which is online software for the cargo management people that enables them to receive the goods from a source and send them to a required destination and track their status from time to time.
Saudi Arabia stands as a titan in the global energy landscape, renowned for its abundant oil and gas resources. It's the largest exporter of petroleum and holds some of the world's most significant reserves. Let's delve into the top 10 oil and gas projects shaping Saudi Arabia's energy future in 2024.
Immunizing Image Classifiers Against Localized Adversary Attacksgerogepatton
This paper addresses the vulnerability of deep learning models, particularly convolutional neural networks
(CNN)s, to adversarial attacks and presents a proactive training technique designed to counter them. We
introduce a novel volumization algorithm, which transforms 2D images into 3D volumetric representations.
When combined with 3D convolution and deep curriculum learning optimization (CLO), itsignificantly improves
the immunity of models against localized universal attacks by up to 40%. We evaluate our proposed approach
using contemporary CNN architectures and the modified Canadian Institute for Advanced Research (CIFAR-10
and CIFAR-100) and ImageNet Large Scale Visual Recognition Challenge (ILSVRC12) datasets, showcasing
accuracy improvements over previous techniques. The results indicate that the combination of the volumetric
input and curriculum learning holds significant promise for mitigating adversarial attacks without necessitating
adversary training.
3. What is Six Sigma
A customer focused business
improvement process
Driven by teamwork, consensus &
logical reasoning
Structured methodology – DMAIC
Focuses on making the process
robust & reduce variations
Applies to any Process
4. What is Six Sigma
Six sigma is a highly disciplined and
quantitative strategic business
improvement approach that seeks to
increase both customer satisfaction
and an organization’s financial health.
Six Sigma helps a company focus on
developing and delivering near-
perfect products (durable goods or
services), to improve customer
satisfaction and the bottom line.
5. What Six Sigma is NOT
Six Sigma is NOT
A Quality Program
Cure for World
Hunger
Only for Technical
People
Just about
Statistics
Used when
solution is known
Used for
Firefighting
6. Six-Sigma – A note from
Originator of Six Sigma
“Six Sigma is not an improvement
program. It is instead a business
philosophy that employs a step by
step approach to reducing variation,
increasing quality, customer
satisfaction, and in time, market
share”
7. Overview of Six Sigma
CULTURAL
CHANGE
TRANSFORM THE
ORGANIZATION
GROWTH
REDUCE COSTS
PAIN, URGENCY,
SURVIVAL
SIX SIGMA AS A
PHILOSOPHY
SIX SIGMA AS A
PROCESS
SIX SIGMA AS
A
STATISTICAL
TOOL
8. What is Six Sigma?
Sigma is a measurement that indicates how
a process is performing
Six sigma stands for Six Standard
Deviations (Sigma is the Greek letter used
to represent standard deviation in statistics)
from mean. Six Sigma methodology
provides the techniques and tools to
improve the capability and reduce the
defects in any process.
Six Sigma is structured application of tools
and techniques applied on project basis to
achieve sustained strategic results.
9. What is Six Sigma
A Vision of a Six Sigma Company
Organizational
Issue
• Problem
Resolution
• Behavior
• Decision Making
• Process
Adjustment
• Supplier
Relationship
• Planning
• Design
• Employee Training
• Chain-of-command
• Direction
• Manpower
Traditional
approach
• Fixing (symptoms)
• Reactive
• Experience-based
• Tweaking
• Cost (piece price)
• Short-term
• Performance
• If Time Permits
• Hierarchy
• Seat-of-pants
• Cost
Six Sigma
Approach
• Preventing
(causes)
• Data-based
• Controlling
• Capability
• Long-term
• Producibility
• Mandated
• Empowered Teams
• Benchmarking and
metrics
• Asset
Traditional
approach
• Fixing (symptoms)
• Reactive
• Experience-based
• Tweaking
• Cost (piece price)
• Short-term
• Performance
• If Time Permits
• Hierarchy
• Seat-of-pants
• Cost
Six Sigma
Approach
• Preventing
(causes)
• Data-based
• Controlling
• Capability
• Long-term
• Producibility
• Mandated
• Empowered Teams
• Benchmarking and
metrics
• Asset
10. Character of 6s
Traditional Quality / Six Sigma Quality Method
ISSUE TRADITIONAL
APPROACH
SIX SIGMA
APPROACH
Index
Data
Target
Range
Method
Action
• % (Defect Rate)
• Discrete Data
• Satisfaction for
Mfg. Process
• Spec Outliner
• Experience + Job
• Bottom Up
• σ
• Discrete +
Continuous Data
• Customer
Satisfaction
• Variation
improvement
• Experience + Job
+ Statistical Ability
• Top Down
11. Aligning The Focus
Six Sigma Journey Started
(Traditional)
1000
Unassigned
Projects Six Sigma
Project
Strategic
DirectionTactical
Direction
Individual
Work
Group
(Lets do it) (Future)
12. What is Six Sigma Definition
2
Sigma
3
Sigma
4
Sigma
5
Sigma
6
Sigma
2σ
3σ
4σ
5σ
6σ
Sigma Level Defects/ Million Opportunities% Yield
308,537
66,807
6,210
233
3.4
69.1
93.3
99.4
99.98
99.9997
13. Six Sigma : The Statistical
Way
LSL USL LSL USL
LSL USL
Process of Target Excessive Variation
Reduce Variation % Center Process
Customers feel the
variation more than
the mean
Center
Proces
s
Reduc
e
Spread
Target
Target
Target
14. Six Sigma – Practical
Meaning
99% Good (3.8 Sigma) 99.99966% Good (6 Sigma)
• 20,000 lost articles of
mail per hour
• Unsafe drinking water
for almost 15 minutes
each day
• 5,000 incorrect surgical
operations per week
• Two short or long
landings at most major
airports each day
• 200,00 wrong drug
prescriptions each year
• No electricity for almost
seven hours each month
• Seven articles lost per
hour
• One unsafe minute every
seven months
• 1.7 incorrect operations
per week
• One short or long
landing every five years
• 68 wrong prescriptions
per year
• One hour without
electricity every 34 years
15. Philosophy of Six Sigma
Know What’s Important to the
Customer (CTQ)
Reduce Defects (DPMO)
Center Around Target (Mean)
Reduce Variation (σ)
18. History of Six Sigma
Quality tools like SPC, Cost of Quality,
Control Charts, Process capability etc. are
known to industry for long time, much before
birth of Six Sigma.
Quality Tools and Quality system
implementation was not in conjunction with
overall business Goals.
Traditional Quality Tools have limitations to
orient the efforts on Quality Improvements to
the Organizational direction basically due to
approach.
Motorola was the first Company to initiate the
Six Sigma breakthrough Strategy.
19. A Little Bit Of History
Six Sigma was developed by Bill Smith, QM at
Motorola
It’s implementation began at Motorola n 1987
It allowed Motorola to win the first Baldrige Award
in 1988
Motorola recorded more than $16 Billion savings
as a result of Six Sigma
Several of the major companies in the world
have adopted Six Sigma since then….
Texas Instruments, Asea Brown Boveri,
AlliedSignal, General Electric, Bombardier, Nokia
Mobile Phones, Lockheed Martin, Sony, Polaroid,
Dupont, American Express, Ford Motor,…..
The Six Sigma Breakthrough Strategy has become
a Competitive Tool
20. Motorola Case Study
In early 1980’ Motorola was facing a
serious competitive challenge from
Japanese Companies.
Motorola was losing the market share
and customer confidence.
Motorola had not done any major
changes to their products.
The competitors from Japan were
offering much better product at much
lower price with no field failures.
21. Motorola Case Study….Continue
When Motorola studies the competitors products,
it was revealed that the variation in key product
characteristics is very low.
The competitors products were available at lower
price.
The competitors products has very low warranty
failure rate.
Motorola was not able to match the competitors
price mainly due to high cost of Poor quality
largely due to high reject rate, high rework /
repair rate, high inspection cost, high warranty
failure rate etc.
THE TECHNICAL TEAM CONCLUDED THAT
THE COPETITORS ARE OFFERING BETTER
PRODUCT AT LOWER COST.
22. Motorola Case Study
Motorola requested to the competitors
from Japan to permit the Team from
Motorola to visit them fro Study.
Motorola sent the team of managers
to Japan to study the “Magic” of
Japanese companies.
What the team revealed?
23. Motorola Case Study
What Motorola learning was as follows:
Motorola was focusing too much on product
Quality i.e. Inspection, rework, repair etc.
The internal defect rate was very high inside
Motorola.
The reliability was slow since some of the
defects were passing on to the customer as
inspection lapses.
A dissatisfied customer was shouting loudly
and was taking away min 10 potential
customers.
As an effect of this, customers were lost to
the competitors.
24. Motorola Case Study
What was wrong?
Japanese were concentrating on
◦ Customers
◦ Processes
◦ People
Variation in product and process parameters was known and
controlled
All people were well trained and highly motivated
All activities and processes were highly standardized i.e. no
person dependence
Defect free lines and robust processes
Very less inspectors
Yet, very low defect rate, internal rejection and customer
complaints
VERY HIGH LEVEL OF CUSTOMER SATISFACTION
25. Motorola Case Study
WHAT WAS THE SECRET?
THE SECRET WAS CONTROL OVER VARIATION
Success factor:
Proactive Vs. Reactive Quality
26. The Impact Of Added
Inspection
3.4 ppm
100,000 ppm
6 ppm
If the likelihood of detecting the defect is
70% and we have 10 consecutive inspectors
with this level of capability, we would expect
about 6 escaping defects out of every
1,000,000 products produced
You can save yourself by producing quality not by
27. Motorola Case Study
In order to address these issues,
Motorola devised the Six Sigma
methodology.
Dr. Mikel Harry and Mr. Bill Smith were
pioneers in Developing and
implementing the Six Sigma
methodology at Motorola.
With implementation of Six Sigma,
Motorola could achieve:
4σ level in one and half year time
5σ level in following year
28. Six Sigma Progress
1985 1987 1992 1995 2002
Johnson & Johnson,
Ford, Nissan,
HoneywellGeneral Electric
Allied Signal
Motorola
Dr Mikel J Harry
wrote a Paper
relating early
failures to quality
29. What can it do?
Motorola:
5-Fold growth in Sales
Profits climbing by 20% pa
Cumulative savings of $14 billion over 11
years
General Electric
$2 billion savings in just 3 years
The no. 1company in the USA
Bechtel Corporation:
$200 million savings with investment of $30
million
It is high time, that Indian Companies also start
implementing Six Sigma for making
breakthrough improvements and to remain
31. Attempting to Define Quality
Experts’ definitions of quality fall into two
categories:
Level one quality is a simple matter of producing
products or delivering services whose
measurable characteristics satisfy a fixed set of
specifications that are usually numerically
defined.
Independent of any of their measurable
characteristics, level two quantity products and
services are simply those that satisfy customer
expectations for their use or consumption.
In short, level one quality means get it in the
specs,
and level two means satisfy the customer.
32. Quality Gap
Quality Gap
Understanding of
Needs
Customer
Perception of
Delivery
Customer
Expectations
Design of Products
Capability to Deliver
Design
Actual Delivery
Design Gap
Perception Gap
Operations Gap
Process Gap
Understanding the
Gap
33. Nine Dimensions of QUALITY
According to modern management
concepts, quality has nine dimensions:
1) Performance: main characteristics of
the product/service
2) Aesthetics: appearance, feel, smell,
taste
3) Special features: extra characteristics
34. Nine Dimensions of QUALITY
4) Conformance: how well the
product/service
conforms to customer’s
expectations
5) Safety: risk of injury
6) Reliability: consistency of
performance
35. Nine Dimensions of QUALITY
7) Durability: useful life of the
product/service
8) Perceived Quality: indirect evaluation
of quality (e.g.
reputation)
9) Service after Sale: handling of
Customer
complaints and
checking customer
satisfaction.
36. Evolution of Quality
Historically Contemporary
Reactive Quality
Quality Checks (QC) -
Taking the defectives
out of what is
produced
Proactive Quality
“Create process that
will produce less or
no defects”
37. Old Concept Of Quality
Past concepts of quality focused on
“conformance to standards”. This definition
assumed that as long as the company
produced quality products and services,
their performance standard was correct
regardless of how those standards were
met. Moreover, setting of standards and
measurement of performance was mainly
confined to the production areas and the
commercial and other service functions
were managed through command control.
38. Value Enrichment
The term ‘Value Enrichment’ for the
company means that they must strive to
produce highest quality products at the
lowest possible costs to be competitive
in the global markets.
For customers, the term ‘Value
Enrichment’ means that they have the
right to purchase high quality
products/services at the lowest cost.
39. Concept Of Value
Value to Customers
Value =
𝐖𝐡𝐚𝐭 𝐘𝐨𝐮 𝐑𝐞𝐜𝐞𝐢𝐯𝐞
𝐖𝐡𝐚𝐭 𝐘𝐨𝐮 𝐏𝐚𝐲
Price
+
Inconvenienc
e
Real
+
Perceived
42. Six Sigma and Cost Of
Quality
Six Sigma has a very significant impact on
the cost of quality. As the Sigma level
moves up, the cost of quality comes down
and vice versa. Traditionally recorded
quality cost generally account for only 4 to
5 percent of sales which mainly comprise
of scrap, re-work and warranty.
There are additional costs of quality which
are hidden and do not appear in the
account books of the company, as they are
intangible and difficult to measure.
43. Visible And Hidden Costs
Visible
Costs
Hidden
Costs
• Scrap
• Rework
• Warranty Costs
• Conversion
efficiency of
materials
• Inadequate
resources
utilization
• Excessive use of
materials
• Cost of re-design
and re—
inspection
• Cost of resolving
customer
problems
• Lost customers /
Goodwill
• High Inventory
44. Cost OF Quality At Various
Levels Of Sigma
6 3.4 <10%
5 233 10-15%
4 6210 15-20%
3 66807 20-30%
2 308537 30-40%
1 6,90000 >40%
Sigma
Defect Rate
(PPM)
Cost Of
Quality
Competitive Level
World Class
Industry
Average
Non
Competitive
45. What is The Cost Of Quality?
Cost of Quality: the cost of ensuring
that the job is done right + the cost of
not doing the job right.
Cost of Conformance + Cost of Non-
Conformance(Prevention and Appraisal) (Internal/External Defects)
46. Cost Of Quality
Prevention Costs
• Quality Planning
• Process Evaluation /
Improvement
• Quality Improvement Meetings
• Quality Training
External Failure Costs
• Complaint Handling
• Rework / Correction
• Re-Inspection
Internal Failure Costs
• Rework / Correction
• Re-Inspection
• Internal Reject
• Loss of Business
Appraisal Costs
• Source Inspection
• In / End-Process Inspection
• Calibration
• Specialist Cost
Direct Costs
Prevention Costs
• Quality Planning
• Process Evaluation /
Improvement
• Quality Improvement Meetings
• Quality Training
External Failure Costs
• Complaint Handling
• Rework / Correction
• Re-Inspection
Internal Failure Costs
• Rework / Correction
• Re-Inspection
• Internal Reject
• Loss of Business
Appraisal Costs
• Source Inspection
• In / End-Process Inspection
• Calibration
• Specialist Cost
48. Fundamental Steps
There are 5 fundamental Steps involved
in applying the breakthrough strategy
for achieving Six Sigma. These steps
are :-
Define
Measure
Analyze
Improve
Control
49. Define Phase
This phase defines the project. It
identifies critical customer requirements
and links them to business needs. It
also defines a project charter and the
business processes to be undertaken
for Six Sigma.
50. Define
Define D CM A I
Define Activities
Identify Project, Champion and Project Owner
Determine Customer Requirements and CTQs
Define Problem, Objective, Goals and Benefits
Define Stakeholders/Resource Analysis
Map the Process
Develop Project Plan
Define Quality Tools
Project Charter and Plan
Effort/Impact Analysis
Process Mapping
Tree Diagram
VOC
Kano Model
Pareto Analysis
51. Measurement Phase
This phase involves selecting product
characteristic, mapping respective
process, making necessary
measurements and recording the
results of the process. This is
essentially a data collection phase.
52. Measure – Operational Definition
Measure M CD A I
Measure Activities
Determine operational Definitions
Establish Performance Standards
Develop Data Collection and Sampling Plan
Validate the Measurements
Measurement System Analysis
Determine Process Capability and Baseline
Measure Quality Tools
Measurement Systems Analysis
Check Sheet
Process Capability
Process FMEA
53. Analysis Phase
In this phase an action plan is created
to close the “gap” between how things
currently work and how the organization
would like them to work in order to meet
the goals for a particular product or
service. This phase also requires
organizations to estimate their short
term and long term capabilities.
54. Analyze
Analyze A CMD I
Analyze Activities
Benchmark the Process or Product
Analysis of the Process Map
Brainstorm for likely causes
Establish Causal Relationships Using Data
Determine Root Cause(s) Using Data
Analyze Quality Tools
Cause and Effect or Event Diagram
Graphical Analysis
Statistical Analysis of Data
Hypothesis Testing
Correlation Regression
DOE
55. Improvement Phase
This phase involves improving
processes/product performance
characteristics for achieving desired
results and goals. This phase involves
application of scientific tools and
techniques for making tangible
improvements in profitability and
customer satisfaction.
56. Improve
Improve I CMD A
Improve Activities
Develop Solution Alternatives
Assess Risks and Benefits of Solution Alternatives
Implement error-proofing solutions
Validate Solution using a Pilot
Implement Solution
Determine Solution Effectiveness using Data
Improve Quality Tools
Brainstorming
FMEA
Risk Assessment
Poka Yoke
57. Control Phase
This Phase requires the process
conditions to be properly documented
and monitored through statistical
process control methods. After a
“setting in” period, the process
capability should be reassessed.
Depending upon the results of such a
follow-up analysis, it may be sometimes
necessary to revisit one or more of the
preceding phases.
58. Control – Develop Standards
Control CIMD A
Control Activities
Determine Needed Controls (measurement, design, etc.)
Implement and Validate Controls
Develop Transfer Plan
Realize Benefits of Implementing Solution
Institutional Changes
Close Project and Communicate Results
Control Quality Tools
Statistical Process Control
Process Map and FMEA
Control Plans
5S
Control Charts
60. Why Project Selection is
Important?
High leverage projects lead to largest
Savings
Large returns are expected by
management to justify the investment
in time and effort
Developing a Six Sigma culture
depend upon successful projects
having significant business impact
61. How To Focus Projects
Process Cost Savings Focus
Project Quality focus
Product focus (Six Sigma Design)
Problem Focus (Least Desirable Use)
62. Project Selection
Align with company objectives and
business plan (Annual Operating Plan)
– Voice of Customer/CT’s Inputs
– Quality (CTQ)/Cost (CTC)/ Delivery
(CTD)
– PPM / COPQ / RTY / Cycle Time
Consistent with principles of Six Sigma
– Eliminate process defects
Concentrate on “Common”
issues/opportunities …not “fir-fighting”
Large enough to justify the investment
63. Project Desirability
• Effort Required:- includes time required
of team members and expenditure of
money.
• Probability of Success:- An assessment
that takes into account various risk factors:
+ Time – uncertainty of the completion
date
+ Effort – uncertainty of the investment
required
+ Implementation – uncertainty of
roadblocks
65. Additional Project Considerations
Projects must serve as a learning
experience for Green Belts to use the six
Sigma tools
Projects scope should not be too large or
take too long to implement
Projects scope should be manageable
and take at least 255 of the potential
Green Belt’s time.
Pareto Chart may be used to Scope the
Project
Desirable to have a measurable variable
for the primary project output/metrics
66. Additional Project Considerations
• Projects must serve as a learning
experience for Green Belts to use the six
Sigma tools
• Projects scope should not be too large or
take too long to implement
• Projects scope should be manageable and
take at least 255 of the potential Green
Belt’s time.
• Pareto Chart may be used to Scope the
Project
• Desirable to have a measurable variable for
the primary project output/metricsDO NOT try to Solve World Hunger
67. Strategy At Various Levels
Almost every Organization can be
divided into 3 basic levels:-
1. Business level
2. Operations level
3. Process level.
It is extremely important that Six Sigma
is understood and integrated at every
level.
68. Strategies At Various Levels
Executives at the business level can use
Six Sigma for improving market share,
increasing profitability and organizations
long term viability.
Managers at operations level can use
Six Sigma to improve yield and reduce
the labor and material cost.
At the process level engineers can use
Six Sigma to reduce defects and
variation and improve process capability
leading to better customer satisfaction.
69. Factors To Control in
Improvement Project
Resources
Team availability
The right tools
Schedule
Be realistic
Be aggressive
Get buy-in
Scope of Work
Watch for scope creep
Stay focused
Anticipate and mitigate risk
Control any two areas, the third floats in
response
70. Meetings – Make Them
Effective
Defined goal for meeting
Notice and agenda
Decision makers prepare and participate
Action Items
Records
Balance Sheet
– Focused on process, not topic
– What helped us get to our goal
– What could have been better
– Take appropriate action
73. Establishing Customer Focus
• Customer – Anyone internal or
external to the organization who
comes in contact with the product
or output of work
• Quality – performance to the
standard expected by the Customer
74. Variation is the Enemy in
Achieving Customer Satisfaction
Variation
•Uncertainty
•Unknown
•Disbelief
•Risk
•Defect Rate
76. Something more on Variation
Any process has variation
There are two kinds of variation
Common cause variation
Special cause variation
Variation is measured in terms of sigma
or standard deviation.
77. Variation and Standard
Deviation
If a good deal of variation exists in a process activity,
that activity will have a very large standard
deviation.
As a result, the distribution will be very wide and flat.
Less Variation More Variation
78. Types of Variation
Special Cause: something different happening
at a certain time or place
Common Cause: always
present to some degree in the
process
We tamper with the system if we treat all variations as if it were special
cause
79. Dealing with Variation
Eliminate special cause variation by
recognizing it and dealing with it
outside of the process
Reduce common cause variation by
improving the process
81. Critical To Quality (CTQ)
are the key measurable characteristics of
a product or process whose
performance standards or specification
limits must be met in order to satisfy the
customer.
They align improvement or design efforts
with customer requirements.
82. Critical To Quality (CTQ)
1. To put it in layman’s terms, CTQs are
what the customer experts of a
product...
2. ...the spoken needs of the customer.
3. The customer may often express this
in plain English, but it is up to us to
convert them to measurable terms
using tools such as QFD, DFMEA,
etc.
83. Critical To Quality (CTQ)
1. List customer needs.
2. Identify the major drivers for these
needs (major means those which will
ensure that the need is addressed).
3. Break each driver into greater detail.
4. Stop the breakdown of each level
when you have reached sufficient
information that enables you to
measure whether you meet the
customer need or not.
84. Example – CTQ Tree
Ease of Operation
Ease of Maintenance
Ease of
Operation
and
Maintenance
Operator Training Time
(hrs.)
Setup Time (minutes)
Operation Accuracy
(errors/1000 ops)
Mean Time to Restore
(MTTR)
# Special Tools
Required
Maintenance Training Time
(hrs.)
Need CTQsDrivers
SpecificGeneral
Hard to Measure Easy to Measure
86. Importance of Project Charter
A project charter is a written document and
works as an agreement between
management and the team about what is
expected.
The charter:
Clarifies what is expected of the team.
Keeps the team focused.
Keeps the team aligned with
organizational priorities.
Transfers the project from the
champion(s) to the project team.
87. Team Charter
Problem Statement
– Currently we carry out reblows to the extent
of about 11-15% resulting in lower
converter life, lower productivity of
converter and increased Ferro-alloy and
oxygen consumption.
Scope
– All batches and all converters in SMS 1.
Project Goal and Measures
– Reblows should be less than 7.5% and 9%.
Expected Business Results
– We hope to save Rs. Xxxxx lakhs per year
due to this reduction in reblows.
88. Team Charter
Team Members
–Supervisor, two operators, technical
services, quality control
Support Required
–Allow for weekly team meetings
–Team budget for quick wins
Schedule
–Measure (7wks), Analyze (4wks),
Improve (6wks), Check (2wks), Control
(1wk), Standardise/Close (1wk)
89. Usual elements of a Project
Charter
Project Description – Business Case
Scope – Process/Product
Goals and Measures (Key Indicators)
Expected Business Results
Team Members
Support Required
Expected Customer Benefits
Schedule
91. Measurement Objective
The Measure phase aims to set a baseline
in terms of process performance
through the development of
clear and meaningful measurement
systems
92. The Measurement Process
TOOLS AND TECHNIQUS OF MEASURE
Develop
Process
Measures
Collect
Process
Data
Check
Data
Quality
Understand
Process
Behavior
Baseline
Process
Capability
and
Potential
How do you
measure
the
problem?
When and
where does
the data
come from?
How does
the process
currently
behave?
What is the
current
performance
of the process
with respect to
the customer
Does the data
represent
what you
think it does
Statistics
Operational
Definitions
Data Worlds
Process
Capability
Cp, Cpk
DPMO
Distributions
First pass
yield
Short/long
term variation
MSA
Gage R&R
Data
Collection
Methods
Data
Collection
Plans
Sampling
93. Statistical and Data World
If the data
is
AttributeCountContinuous
Relevant
statistical
model is …
Binomial
Distribution
Defects per
Unit (DPU)
Always
Poisson – if
process is
in control
Poisson
Distribution
When does
the
statistical
model
apply
Common
statistics
are…
Always
Binomial –
if process
is in control
Percentage
(Proportion)
Average (mean),
Standard
Deviation (sigma)
Not always –
validity of
normality needs
to be checked
Normal
Distribution
95. Statistics
The science of:
–Collecting,
–Describing
–Analyzing
–Interpreting data...
And Making Decisions
96. What are Statistics?
Descriptive Statistics
– Summarize and describe a set of data
– Mean, median, range, standard deviation,
variance, ....
Analytical Statistical (or Statistics)
– Techniques that help us make decisions in
the face of uncertainty
– Use concepts of descriptive statistics as a
base
– Hypothesis testing, means comparisons,
variance comparisons, proportions
comparisons, ...
97. Sample Versus Population
Using a small amount of data (Sample)...
to make assumptions (inferences)...
on a large amount of data (population).
Population: the total collection of
observations or measurements that are if
interest.
Sample: A subset of observations and
measurements taken form the population.
Why do we use samples?
Time
Cost
Destructive testing (need product left to sell !!)
Other?
98. Measures of Central
Tendency
What is the Median value of
Distribution?
– Median
What value represents the
distribution?
– Mode
What value represents the entire
distribution?
– Mean (x̄ )
What is the best measures of central
tendency?
99. Data Distributions
Mean: Arithmetic average of a set of
values
– Reflects the influence of all values
– Strongly influenced of all values
Median: Reflects the 50% rank – the
center number after a set of numbers
has been sorted from low to high.
– Does not include all values in calculation
– Is “robust” to extreme scores
Mode: The value or item occurring most
frequently in a series of observations or
statistical data.
100. Variable Data Location -
MeanMonth # of Units
Jan-2006 233
Feb-2006 281
Mar-2006 266
Apr-2006 237
May-2006 260
Jun-2006 250
Jul-2006 237
Aug-2006 275
Sep-2006 218
Oct-2006 279
Nov-2006 227
Dec-2006 246
Jan-2007 258
Feb-2007 272
Mar-2007 229
Apr-2007 240
May-2007 287
Jun-2007 260
Jul-2007 251
Aug-2007 288
Sep-2007 256
Oct-2007 219
Nov-2007 260
Dec-2007 249
n=24 = 𝟔𝟎𝟕𝟖
We have data on the monthly demand history of
one of our key product lines. Let’s calculate the
statistics for location.
Mean (𝑿)
Add all of the monthly numbers
Divide by the number of months in the
sample.
N=24, = 𝟔𝟎𝟖𝟕
𝑿 =
𝟔𝟎𝟖𝟕
𝟐𝟒
= 𝟐𝟓𝟑. 𝟐𝟓
Our average monthly shipment is 253 units
𝝁 =
𝒊=𝟏
𝑵
𝑿𝒊
𝑵
𝒙 =
𝒊=𝟏
𝒏
𝑿𝒊
𝒏
Populatio
n
Sample
101. Variable Data Location -
MedianMonth # of Units
Jan-1999 233
Feb-1999 281
Mar-1999 266
Apr-1999 237
May-1999 260
Jun-1999 250
Jul-1999 237
Aug-1999 275
Sep-1999 218
Oct-1999 279
Nov-1999 227
Dec-1999 246
Jan-2000 258
Feb-2000 272
Mar-2000 229
Apr-2000 240
May-2000 287
Jun-2000 260
Jul-2000 251
Aug-2000 288
Sep-2000 256
Oct-2000 219
Nov-2000 260
Dec-2000 249
Month # of Units
Sep-1999 218
Oct-2000 219
Nov-1999 227
Mar-2000 229
Jan-1999 233
Jul-1999 237
Apr-1999 237
Apr-2000 240
Dec-1999 246
Dec-2000 249
Jun-1999 250
Jul-2000 251
Sep-2000 256
Jan-2000 258
May-1999 260
Jun-2000 260
Nov-2000 260
Mar-1999 266
Feb-2000 272
Aug-1999 275
Oct-1999 279
Feb-1999 281
May-2000 287
Aug-2000 288
Statistics for
location ~
Median (x)
• Sort the data from
lowest to highest
• If there is an even
number of
observations, the
median is the
average of the two
middle values
(𝟐𝟓𝟏 + 𝟐𝟓𝟔)
𝟐
= 𝟐𝟓𝟑. 𝟓
102. Variable Data Location -
MedianMonth # of Units
Jan-1999 233
Feb-1999 281
Mar-1999 266
Apr-1999 237
May-1999 260
Jun-1999 250
Jul-1999 237
Aug-1999 275
Sep-1999 218
Oct-1999 279
Nov-1999 227
Dec-1999 246
Jan-2000 258
Feb-2000 272
Mar-2000 229
Apr-2000 240
May-2000 287
Jun-2000 260
Jul-2000 251
Aug-2000 288
Sep-2000 256
Oct-2000 219
Nov-2000 260
Dec-2000 249
Month # of Units
Sep-1999 218
Oct-2000 219
Nov-1999 227
Mar-2000 229
Jan-1999 233
Jul-1999 237
Apr-1999 237
Apr-2000 240
Dec-1999 246
Dec-2000 249
Jun-1999 250
Jul-2000 251
Sep-2000 256
Jan-2000 258
May-1999 260
Jun-2000 260
Nov-2000 260
Mar-1999 266
Feb-2000 272
Aug-1999 275
Oct-1999 279
Feb-1999 281
May-2000 287
Aug-2000 288
Statistics for
location ~
Mode
• The most
frequently
occurring
value is the
mode
260 is the mode
103. Variable Data Location -
Mode
Notes on mean
–A measure of central tendency
–Limitations:
Reflects the influence of all values
Strongly influenced by extreme values
Median (the centre number after sorting high to low) is
robust to extreme values.
104. Variable Data Description –
Range, Standard DeviationMonth # of Units
Jan-2006 233
Feb-2006 281
Mar-2006 266
Apr-2006 237
May-2006 260
Jun-2006 250
Jul-2006 237
Aug-2006 275
Sep-2006 218
Oct-2006 279
Nov-2006 227
Dec-2006 246
Jan-2007 258
Feb-2007 272
Mar-2007 229
Apr-2007 240
May-2007 287
Jun-2007 260
Jul-2007 251
Aug-2007 288
Sep-2007 256
Oct-2007 219
Nov-2007 260
Dec-2007 249
• Let’s use this same data to
calculate the statistics for
dispersion
These statistics are
Range and Standard
Deviation
105. Example – commuting time
Commute time (mins)
19.5 22.4 20.7 18.8 18.2
20.0 19.6 19.8 21.0 19.8
20.7 21.9 22.0 22.6 19.4
22.8 18.1 17.5 21.3 19.1
18.4 19.8 21.0 18.5 19.2
19.2 19.4 19.3 24.8 21.2
21.2 18.3 18.2 17.4 19.9
21.0 18.9 16.4 17.6 19.5
19.2 23.9 20.6 21.9 18.7
19.5 20.1 17.1 22.1 19.2
19.6 20.3 20.8 20.7 22.4
19.9 21.1 20.4 16.7 19.1
18.3 22.4 27.1 17.6 18.8
22.5 19.9 21.8 20.4 17.7
21.3 17.8 18.7 15.8 18.9
21.7 20.1 19.6 18.4 21.7
18.7 18.8 20.5 18.6 20.9
22.0 15.8 19.4 20.2 18.7
23.6 21.0 19.9 20.1 18.3
21.9 19.7 21.1 19.9 22.9
• Collect over a hundred
occurrences.
• Tabulate in chronological
order.
• Does the data show variation?
• Can you make out anything
with this arrangement of data?
• Let us try and make some
sense of this data…
106. Measure of variation – Standard
Deviation and Range
Category 1
15 2018 22 24 25
19.50 19.75 20.00 20.25 20.50
..
Summary for Commute time Anderson – Darling Normality Test
A-Squared
P-Value
0.42
0.312
What are the relative merits and demerits of standard deviation over range?
Mean
St.Dev
Variance
Skewness
Kurtosis
N
Minimum
1st Quartile
Median
3rd Quartile
Maximum
95% Confidence Interval for Mean
95% Confidence Interval for Mean
95% Confidence Interval for Mean
19.632
20.006
1.884
3.550
0.54470
1.30256
100
15.754
18.714
19.819
21.186
27.054
20.380
19.448 20.263
1.654 2.189Mean
Median
One measure
of variation
(std. dev)
Another
Measure of
variation
(Range)
Outlier
*
107. Variable Data Dispersion –
Standard Deviation
“s” or “standard deviation”
What does it mean?
–Standard deviation is a measure of
dispersion (or how our data is spread
out).
–Range will tell us the difference between
the highest and lowest values in a data
set, but nothing about how the data are
distributed.
–We need deviation to statistically describe
the distribution of values.
108. Variable Data Dispersion –
Standard Deviation
How we calculate it…
A measure of how far each point deviates from the
mean
We square each distance so that all the numbers
are positive
The sum of the squares, divided by the sample size,
is equal to the variance
The square root of the variance is the standard
deviation
– Variance can be added; standard deviations
cannot
𝜎 = 𝑖=1
𝑛
(𝑥𝑖 − 𝜇)2
𝑁
s = 𝑖=1
𝑛
(𝑥𝑖 − 𝑥)2
𝑛 − 1Population Sample
109. Variable Data Dispersion –
Standard Deviation CalculationMonth # of Units
Jan-2006 233
Feb-2006 281
Mar-2006 266
Apr-2006 237
May-2006 260
Jun-2006 250
Jul-2006 237
Aug-2006 275
Sep-2006 218
Oct-2006 279
Nov-2006 227
Dec-2006 246
Jan-2007 258
Feb-2007 272
Mar-2007 229
Apr-2007 240
May-2007 287
Jun-2007 260
Jul-2007 251
Aug-2007 288
Sep-2007 256
Oct-2007 219
Nov-2007 260
Dec-2007 249
-20.25
27.75
12.75
-16.25
6.75
-3.25
-16.25
21.75
-35.25
25.75
-26.25
-7.25
4.75
18.75
-24.25
-13.25
33.75
6.75
-2.25
34.75
2.75
-34.25
6.75
-4.25
-20.25
27.75
12.75
-16.25
6.75
-3.25
-16.25
21.75
-35.25
25.75
-26.25
-7.25
4.75
18.75
-24.25
-13.25
33.75
6.75
-2.25
34.75
2.75
-34.25
6.75
-4.25
𝑿𝒊 − 𝑿 (𝑿𝒊−𝑿) 𝟐
𝑺 = 𝒊=𝟏
𝒏
(𝒙𝒊 − 𝒙) 𝟐
𝒏 − 𝟏
𝑿 = 𝟐𝟓𝟑. 𝟐𝟓
Calculate
the Mean
Count the
Samples
n = 24
Square each
subtraction
result
Subtract the
mean from
each value
Sum the Squares
Calculate the Denominator
Complete the Calculation
𝒊=𝟏
𝒏
(𝒙𝒊 − 𝒙) 𝟐= 𝟗. 𝟖𝟑𝟏
𝒏 − 𝟏 = 𝟐𝟒 − 𝟏 = 𝟐𝟑
𝒔 =
𝟗. 𝟖𝟑𝟏
𝟐𝟑
= 𝟐𝟎. 𝟕
110. Variable Data Dispersion –
Standard Deviation
𝜎 = 𝑖=1
𝑛
(𝑥𝑖 − 𝜇)2
𝑁
Standard deviation of a population
– If your data is from a population versus a
sample from a population, use this formula to
calculate standard deviation
– The difference is the denominator
“N” versus “n-1”
111. Fundamental Topic
The Normal Curve
◦ Processes have natural variation
◦ Many processes behave “normally”
◦ Characterized by Bell Shaped Curve
– Mean near peak
– Curve is symmetric
◦ Mean
◦ Standard Deviation
Histogram of Diameter, with Normal Curve
Diameter
Frequency
112. Measures of Variability
•The Range is the distance between the extreme
values of data set. (Highest – Lowest)
•The Variance(S ) is the Average Squared
Deviation of each data point from the Mean.
•The Standard Deviation (s) is the Square Root of
the Variance.
•The range is more sensitive to outliners than the
variance.
•The most common and useful measure of
variation is the Standard Deviation.
113. Sample of Statistics versus
Population Parameters
EstimateStatistics Parameters
µ = Population Mean
s = Sample Standard
Deviation
X = Sample Mean
σ = Population
Standard Deviation
116. Normal Distribution
Description of a NORMAL
DISTRIBUTION
LOCATION:
•The Central Tendency
•It is usually expressed as the
AVERAGE
SPREAD:
•The dispersion
•It is usually expressed as
standard deviation (Sigma)
LOCATION
SPREAD
117. Properties of Normal Distribution
•Normal Distribution is Symmetric
–Has equal number of points on both
sides
–Mean Median and Mode Coincide
•Normal Distribution is Infinite
–The chance of finding a point anywhere
on the plus and minus side (around the
mean) is not absolutely Zero.
118. Properties Of Normal Distribution
Normal Curve & Probability Areas
-3𝝈 -2𝝈 -1𝝈 0 1𝝈 2𝝈 3𝝈
68%
95%
99.73%
119. Let’s Summarize…
We need data study, predict and improve
the processes.
Data may be Variable or Attribute.
To understand a data distribution, we need
to know its Center, Spread and Shape.
Normal Distribution is the most common
but not the only shape.
120. Standard Deviation -
Graphically
0
1
2
3
4
5
Monthly Demand in Units
Frequency
Month # of Units
Jan-1999 233
Feb-1999 281
Mar-1999 266
Apr-1999 237
May-1999 260
Jun-1999 250
Jul-1999 237
Aug-1999 275
Sep-1999 218
Oct-1999 279
Nov-1999 227
Dec-1999 246
Jan-2000 258
Feb-2000 272
Mar-2000 229
Apr-2000 240
May-2000 287
Jun-2000 260
Jul-2000 251
Aug-2000 288
Sep-2000 256
Oct-2000 219
Nov-2000 260
Dec-2000 249
Let’s take our demand data and develop
a histogram
1. Set up the scale and limits per subdivision
2. Plot the count of values that fall within each
subdivision on the scale
123. Standard Deviation – Simple
ApplicationFrequency
800
600
400
200
I have a process with mean of 43 and a standard deviation of
3
1200
1400
1000
37
43
42
41
40
39
38
48
47
46
45
44
49
35
36
51
50
68.3% of the data lies
between what points?
95.4% of the data lies
between what points?
99.7% of the area lies
between what points?
124. Standard Deviation – Simple
ApplicationFrequency
800
600
400
200
I have a process with mean of 43 and a standard deviation of
3
1200
1400
1000
37
43
42
41
40
39
38
48
47
46
45
44
49
35
36
51
50
68.3% of the data lies
between 40 and 45
𝑋 ± 1𝜎 = 43 ± 3
95.4% of the data lies
between 38 and 47
𝑋 ± 2𝜎 = 43 ± 6
99.7% of the area lies
between 36 and 49
𝑋 ± 3𝜎 = 43 ± 9
𝑿 = 𝟒𝟑
±3𝝈
±2𝝈
±1𝝈
125. Standard Deviation – Class
Exercise
What is the probability that a random
sample taken from this process…
Will have a value between 40 and 45?
Will have a value between 36 and 48?
Will have a value between 33 and 51?
68.3%
95.4%
99.7%
127. Probability
What is the role of Probability in
Statistics?
Any conclusion we reach on a
population, based on what we know
about a sample, is subject to
uncertainty.
This uncertainty is calculated and
described using probability theory
Every output (response) from a
process adds up to 100% of the
128. Probability Measure
Every event (=set of outcomes) is assigned a
probability measure.
The probability of every set is between 0 and 1,
inclusive.
The probability of the whole set outcomes is 1.
If A and B are two event with no common
outcomes, then the probability of their union is
the sum of their probabilities.
129. Probability Measure
Probability of an event A = P (A)
P (A) =
𝑪𝒉𝒂𝒏𝒄𝒆𝒔 𝒐𝒇 𝒇𝒂𝒗𝒐𝒓𝒊𝒏𝒈 𝒆𝒗𝒆𝒏𝒕
𝑻𝒐𝒕𝒂𝒍 𝒑𝒐𝒔𝒔𝒊𝒃𝒍𝒆 𝒆𝒗𝒆𝒏𝒕𝒔
Cards
Events: a red card (1/2); a jack (1/13)
Chances of calling correctly on toss of
a coin is ½ i.e. 0.5
130. Probability
Building an Understanding
We’ll start with a pair of dice
Our customer will only accept combinations
that equal 3,4,5,6,7,8,9,10 and 11.
What is the probability of meeting his
requirement?
131. Probability
Building an Understanding
The customer defines a response of 2 or 12 as a defect
Die 1 Roll
1 2 3 4 5 6
1 2 3 4 5 6 7
2 3 4 5 6 7 8
3 4 5 6 7 8 9
4 5 6 7 8 9 1
0
5 6 7 8 9 1
0
11
6 7 8 9 1
0
11 1
2
Die2Roll
Calculate all possible
responses from the
combinations of inputs
How many total combinations exist?
How many times is my response a 2?
What is the probability of a response of 2?
How many times is my response a 12?
What is the probability of a response of
12?
What is the probability of a defect? (2 or 12)
𝟏𝑹𝒆𝒔𝒑𝒐𝒏𝒔𝒆 𝒊𝒏 𝟑𝟔 =
𝟏
𝟑𝟔
= 𝟎. 𝟎𝟐𝟕𝟖 = 𝟐. 𝟕𝟖%
𝟔 𝒅𝒊𝒆 𝟏 × 𝟔 𝒅𝒊𝒆 𝟐 = 𝟑𝟔 𝑻𝒐𝒕𝒂𝒍 𝑪𝒐𝒎𝒃𝒊𝒏𝒂𝒕𝒊𝒐𝒏𝒔
𝟏𝑹𝒆𝒔𝒑𝒐𝒏𝒔𝒆 𝒊𝒏 𝟑𝟔 =
𝟏
𝟑𝟔
= 𝟎. 𝟎𝟐𝟕𝟖 = 𝟐. 𝟕𝟖%
𝟎. 𝟎𝟐𝟕𝟖 + 𝟎. 𝟎𝟐𝟕𝟖 = 𝟎. 𝟎𝟓𝟓𝟔 = 𝟓. 𝟓𝟔%
132. Probability
Building an Understanding
Die 1 Roll
1 2 3 4 5 6
1 2 3 4 5 6 7
2 3 4 5 6 7 8
3 4 5 6 7 8 9
4 5 6 7 8 9 1
0
5 6 7 8 9 1
0
11
6 7 8 9 1
0
11 1
2
Die2Roll
• Another example
What is the probability of rolling
a 7 using a fair pair of dice?
Die 1 Die 2 Probability
1 6 0.0278
2 5 0.0278
3 4 0.0278
4 3 0.0278
5 2 0.0278
6 1 0.0278
Total 0.1668
The probability of each roll
is included in each block
16.68% Probability
133. Probability
Value
(Response)
Frequency Probability
2 1 0.0278
3 2 0.0556
4 3 0.0833
5 4 0.1111
6 5 0.1389
7 6 0.1667
8 5 0.1389
9 4 0.1111
10 3 0.0833
11 2 0.0556
12 1 0.0278
Total 1.0000
Probability of any given value on Die
1 𝑭𝒐𝒓 𝒓𝒐𝒍𝒍𝒊𝒏𝒈 𝒕𝒉𝒆 𝒅𝒊𝒄𝒆, 𝒘𝒉𝒂𝒕 𝒊𝒔 𝒕𝒉𝒆
𝒑𝒓𝒐𝒃𝒂𝒃𝒊𝒍𝒊𝒕𝒚 𝒅𝒊𝒔𝒕𝒓𝒊𝒃𝒖𝒕𝒊𝒐𝒏?
𝟏
𝟔
= 𝟎. 𝟏𝟔𝟔𝟔 = 𝟎. 𝟏𝟔𝟔𝟕
Probability of any given value on Die
2 𝟏
𝟔
= 𝟎. 𝟏𝟔𝟔𝟔 = 𝟎. 𝟏𝟔𝟔𝟕
𝟏
𝟔
×
𝟏
𝟔
=
𝟏
𝟑𝟔
= 𝟎. 𝟎𝟐𝟕𝟕 = 𝟎. 𝟎𝟐𝟕𝟖
Probability of any given combination
135. Probability
Our customer will only accept combinations that equal
3,4,5,6,7,8,9,10,11
We have a 99.44% probability of
meeting the customers specification
The curve of this distribution becomes
it’s Probability Density Function
0
5
10
15
20 2
3
4
5
6
7
LSL USL
Probability
Response (Dice Total)
Value
(Response)
Frequenc
y
Probabilit
y
2 1 0.0278
3 2 0.0556
4 3 0.0833
5 4 0.1111
6 5 0.1389
7 6 0.1667
8 5 0.1389
9 4 0.1111
10 3 0.0833
11 2 0.0556
12 1 0.0278
136. Probability
Our customer will only accept combinations that equal
3,4,5,6,7,8,9,10,11
We have a 99.44% probability of
meeting the customers specification
The curve of this distribution becomes
it’s Probability Density Function
0
5
10
15
20
LSL USL
Probability
Response (Dice Total)
Value
(Response)
Frequenc
y
Probabilit
y
2 1 0.0278
3 2 0.0556
4 3 0.0833
5 4 0.1111
6 5 0.1389
7 6 0.1667
8 5 0.1389
9 4 0.1111
10 3 0.0833
11 2 0.0556
12 1 0.0278
137. Probability Theory
What is a Probability Density Function?
A Mathematical Function
It models the probability density reflected in a histogram
With more observations
Class intervals become narrower and more numerous
The histogram of the variable takes on the appearance of
a smooth curve
The total area under the curve must equal 1.
The probability that a random variable will assume
a value between any two points is equal in value to
the area under the random variable’s probability
density function between these two points.
h
What does this mean to us?
140. Probability Theory
What do we know about Probability Distribution?
The area under the curve always equals 1
We can determine the probability that a value of a
random variable will fall between 2 points on the
curve by calculating the area under the curve
between the two points
Why would we
want to do this?
How do we do
this?
141. Using Probability Distribution
The Standard Normal Distribution
Let’s take a look at the most important
PD…the standard normal distribution
We can transform each point on our normal
curve into a standard normal curve value
using the Z transform
𝒁 𝒑𝒐𝒑𝒖𝒍𝒂𝒕𝒊𝒐𝒏 𝒁 𝒔𝒂𝒎𝒑𝒍𝒆
142. Using Probability Distribution
• Standard Normal Curve Characteristics
The Standard Normal Distribution
𝑿 = 𝟎
𝑿 = 𝟐𝟓𝟑
𝟏𝝈 = 𝟏. 𝟎 𝟏𝝈 = 𝟏. 𝟎 𝟏𝝈 = 𝟏. 𝟎 𝟏𝝈 = 𝟏. 𝟎 𝟏𝝈 = 𝟏. 𝟎 𝟏𝝈 = 𝟏. 𝟎
𝟏𝝈 = 𝟐𝟏 𝟏𝝈 = 𝟐𝟏 𝟏𝝈 = 𝟐𝟏 𝟏𝝈 = 𝟐𝟏 𝟏𝝈 = 𝟐𝟏 𝟏𝝈 = 𝟐𝟏
It has a standard
deviation of 1.0
𝒁 𝒔𝒂𝒎𝒑𝒍𝒆 =
𝑿 − 𝑿
𝑺
It has a mean of 0.0
The area under the curve
equals 1
The curve is symmetrical
After the Z
Transform
The
Original
Distribution
143. Using Probability Distribution
The Standard Normal Distribution
The “How”
Find the points on the Standard Normal
Distribution that correspond to your values
Determine the area under the standard
normal curve that is between the points you
have found
If our data is normal, we can use the
Standard Normal Distribution
This saves us from having to do the
calculation for each specific situation!
144. Using Probability Distribution
The Standard Normal Distribution
A “Why” Example:
The unit sales of Product A follows a
normal distribution and has a monthly
average of 253 units with a standard
deviation of 21 units
= 253
S = 21
What is the probability
that next months sales
will be greater than 300
units?
𝑿
145. Using Probability Distribution
The Standard Normal Distribution
What is the probability that next month’s
unit sales will be greater than 300?
1. Find the point on the Standard Normal
Distribution that corresponds to 300
=25 S = 21
𝒁 𝒔𝒂𝒎𝒑𝒍𝒆 =
𝑋 − 𝑋
𝑆
=
300 − 253
21
= 2.24
𝑿
This is telling us that 300 is 2.24 standard deviations from the
mean
146. Using Probability Distribution
The Standard Normal Distribution
2) Determine the area under the
standard normal curve that is to the
right of 2.24
– How?
– Use the Table of the Standard Normal
Distribution
2.24
148. Using Probability Distribution
The Standard Normal Distribution
This table shows the area between 0 (the mean of a standard
normal table) and Z
Because the curve is symmetric…
The area of each ½ is 0.500
The area to the right of a positive value is 0.500 minus the
area between 0 and the Z value
For Z = 2.24 (the equivalent of 300)
Locate the row labeled .04
The area is 0.4875
Subtract this area from 0.500
0.500 – 0.4875 = 0.0125
I have a 1.25% probability that my unit sales next month
will be greater than 300 units
2.24
149. Normal Distribution
If you know your average value ( ) and
your standard deviation (s) then for a
given specification limit, it is possible to
predict rejections (if any), that will occur
even if you keep your process in control.
Example:
= 2.85, s = 0.02 (The dimensions
relate to a punched part).
Lat us find the percentage rejection if the
specified value is 2.85±0.04 i.e. the part
is acceptable between 2.81-2.89
151. Normal Distribution
Let A, B and C represent the areas under the curve
for the following conditions:
A – rejections for undersize
B – acceptable range
C – rejections for oversize
Total Area = A+B+C
Total Rejections = A+C
BA C
2.85
2.892.81
152. Normal Distribution
We will introduce a concept called Z which
we can use with a one-sided
distribution to
determine the area
under A, B and C and
thus the percentage
rejections and acceptable
components.
BA C
2.85
2.892.81
153. Normal Distribution
The area from Normal table
corresponding to 2 is 0.02275
Hence Rejection for Over size (Area
C) = 2.275%
Similarly one can find the rejection for
undersize
155. Binomial Distribution
When applicable:
When the variable is in terms of attribute data
and in binary alternatives such as good or bad,
defective or non-defective, success or failure etc.
Conditions:
The experiment consists of ‘n’ identical trials
There are only two possible outcomes on each
trial. We denote as Success(S) and Failure(F).
The probability of ‘S’ remains the same from trial
to trial and is denoted by ‘p’ and the probability of
‘F’ is ‘q’.
p+q = 1
The trials are independent
156. Binomial Distribution
For a random experiment of sample size n where
there are two categories of events, the probability of
success of the condition x in one category (where
there is n-x in the other category) is
𝑃(𝑋 = 𝑥) =
𝑛
𝑥
𝑝 𝑥
(𝑞) 𝑛−𝑥
, 𝑥 = 0,1,2, , 𝑛
Where (𝒒 = 𝟏 − 𝒑) is the probability that the vent
will not occur.
Where
𝑛
𝑥
=
𝑛!
𝑥! 𝑛−𝑥 !
157. Binomial Distribution
Consider now that the probability of having the
number “2” appear exactly three times in seven
rolls of a six die is
𝑷 𝑿 = 𝟑 =
𝒏
𝒙
𝒑 𝒙(𝟏 − 𝒑) 𝒏−𝒙
= 𝟑𝟓 𝟎. 𝟏𝟔𝟕 𝟑 𝟏 − 𝟎. 𝟏𝟔𝟕 𝟕−𝟑 = 𝟎. 𝟎𝟕𝟖𝟒
158. Poisson Distribution
When applicable:
No. of accidents in a specified period of time
No. of errors per 100 invoices
No. of telephone calls in a specified period of time
No. of surface defects in a casting
No. of faults of insulation in a specified length of cable
No. of visual defects in a bolt of cloth
No. of spare parts required over a specified period of
time
The no. of absenteeism in a specified no. of time
The number of death claims in a hospital per day
The number of breakdowns of a computer per month
The PPM of Toxicant found in water or air emission from
a manufacturing plant
159. Poisson Distribution
Two Properties of a Poisson Experiment
1) The Probability of an occurrence is he
same for any two intervals of equal length.
2) The occurrence or nonoccurrence in any
interval is independent of the occurrence or
nonoccurrence in any other interval.
160. Poisson Distribution
Conditions:
The experimental consists of counting
the number of times a particular event
occurs during a given unit of time or in a
given area or volume or weight or
distance etc.
The probability that an event occurs in a
given unit of time is same for all the
units.
The no. of events that occur in one unit
of time is independent of the number that
occur in other units.
The mean no. of events in each unit will
be denoted by .
161. Poisson Distribution
The Poisson Random Variable ‘X’ is the number of
events that occur in specified period of time.
𝑃 𝑋 = 𝑥 =
𝑒−𝝺
𝞴 𝑥
𝑥!
𝑥 = 0,1,2,3 …
A company observed that over several years they had a mean
manufacturing line shutdown rate of 0.10 per day. Assuming a
Poisson distribution, determine the probability of two
shutdowns occurring on the same day.
For the Poisson distribution, 𝝺 = 𝟎. 𝟏𝟎 occurrence/day and 𝐱 =
𝟐 results in the probability
𝑃 𝑋 = 2 =
𝑒−𝝺 𝞴 𝑥
𝑥!
=
𝑒−0.10.12
2!
= 0.004524
162. Poisson Distribution
Suppose the number of breakdowns of machines
in a day follows Poisson Distribution with an
average number of breakdowns is 3.
Find the probability that there will be no
breakdowns tomorrow.
𝞴 = 3
𝐏(𝐗 = 𝟎) =
𝒆−𝟑
𝟑 𝟎
𝟎!
= 𝒆−𝟑
= 𝟎. 𝟎𝟒𝟕𝟗𝟕
163. Poisson Distribution
Patients arrive at the emergency
room of Mercy Hospital at the
average rate of 6 per hour on
weekend evenings.
What is the probability of 4
arrivals in 30 minutes on a
weekend evening?
Example: Mercy Hospital
165. Process Accuracy And
Precision
We have curves that describe our
process
Some questions we may ask…
Is my process accurate?
Is my process precise?
167. Process Accuracy And
Precision
LSL Target USL
•Precision describes
spread
•How does the spread
of my process compare
to the customer’s
specification limits?
172. Capability
In Statistic Terms…
LSL USLLSL USL
LSL USL LSL USL
Mean is not centered in Specification Mean is centered in Specification
SmallStandard
Deviation
LargeStandard
Deviation
173. SPC
PROCESS
The combination of people, equipment,
materials, methods, measurement and
environment that produce output – a
given product or service.
Process is transformation of given
inputs into outputs
174. SPC
VARIATION
The inevitable differences among
individual outputs of a process.
The sources of variation can be
grouped into two major classes,
Common Causes & Special Causes
177. SPC
COMMON CAUSE
A source of variation that affects all the
individual values of the process output
being studied
This is the source of the inherent
process variation.
178. SPC
Common Causes:
1. Plenty in Numbers
2. Results in less Variation
3. Part of the Process
4. Results in constant Variation
5. Predictable
6. Management Controllable
7. Statistics shall apply
179. SPC
Examples of Common Causes,
MAN
MACHINE
MATERIAL
Differences in Competency (setting,
operating & inspection) of Employees
working in shifts.
Difference in Quality of Product when
Production of same Part is being
carried out as per plan. UPS provided
for Electricity Supply
Difference in Mechanical & Chemical
Properties in 2 different lots of Material
of same grade received from suppliers
(Raw Material Manufacturers)
180. SPC
SPECIAL CAUSE:
A source of variation that affects only
some of the output of the process; it is
often intermittent and unpredictable. A
special cause is some times called
assignable cause. It is signaled by one
or more points beyond the control limits
or a non-random pattern of points within
the control limits.
181. SPC
Special Causes:
1. Few in numbers
2. Results in large variation
3. Visitors to the process
4. Variation due to external factors
5. Fluctuating Variation
6. Unpredictable
7. Controllable by Operating personnel
8. Statistics shall not apply
Recognize and deal with special causes outside the (Six Sigma)
process
Implement Corrective and Preventive Action (CAPC)
182. SPC
Examples of Special Causes,
MAN
MACHINE
MATERIAL
METHOD
MEASUREMENT
Untrained Employee working on the Machine
Production of Product on Conventional Lathe
machine where Product Run out requirement
is 2 microns. Major & frequent breakdowns of
Machine. Frequent Power Failures.
Use of different grade of raw material
Setting of process Parameters which are not
proven.
Tool breakage
Use of Micrometer having range of 0-25 mm
to check O.D. of 25 mm ± 0.1 mm.
183. Types of Control Charts
VARIABLE
𝑿, R
𝑿, s
𝑿, mR
CUSUM
ATTRIBUTE
p
np
c
u
184. Control Charts
Overview
The first step for control charting is to
identify the CTQ’s of the process which
is required to be brought under control
Types of Control Charts
Depends on the nature of the variable
needed to control:
Variable Control Charts
Attribute Control Charts
186. Variable Control Chart
Xbar – Rbar
When to use:
When studying the behavior of a single measurable
characteristic produced in relatively high volumes.
How:
By plotting sample averages (X-bar) and ranges (R) on separate
charts. This allows for independent monitoring of the process
average and the variation about that average.
Conditions:
Constant sample size.
One characteristic per chart.
Should have no less than 20 samples before calculating
control limits.
187. Variable Control Chart
Xbar – Rbar
1. Most common type of control chart
for analyzing continuous variables.
2. The xbar part of the chart notes the
variation between the averages of
consecutive sub-groups of data
points.
3. The R part of the chart notes the
changes of variation within each of
the consecutive sub-groups.
188. Variable Control Chart
RATIONAL SUBGROUP CONCEPT
Subgroups or samples should be selected so
that if assignable causes are present, the chance
for differences between subgroups will be
maximized, while the chance for differences due
to these assignable causes within a subgroup will
be minimized.
Time order is frequently a good basis for forming
subgroups because it allows to detect assignable
causes that occur over time.
Two general approaches for constructing rational
subgroups:
◦ Construction units of production
◦ Random sample of all process output over the
sampling interval
189. Control Chart
Reviewing plots & Analysis of trends:
Ensure that all points of both X and R charts
within control limits.
If any point touching to any of the control
limits, review process related remark
corresponding to particular sub-group.
This is assignable cause.
Study particular trends if any
◦ Case study:
◦ Consider process of side member sub-
assembly where critical dimensional
characteristics i.e. concentricity of mounting
holes is controlled.
190. Control Chart
TRENDS ANALYSIS IN SPC CHARTS
ALL POINTS WITHIN CONTROL LIMIT
S.NO Trend Type Meaning Precautions for
better process
control
1. All points within
control limits with
zigzag pattern
Process under control,
variation due to random
causes.
Zigzag pattern changing
with each point over
judgment
Let process continue. Try
to make it a natural
process
2. 7 more consecutive
points on one side
of center line
Process Centre shifted
towards one of the
specification limit
Do changes to bring
process to Centre
3. Cyclic trends Assignable cause
happening periodically
Study assignable cause
and reason. Study to
prevent
4. Continuous
inclination towards
one of the control
limits
Assignable cause for
process drift. If not
prevented, product may
go out of control
Study assignable cause,
set process to prevent
drifting
191. Control Chart
TRENDS ANALYSIS IN SPC CHARTS
ALL POINTS WITHIN CONTROL LIMIT
S.NO Trend Type Meaning Precautions for
better process
control
1. All points suddenly
going out of control
limits
Assignable cause present,
study specific process
event associated with
period of specific point
Study probable causes for
assignable cause taking
place try to resolve the
same
2. Any point going out
of control limits
with definite trend
Process going out of
control due to assignable
cause
Study the trend type &
establish controls to
prevent the assignable
cause occurring
192. Typical Out-Of-Control
Patterns
Point outside control limits
Sudden shift in process average
Cycles
Trends
Hugging the center line
Hugging the control limits
Instability
196. Control Charts
PURPOSE OF CONDUCTING SPC
STUDIES:
To study and analyze process variation
To find out trends in processes
To identify random & sporadic causes
To manufacture products of consistent
quality
To prevent wastage of material
198. Capability vs Stability
Capability has a meaning only when a
process is stable.
If a process is out of control, first we need to
stabilize the process.
Improvement in the inherent variation can be
made only when the process is stable.
Control Charts are used to study stability.
The first job of Six Sigma practitioner is to
identify and remove Special Causes of
Variation.
Once the process is made predictable, the
next job is to identify the causes of inherent
variation and remove them.
204. Calculating Performance
𝑪 𝑷 =
𝑼𝑺𝑳 − 𝑳𝑺𝑳
𝟔𝝈
𝑪 𝒑𝒌 = 𝑴𝒊𝒏
𝑿 − 𝑳𝑺𝑳
𝟑𝝈
,
𝑼𝑺𝑳 − 𝑿
𝟑𝝈
• If the formulae are same, what is the difference?
• The difference is in Sigma Calculation!
• Sigma in Capability covers Short Term Variation.
• Sigma in performance covers Long term Variation.
• How is the Data Collection Different?
205. Process Capability Ratios
ContinuousImprovement
LSL USL
𝑪 𝒑 = 𝟐. 𝟎
𝑪 𝒑 < 𝟏. 𝟎
LSL USL
IncreasedNumberofDefects
Process
Capability
Real
Capability
𝑪 𝒑 = 𝟐. 𝟎
𝑪 𝒑 = 𝟐. 𝟎
𝑪 𝒑 = 𝟐. 𝟎
𝑪 𝒑 = 𝟐. 𝟎
𝑪 𝒑 = 𝟐. 𝟎
𝑪 𝒑 = 𝟐. 𝟎
𝑪 𝒑𝒌 = 𝟐. 𝟎
𝑪 𝒑𝒌 < 𝟐. 𝟎
𝑪 𝒑𝒌 = 𝟏. 𝟎
𝑪 𝒑𝒌 = 𝟎. 𝟎
𝑪 𝒑𝒌 < 𝟎. 𝟎
𝑪 𝒑𝒌 < −𝟏. 𝟎
Understanding 𝑪 𝑷 and 𝑪 𝑷𝑲
𝑪 𝑷 only works for a process that is centered on the target
𝑪 𝑷𝑲 is a better measure for tracking performance
208. Let’s Summarize
A process cannot be improved till it is
Stabilized.
Capability data should be utilized for
stable processes
Subgroups should contain consecutive
data, not random data.
Performance calculations should be
done based on large amount of data
representing Long Term Variation.
210. Discrete Data Capability
A discrete defect is an attribute, which can
be counted.
Such as:
Scratches, Spots, Dent Marks, Cracks etc.
In these cases ½ does not make sense.
A defect is non conformance to the
standards.
A defective unit can have more than one
defect.
A sample of 100, may have 2 defectives
but 5 defects.
211. Discrete Data Capability
Defect Opportunities:
Defect opportunities are various types of
defects, that may occur.
These creates dissatisfaction to the
customers.
This is different than defects that occur.
Example : 12 type of defects that can occur
on painted part.
However, on a part produced, we may observe
0 to up to 12 defects.
Thus a part may be defect free or may have1to
12 defects.
212. Discrete Data Capability
Example:
A sample of 100 nos have been taken.
Following are the results of inspection:
No of Defectives – 3
No of defects – 10
No of Opportunities - 12
213. Discrete Data Capability
Example:
The capability can be calculated as
follows:
No of units = U =100
Defects = D =10
No of Opportunities = O = 12
Total defect opportunities = UxO =
100x12 =1200
DPO = Defects per opportunity =
10/1200 =1/2 = 0.0083
214. Discrete Data Capability
Example:
Defect per million opportunities (DPMO)
=DPO x 1,000,000
=0.0083 x 1,000,000
=8300 DPMO
From the tables, the corresponding
sigma level is 3.9.
215. Discrete Data Capability
The same formula also can be
expressed as
DPMO =
𝑵𝑶. 𝑶𝑭 𝑫𝑬𝑭𝑬𝑪𝑻𝑺×𝟏𝟎 𝟔
𝑵𝑶 𝑶𝒇 𝑼𝑵𝑰𝑻𝑺×𝑶𝑷𝑷./𝑼𝑵𝑰𝑻
216. Discrete Data Capability –
Example of DPMO
Suppose we observe 200 letters delivered
incorrectly to the wrong addresses in a
small city during a single day when a
total of 200,000 letters were delivered.
What is the DPMO in this situation?
DPMO =
𝟐𝟎𝟎 × 𝟏𝟎 𝟔
𝟐𝟎𝟎,𝟎𝟎𝟎 ×𝟏
= 𝟏, 𝟎𝟎𝟎
So, for every only million letters delivered this city’s postal
managers can expect to have 1,000 letters incorrectly sent to
the wrong address.
What is the Six Sigma Level for this
Process?
217. DPMO Example
IRS tax form advice
Survey of responses indicates
predicted error rate
If 40% then:
DPO = 0.40
DPMO = 0.40 defects/opportunity *
1,000,000 opportunities/million
opportunities
400,000 DPMO = 1.75 Sigma
218. DPMO Example
Example of Rolled throughput yield
If there are five processes with following yields:
Rolled throughput yield for this process is =
0.9 × 0.99 × 0.95 × 0.96 × 1 = 0.7279 = 0.73 = 73%
Process No. Yield in %
1 90
2 99
3 95
4 96
5 100
219. DPMO - Exercise
You have 100 documents
You take a sample of 10 documents
There are 10 opportunities for defect on each
document.
5 defects were found.
What is DPMO
Attendance Policy
June 23, 2000
Crane Operational
Excellence Program
All Operational
Excellence Leaders should
be aware.
220. Complexity and Capability
Payroll and Labor Tracking Process
Does complexity have an important impact on
process capability and quality?
There are many opportunities for defects…
Step 1
97.4%
Read
and
record
daily
start and
stop time
𝒀 𝑹𝑻
Output
79.1%
Step 6
99.9%
Create
payroll
checks
Step 5
95.5%
Transfer
hour
totals to
payroll
generatio
n system
Step 4
91.8%
Total
weekly
work
hours
and job
accounts
. Submit
time card
Step 3
98.0%
Total
daily
work
hours
Step 2
94.6%
Read
and
record
daily
start and
stop time
Rolled Throughput Yield Example
=
221. Complexity and Capability
Payroll and Labor Tracking Process
Our goal, reduce the total number of opportunities and
increase the capability of remaining opportunities
Step 1
97.4%
Output
79.1%
Step 6
99.9%
Step 5
95.5%
Step 4
91.8%
Step 3
98.0%
Step 2
94.6%
Rolled Throughput Yield Example
=
𝒀 𝑹𝑻
Output
98.9%
Step 3
99.9%
Print payroll
checks from
computer
generated
database
Step 2
99.4%
Scan
employee
badge and
job card for
labor start
and stop
time
Step 1
99.6%
Scan
employee
badge for
start and
stop time
=
222. Complexity and Capability
Notice any Difference?
Step 1
93.32%
Output
81.26%
Step 3
93.32%
Step 2
93.32%
Step 2
99.999997%
Rolled Throughput Yield Example
=
=
Output
79.1%
Step 2
99.999997%
Step 2
99.999997%x x
xx
A Three Sigma Process
A Six Sigma Process
225. Hypothesis Testing Concept
Hypothesis testing is one of the most
scientific ways of decision making.
It works very much like a court case.
We have a suspect, we have to take
decision whether He / She is innocent or
guilty.
Suppose there is person charged with
murder, and both sides (defense and
prosecution) do not have any evidence,
what would be decision?
Innocent unless proven guilty?
Guilty unless proven Innocent?
Null Hypothesis
226. Null Hypothesis
Null hypothesis is represented by Ho
It is statement of Innocence.
It is something that has to be assumed
if you cannot prove otherwise.
It is statement of No Change or No
Difference.
227. Null Hypothesis – A Court
Case
Just Like a court case, we first assume the
accused (X) is innocent and then try to prove
it otherwise based on evidence (Data).
If evidence (Data) does not show sufficient
difference, we cannot reject the
innocence(Ho)
But if Evidence (Data) is strong enough, we
reject the Innocence (Ho) and pronounce the
suspect Guilty (Ha).
The statement that will be considered valid if
null hypothesis is rejected is called Alternate
Hypothesis (Ha)
228. Null hypothesis – A Concept
Hypothesis testing is a philosophy that
real life situations.
You cannot prove two things equal.
You cannot prove two things different by
proving only one difference
If you cannot prove 2 things different,
you have to assume that they are equal.
But if you cannot prove them Different,
are they really Equal?
What is the RISK involved?
229. Hypothesis Testing Concept
In Truth, the Defendant is:
Correct Decision
Innocent individual goes
Free
Incorrect Decision
Guilty Individual Goes Free
Incorrect Decision
Innocent Individual Is
Disciplined
Correct Decision
Guilty Individual Is
Disciplined
𝑯 𝑨: Guilty𝑯 𝒐: Innocent
Verdict
Innocent
Guilty
230. Hypothesis Testing Concept
Correct Decision Incorrect Decision
Type II Error Probability = 𝛽
Incorrect Decision
Type I Error Probability = 𝛼
Correct Decision
𝑯 𝑨is True𝑯 𝒐is True
𝑯 𝒐is True
𝑯 𝑨is True
Decision
True, But Unknown State of the World
231. Hypothesis Testing Concept
Hypothesis testing Justice System
State the Opposing Conjectures, Ho and HA.
Determine the amount of evidence required,
n, and the risk of committing a “type error”,
What sort of evaluation of the evidence is
required and what is the justification for this?
(type of test)
What are the conditions which proclaim guilt
and those which proclaim innocence/
(Decision Rule)
Gather & Evaluate the evidence.
What is the verdict? (Ho or HA?)
Determine “Zone of Belief” : Confidence
Interval.
What is appropriate justice? – Conclusions
232. Hypothesis Testing
1. Null Hypothesis (Ho) – statement of no change or
difference. The statement is assumed true until
sufficient evidence is presented to reject it.
2. Alternate Hypothesis (Ha) – statement of change or
difference. This statement is considered true if Ho is
rejected.
3. True I Error – the error in rejecting Ho when it is in
true fact, there is no difference.
4. Alpha Risk – the maximum risk or probability of
making a Type I Error. This Probability is always
greater then zero, and is usually established at 5%.
The researcher makes the decision to the greatest
level of risk that is acceptable for a rejection of Ho.
Also known as significant level.
5. Type II Error – The error in failing to reject Ho when it
in fact false, or saying there is no difference when
there really is a differerence.
233. Hypothesis Testing Concept
6) Beta Risk – The risk probability or
making a Type II Error, or overlooking
an effective treatment or solution to the
problem.
7) Significant Difference – The term
where a difference is too large to be
reasonably attributed to chance.
234. 𝛼 𝑎𝑛𝑑 𝛽 Risks
𝛼 Risk is also called producer’s risk.
𝛽 Risk is also called consumer’s risk.
Can we commit both type I and type II
error at the same time?
As it necessary that we will have both 𝛼
and 𝛽risks?
Are𝛼 and 𝛽 risks equal?
Is 𝛼 and 𝛽 = 1?
Is there any relationship between 𝛼 and
𝛽?
Which risk is more important?
235. 𝛼 𝑎𝑛𝑑 𝛽 Risks
An 𝛼 Risk of 5% is generally
accepted.
An 𝛽 Risk of 10% is generally
Accepted.
Since Ha cannot be proved, our
attempt is to try and reject it.
What risk do we get in trying to reject
the Ho.
Minitab represents 𝛼 risk by p-panel!
236. Steps in Hypothesis Testing
Define Ho
Define Ha
Select Appropriate Test.
Decide Significance Level (𝛼 and 𝛽)
Decide Sample Size
Collect Data
Conduct Test
Interpret!
237. Define Ho/Ha For following
Cases
To find if a distribution is normal or not.
Ho =>
Ha =?
To find if the defects from three machines
are same or different
Ho =>
Ha =>
To find if 2 groups of students from
different streams have differing IQ
Ho =>
Ha =>
239. Statistical Error Definitions
Null Hypothesis Ho:
“Status quo”
“Nothing is different”
Equality
We fail to reject Ho based
on statistical evidence
Alternate Hypothesis Ha:
“Something is different”
Statement about the
population that requires
strong evidence to prove
If we reject Ho, we in
practice accept Ha.
Alpha Risk (𝛼)
Also called type I Error
Hypothesis the null
hypothesis when it is fact
true.
Beta Risk (𝛽)
Also called a Type II Error
Accepting the null
Hypothesis when it is in fact
false.
240. Statistical Error
Typical 𝛼 𝑎𝑛𝑑 𝛽Risks
Typically, the 𝛼 level is set at 0.05 and
the 𝛽 level is set at 0.10
They can be set at any level
depending on what you want to know
The risk is also called the “p-value”
1-𝛼 = confidence that an observed outcome in
the sample is “real”
We typically look for a p-value of 0.05 because:
1-0.05 = 0.95 (or 95% confidence)
241. The Central Limit Theorem
Normally
Why are distributions normal?
When all factors are random
Some measurements are actually averages
over time of “micro-measurements”
In other words, what we see as a
measurement is
actually an average
The Central Limit Theorem explains why a
distribution of averages tends to be normal
242. Confidence
Sample statistics estimate the mean or standard deviation of a
population
The “True” population mean and standard are unknown
Confidence limits, levels, and intervals are used to determine the
population statistics
For means…
We use t distribution to
calculate limits, levels, and
intervals
For Standard Deviations…
We use the 𝑐2
distribution to
calculate limits, levels, and
intervals
243. Definition
Confidence Level:
The level of risk we are willing to take
How sure we want to be that the population mean or standard deviation
falls between the confidence level is typical
95% confidence level is typical.
95% chance that the population mean or standard deviation falls between
the limits.
5% chance (alpha risk) that the population mean or standard deviation
isn’t contained within the calculated limits.
Risk (𝛼/2) Risk (𝛼/2) Risk (𝛼)
244. Definition
Confidence Limit
Upper and Lower limits that bracket the “true”
mean or standard deviation of a population
Calculation from the sample data and the appropriate
test statistic.
Test statistic is dependent on the risk we accept that
our results will be wrong.
245. Definition
Confidence Interval
The interval defined by the upper and
lower confidence limits.
A range of values based on
Sample mean or sample standard deviation
Sample size
Confidence level
Appropriate test statistic
Contains
Population mean or
Population standard deviation
249. Confidence Limit - Example
The tensioning device (rubber band) used on the Silobuster has come under scrutiny
Two sets of tensioners are measured and descriptive statistics are run. What is
the 95% confidence interval for the variation?
≤ 𝝁 ≤
Set 1
Mean: 0.250”
Standard Deviation:
0.005”
Sample Size: 25
Set 2
Mean: 0.250”
Standard Deviation:
0.005”
Sample Size: 100
We are 95% confident that the
interval 0.2479 to 0.2521 brackets
the true process standard
deviation (0.0042 width)
We are 95% confident that the
interval 0.2490 to 0.2510 brackets
the true process standard
deviation (0.0020 width)
𝑿 - 𝒕(
𝜶
𝟐
,𝒏−𝟏)(
𝒔
𝒏
) 𝑿 + 𝒕(
𝜶
𝟐
,𝒏−𝟏) (
𝒔
√𝒏
)
. 𝟐𝟓𝟎 ± 𝟐. 𝟎𝟔𝟑𝟗
. 𝟎𝟎𝟓
𝟐𝟓
= . 𝟐𝟒𝟕𝟗 𝒕𝒐 . 𝟐𝟓𝟐𝟏 . 𝟐𝟓𝟎 ± 𝟏. 𝟗𝟖𝟒𝟐
. 𝟎𝟎𝟓
𝟏𝟎𝟎
= . 𝟐𝟒𝟗𝟎 𝒕𝒐 . 𝟐𝟓𝟏𝟎
252. Confidence Limit Formulas
Variation
The tensioning device (rubber band) used on the Silobuster has come under scrutiny
Two sets of tensioners are measured and descriptive statistics are run. What is
the 95% confidence interval for the variation?
𝒔
𝒏 − 𝟏
𝒙 𝟐 𝒍𝒐𝒘𝒆𝒓 𝒗𝒂𝒍𝒖𝒆
≤ 𝝈
≤ 𝒔
𝒏 − 𝟏
𝒙 𝟐 𝒖𝒑𝒑𝒆𝒓 𝒗𝒂𝒍𝒖𝒆
𝟎. 𝟎𝟎𝟓
𝟐𝟒
𝟑𝟗.𝟑𝟔
= 0.0039 and𝟎. 𝟎𝟎𝟓
𝟐𝟒
𝟏𝟐.𝟒𝟎
= .0070 𝟎. 𝟎𝟎𝟓
𝟗𝟗
𝟏𝟐𝟖𝟒𝟐
= 0.0044 and 𝟎. 𝟎𝟎𝟓
𝟗𝟗
𝟕𝟑.𝟑𝟔
= .0058
Set 1
Mean: 0.250”
Standard Deviation:
0.005”
Sample Size: 25
Set 2
Mean: 0.250”
Standard Deviation:
0.005”
Sample Size: 100
We are 95% confident that the
interval 0.0039 to 0.0070 brackets
the true process standard
deviation (0.0031 width)
We are 95% confident that the
interval 0.0044 to 0.0058 brackets
the true process standard
deviation (0.0014 width)
253. TEST OF HYPOTHESIS -
roadmap
You want to compare the averages/ medians of samples
of data to decide if they are statistically different
Are samples normally distributed
Compare median values
instead if average
How many samples do you
wan to compare
Kruskall Wallis
Test
For samples that do not
have any outliners
One-way ANOVA
For comparing averages of
three or more samples
against one another
1 Sample t-test
Comparing av. of
one sample against
target
Paired t-test
For comparing averages
of two samples that
contain data that is linked
in pairs
Two Sample t-test
For comparing averages
of two samples against
each other
Mood’s Median
Test
For samples that have
some outliners
Transform Data
Yes
2
1
or
3 or more
No
No
or
255. EXERCISE
Represent the following data in
graphical form:
Temperature
100
100
120
120
Response
275
285
270
325
Pressure
250
300
250
300
256. EXERCISE - continued
a) Determine what parameter settings
yield the largest response.
b) Determine what parameter settings
of pressure would be bets if it were
important to reduce the variability of
the responses that results from
frequent temperature variations
between two extremes.
258. Design Of Experiments
Design of Experiments (DOE) is a valuable
tool to optimize product and process
designs, to accelerate the development
cycle, to reduce development costs, to
improve the transition of products from
research and development to
manufacturing and to effectively trouble
shoot manufacturing problems. Today,
Design of Experiments is viewed as a
quality technology to achieve product
excellence at lowest possible overall
cost.
259. Design of Experiments
General Comments
Keep your experiments simple
Don’t try to answer all the questions in one study
Use 2 level designs to start
Try potential business results to the project
The best time to design an experiment is after the previous
one is finished
Always verify results in a follow-up study (
verification)
Be ready for changes
A final report is a must to share the knowledge
Avoid DoE infatuation…do your homework first!
Measure & Analyze to reduce potential variables
Use Graphical Analysis
Use the basic tools of Operational Execllence
260. Design of Experiments
Be Proactive
DOE is a proactive tool
If DOE output is inconclusive:
You may be working with the wrong variables
Your measurement system may not be capable
The range between high and low levels may be sufficient
There is no such thing as a failed experiment
Something is always learned
New data prompts us to ask new questions and generates
follow-up studies
Remember to keep an open mind
Let the data/output guide your conclusions
Debunk or validate tribal knowledge
Don’t let yourself be “confused by the facts.”
261. Design Of Experiments
Types of Experiments
Traditional
Approach
Six
Sigma
Approach
Very
Informal
Very
Formal
• Trial and Error Methods
Introduce a change and see what happens
• Running Special Lots or Batches
Produced under controlled conditions
• Pilot Runs
Set up to produce a desired effect.
• One-Factor-at –a-Time Experiments
Vary one factor and keep all other factors
constant
• Planned Comparisons of Two to Four Factors
Study separate effects and interactions
• Experiment With 5 to 20 Factors
Screening Studies
• Comprehensive Experimental Plan With Many
Phases
Modeling, multiple factor levels,
optimization
Very
Informal
Very
Formal
• Trial and Error Methods
Introduce a change and see what happens
• Running Special Lots or Batches
Produced under controlled conditions
• Pilot Runs
Set up to produce a desired effect.
• One-Factor-at –a-Time Experiments
Vary one factor and keep all other factors
constant
• Planned Comparisons of Two to Four Factors
Study separate effects and interactions
• Experiment With 5 to 20 Factors
Screening Studies
• Comprehensive Experimental Plan With Many
Phases
Modeling, multiple factor levels,
optimization
262. Design Of Experiments
Barriers to Successful DoE’s
Problem or objective unclear
Results of the experiments unclear
Be present during the DoE
Identify and record unexpected noise or other variables
Measurement Error
Lack of Management Support
Lack of Experimental Discipline
Don’t use a DoE as the first pass to identify key X’s
Manage the constants and the noise
Process map, C&E, Constant or Noise or Experimental
Unstable process prior to running DoE
Process map, C&E, Constant or Noise or Experimental,
Manage the C’s and N’s to reduce extraneous variation
263. Design Of Experiments
Objective
Establish the objective for the
experiment
It should be stated in such a way to provide
guidance to those involved in designing the
experiment.
264. Design Of Experiments
Planning the Experiment
Team in involvement
Maximize prior knowledge
Pursue measurable objectives
Plan the execution of all phases
Rigorous sample size determination
Allocate sufficient resources for data
collection and analysis.
265. Design Of Experiments
The following are some of the objectives of
experimentation in an industry:
Improving efficiency or yield
Finding optimum process settings
Locating sources of variables
Correlating process variables with
product characteristics
Comparing different processes,
machines, materials etc.
Designing new processes and products.
266. Various Terms Used In
Experimentation
Factor:
One of the controlled or uncontrolled variables whose
influence on the response is being studied. May ne variable
or classification data.
Level:
The values or the factor being studied usually high(+) and
low(-)
Treatment Combination:
An experiment run using a set of the specific levels or each
input variable
Response Variable:
The variable that is being studied. “Y’ factor in the study.
Measured output variable.
Interaction:
The combined effect of two or more factors that is observed
which is in addition to the main effect of each factor
individually.
267. Various Terms Used In
Experimentation
Confounding:
One or more effects that can not unambiguously be
attributed to a single factor or interaction.
Main effect:
Change in the average response observed during a
change from one level to another for a single factor.
Replication:
Replication of the entire experiment. Treatment
combinations are not repeated consequently.
Test run:
A single combination of factors that yields one or more
observation of the response.
Treatment:
A single level assigned to a single factor during an
experiment.
268. Trial And Error
Perhaps the most well known and used
methodology.
The objective is to provide a quick fix to a
specific problem.
The quick fix occurs by randomly and no-
randomly making changes to process
parameters.
Often changing two or more parameters at the
same time.
The result often is a “Band-Aid” fix as the
symptoms of the problem are removed, but the
cause of the problem goes undetected.
In trial and error experimentation, knowledge is
not expanded but hindered.
Implement multiple expensive fixes are not
necessary.
269. One-Factor-At-A-Time (OFAT)
The old dogma in experimentation is to hold
everything constant and vary only one-factor-
at-a-time.
◦ Assumes any changes in the response would be due
only to the manipulated factor.
But are they?
◦ Is it reasonable to assume that one can hold all
variables constant while manipulating one?
Experience tells us this is virtually impossible.
Imagine there area large number of possible
factors affecting the response variable:
◦ How long would OFAT take to identify critical factors
and where they should be run for best results?
◦ How much confidence would you have that the
knowledge gained would apply in the real world?
270. OFAT
Although OFAT may simplify the
analysis of results, the experiment
efficiency given up is significant:
◦ Don’t know the effects of changing one
factor while other factors are changing (a
reality).
◦ Unnecessary experiments may be run.
◦ Time to find casual factors (factors that
affect the response) is significant.
271. Classification Of Factors
1. Experimental Factors are those which we
really experiment with by varying them at
various levels.
2. Control Factors are those which are kept
at a constant (controlled) level throughout
experimentation.
3. Error or Noise factors are those which can
neither be changed at our will nor can be
fixed at one particular level. Effect of these
factors causes the error component in the
experiment and as such these factors are
termed as error or noise factors.
272. Experimental Design
Visualization of The 21
Design (2 Levels
– 1 factor)
This is often the method used today for
process optimization. It is the “only one
factor at a time” concept
High
Factor 1
Low
273. Experimental Design
Visualization of The 22
Design (2 Levels
– 2 factor)
The most basic of true designs. There
are 4 runs.
High
Factor 1
HighFactor 2Low
Low
274. Experimental Design
Visualization of The 23
Design (2 Levels
– 3 factor)
A little more complicated design but still
very practical. There are only 8 runs.
High
Factor 1
HighFactor 2Low
Low
High
Factor 3
Low
276. Experimental Design
Factor 4Low High
Factor 4
High
Factor 5
Low
Visualization of The 𝟐 𝟓
Design (2 Levels – 5 factors)
Here is where it’s time to stop drawing but it represents the complexity
associated with a 5 factor design.