2. What is six sigma ?
• It is a comprehensive and flexible system for achieving, sustaining and
maximising business success.
• 6 sigma methodology involves -
1. Listening to the customer needs
2. Use of facts through data collection and statistical analysis
3. Managing, improving and re-engineering production and business
processes.
• The 2 key aspects of a six sigma organisation are – customer
satisfaction and business excellence.
• Bill Smith is known as the Father of Six sigma for his 1987 Motorola Six
Sigma technology that stated that defect rate cannot be more than 3.4
parts per million opportunities.
Business
Excellence
Cost
reduction
Increase in
productivity
Growth of
market share
Customer
retention
Cycle time
reduction
Defects
reduction
NPD
3. Sigma capability
• It is defined as the indicator of how well the process is performing.
• Denoted as z value defined as
Z=
𝑥−𝜇
𝜎
Where mu is the process mean or average and sigma is the spread / distribution
about the mean.
• This measures the capability of the process to produce defect free outputs.
• Greater the value of z, he better the process is.
4. 6 MAIN
THEMES OF
SIX SIGMA
Focus on the
customer
Data and fact
driven
management
Process focus
Pro-active
management
Boundary
less
collaboration
Driver for
perfection
SIX
MAIN
THEMES
OF
A
SIX
SIGMA
ORGANISATION
5. ➢Focus on the customer :
❖Requirements of the customer are assessed.
❖Performance of the organization products is then evaluated.
❖Unmet needs are addressed through product or process change.
❖Customers get the highest priority.
➢Data & fact driven management :
❖Focus on taking measurements – what info is needed and what is the source ?
❖No room for decisions based on opinions / assumptions / feelings.
❖Data analysis using appropriate tools and info generated must be used to make
decisions for improvements.
❖This is a closed loop system where measurements from the output are taken to take
corrective actions to improve subsequent process.
❖Very important hallmark of six sigma system.
6. ➢Process focus :
❖Proper understanding of actual process that takes place on shop floor by
mapping it on charts or flow diagrams involving a series of steps.
❖This helps to ensure in depth quality requirements and controls and helps to
make full analysis for control and improvement.
➢Pro-active management :
❖Responsible for setting goals and clear priorities
❖Frequent reviews
❖Implement changes to prevent errors from reaching the customer.
❖Top management focus and support.
7. ➢Boundary less collaboration :
❖Cross – functional teams with good communication to avoid delays, redesigns,
rework, or wastage of resources.
❖Good teamwork is needed to support one another.
❖Common goal
❖Savings potential
➢Driver for perfection :
❖Diligent efforts
❖Repeated iterations
❖Only goal : not more than 3.4 defects per million opportunities (DPMO)
8. Six sigma roadmap and Important phases of a
process improvement cycle
DMAIC
Define
Measure
Analyse
Improve
Control
9. DEFINE….
• Project leader is responsible for setting targets, listening to the customer requirements &
identifying the critical to quality (CTQ) parameters.
• Gives the most important equation : y = f(x) where y are the parameters critical to quality
and indicate customer expectations and x are the influencers/ variables that can influence
the critical to quality y’s.
• Standards need to be established
• Understanding how the customer requirements change with the passage of time (VOC)
• Project goals and supporting team both need to be laid.
Teams involved Role
Top management To establish vision/ goals, allocate resources
Trained belts To provide technical support
Project team Design project charter, timeline, cost estimations
Project sponsors / Champions Line owners, select project and execute, provide resources, remove
barriers
Financial representatives Derive savings, project benefits, ROI
10. MEASURE… ANALYZE…
• Map the complete process using flow
diagrams for detailed understanding.
• Identify CTQ parameters that need to be
measured.
• Establish sampling plan and data collection
sources.
• Data collection & ensure data is completely
relevant and hygienic
• Use statistical analysis for analysing random
variables.
• Determine the current process performance
and capability against theVOC.
Statistical data analysis
Cause & Effect
Correlation & Regression
11. IMPROVE… CONTROL…
• To establish and validate
statistical hypothesis
• Eliminate root causes of
the problem
• Optimize process by
implementing counter
measures.
• Reduce process
variability.
Establish monitoring and control
plan
Statistical Process Control
Control charts
Standardize documentation
Employee training
Scope of Appreciation / Applause
Helps to maintain the gains over the
long horizon.
13. What is a DEFECT ??
• Defined as the occurrence at any process step when the actual outcome of the process does not
match with the expected outcome (means expected outcome has been defined well in advance).
• Any flaw/ error/ discrepancy.
• Leads to a defective product.
Impact of a defect –
• Internal failure costs involved : material, labour, energy, utilities cost
• Defect may reach the consumer, external failure costs involved : warranty cost, liability cost, recall
cost, loss of reputation, drop in sales, loss of market.
• More defect generation reduces line productivity and results in decreased capacity utilisation.This
ultimately affects the market delivery of the product in time. Catering high demands at peak seasons
becomes difficult in some cases.
• Early detection of the defects can result in identification and rectification of the root cause more
easily and on time.
• Giving liberty in terms of defect %, creates culture that some % defect is OK that can be allowed to
reach market. However, need to develop culture to encourage workers to bring attention to
problems.
14. YIELD-
• Fraction defective / defect rate (p) = defective units produced / total units in
• Yield = 1 – p with no rework/ retest / scrap
• Process yield with n such steps each having a step yield of p = 1 − 𝑝 𝑛
• Process yield for 3 steps each with a step yield of a, b, c respectively = a X b X c
• Example 1: 3 step process with fraction defective at each step = 1%
P = 0.01
Yield = 1 – p = 0.99
Process yield = (0.99)^3 = 97.02 %
• Example 2: 10 step process with p = 10%
1 – p = 0.9
Process yield = (0.9)^10 = 34.86 %
15. • Example 3: 10 step process with p = 1%
1-p = 1-0.01 = 0.99
Process yield = (0.99)^10 = 90.43 %
• Example 4: 10,000 step process with p = 1%
Process yield = (1-0.01)^10000 = 0
• Example 5: 10,000 step process with p = 0.621%
Process yield = (1-0.00621)^10000 = 0
• Example 6: 10,000 step process with p = 3.4 X 10^(-4)%
1-p = 0.9999966
Process yield = (0.9999966)^10000 = 96.65 %
Which clearly justifies that low fraction defectives (p) are very necessary to ensure positive yield for
complex products.
Implication : Even at such low defect rate, 3.35 % sales loss to BMW manufacturer (for ex.) which is
unaffordable.
16. PPM –
• Parts per million is used to quantify very very small volumes.
• PPM = no of defective units / million
• Example 1: 99.379% yield at one step, what is the ppm ?
1-p = 0.99379
So, p = 0.00621 = 6210 ppm
• Example 2: 96.65 % yield for a process with 10,000 steps, what is the ppm defective ?
1-p = (0.9665)^(1/10000) = 0.999997
P = 3.4 X 10^(-6)
P = 3.4 ppm
17. What is a DEFECTIVE PRODUCT ??
• Defective product is the only one that when a decision has been made that the item is not
acceptable.
• The decision is based on either one / accumulation of multiple factors making the
characteristics of the product unacceptable.
• DPU is defined as the average number of defects per unit of product.
• DPU = number of defects / number of units
• DPMO is defined as defect per million opportunities
• DPMO = DPU X 1 million /Total opportunities of defect in 1 unit
• However, ppm speaks only in terms of defective units in a million population.
18. “It is a preconception
that quality is all
about testing.”
19. QUALITY
• Dr. Joseph M. Juran defined quality as fitness for
use and product meeting / exceeding customer
requirements.
• Consumer needs should be in the form of some
measurable characteristics with predefined limits
of variability.
• According to Dr. A. Blanton Godfrey, quality is
relative, with consumer focus simply on value
seeing it as a ratio of quality of price and only
when we offer more value than the competitors.
• Dimensions of quality :
Product performance, reliability, durability,
serviceability, sustainability
• Identify theVOC
• Product designer will take these needs.
• Select features of the product and create
design.
• Select target and limits of variation.
• Produce product at a reasonable cost.
• Feature CTQ measurable characteristics.
• Therefore, identifying theVOC and
translating the voice into critical to
quality parameters and evaluating/
improving the current performance of
CTQs are fundamental aspects of quality
management.
QUALITY MANAGEMENT
SYSTEM (QMS)
20. Total Quality cost (TQC)
• TQC refers to how the organisation is financially performing in
delivering products that satisfy its consumers.
• It includes the financial losses due to not producing quality products
and the economic gains due to delivery of quality products.
21. Prevention cost
•Training sessions
•Process control
•Improvement projects
•Quality system development
Appraisal cost
•Material inspection and testing
•Product inspection and testing
•Equipment integrity
Internal failure cost
•Scrap, rework, retest
•Resources and yield loss
•Manpower
•Energy and utilities cost
•Production downtime
External failure cost
•Product recall
•Warranty cost
•Loss of market shares
•Loss of reputation
•Loss in sales
•Price reduction
22. Understanding customer expectations : KANO
model theory
• Differentiate between “design quality” (identify theVOC – what the customer
wants and that becomes the design specs, product features, and translateVOC to
CTQ measurable parameters ) and the “conformance quality” (that matches the
design specs without any discrepancies).
• Understand theVOC and categorize and prioritize as all the attributes of product/
service are not equal in the eyes of the consumer.
23. • A – is the basic quality required to ensure
the market of the product.This is not
generally mentioned by the customers
but they do mention it only when such
attributes are absent from the product.
Absent : unhappy
Fully implemented : OK, not happy
• B – Here the satisfaction is directly
proportional to the performance.
Linear relationship
• C – Delighters, Excitements, WOW –
creation of excitement which is different
from expectations.
Helps in building brands.
Characteristic
Satisfaction
Unhappy
Absent
Fully
implemented
Satisfied
Basic/ expected
quality
Performance OR 1-
D quality
Excitement
A
B
C
24. • D – Indifferent quality
Those attributes to which no importance is attached by the consumer.
No satisfaction & No dis-satisfaction
• E – Reverse quality
Those resulting in dis-satisfaction and is mainly due to the fact that not all
customers are alike.
**It is through this theory that a Kano questionnaire is prepared to listen to the
consumer needs. An evaluation table is prepared and the attributes are then
classified after the survey.
26. Define a problem…..
• It is an undesirable deviation of the required attribute in the output of a process
(product/ service).
• This attribute may be any – quality characteristic, availability (quantity/ time) ,
consumption of resources.
• It is a gap between the current and desirable state.
• Ex : Burnt cookie produced is the problem of the process. However, its actual cause
may be high baking temperature which is a part of process input.
• Therefore, problem is always in the output while the cause of the problem lies in the
process input.
• We need to “define” the problem so that it can be improved well in time and we
exceed customer expectations.
28. Probability & Statistics
▪ Probability is the chance of an event happening when an experiment is carried out.
▪ It is used to infer what we observe if we take the measurement of our population.
▪ Statistics is used to infer what the model of the population is as it provides a means
of describing the population with variability and methods of estimating the
population quality from samples.
▪ Measurements are done on samples and the statistical data generated is used
to infer the population characteristics / parameters.
▪ Population : system under study
▪ Sample: a subset of population which has been chosen in such a way that each
item has an equal chance of being included (random sample)
29. Qualitative/
Attribute based
Normal OR
Differential
Ex. Colour,
nationality, religion
Ordinal
Ex. Ranking scale
(poor, average,
good, excellent)
Quantitative/
Measurement
based
Measure-able
Ex. Length, width,
diameter, purity,
temperature
Types Of Sample Data
30. Descriptive & Inferential Statistics
• Descriptive statistics :
- Using empirical methods to describe the population.
- Taking data from a population, arranging it and summarizing it to get useful information.
- Does not allow to make conclusions beyond the data we have analysed.
- Tools used:
❖Frequency distributionOR Histogram
❖Cumulative frequency distribution
❖Box &Whisker Plot
❖Calculated parameters to measure location and dispersion
• Inferential Statistics :
When the model of the population is not known, statistics can be used to infer what the model of the
population is.This is called inferential statistics which is just the estimation of parameters and testing
a statistical hypothesis.We use samples that are representative of the population (not completely
may be) and make estimations/ generalizations about the population with the help of estimators.
Minimum variance unbiased estimators (MVUB) such as x bar and s square are generally used to
estimate mu and sigma square.
31. 1. Histogram
• Tool to describe the variability in the population within the possible range of values.
• Conclusions from a histogram –
1. Where on x-axis is the centre point located around which the population is
distributed.
2. Variation in the data
3. Variability is in acceptable level or not in case specification limits are laid
4. To identify problems in case the graph depicts a bimodal distribution.
• Cumulative frequency distribution helps to estimate what part of the population is
less than or equal to the given value of x.
32. 2. Box &Whisker plot
• A graph that gives us a good indication of how the values in data are spread
out.
• A box and a whisker diagram is a standard way of displaying distribution of
data based on a five number summary –
Min, First quartile, Median,Third quartile, Max.
• Indication of data symmetry and skewness
• Helps to identify outliers
33. 3. Calculated parameters
• To measure location :
1. Mean / Average : centre point
2. Median : 50th percentile
3. Mode : most frequent data point
• To measure dispersion :
1. SD : to measure the process variability from mean
2. Range : Max – Min
3. Variance
34. Sample Statistics -Terminology
❑Average/ Mean (x bar) : Centre point around which the population is distributed.
ҧ
𝑥 =
𝑥𝑖
𝑛
❑Standard deviation (s) : amount of variability/ dispersion about the mean
𝑠 =
ҧ
𝑥−𝑥𝑖
2
𝑛−1
= sq. root of variance
❑Variance (s2) : weighted average of squared deviations of variable data points from mean.
Indicates dispersion around the mean.
❑x bar & s are sample statistical data while mu and sigma are known as population parameters.
35. Lets give a thought…
Q1. How are quality and variability inter-related ?
The answer is simple !!All industrial processes have some variability and no process is
an ideal process.
Higher SD value implies a more variable process which leads to a poor quality product
and more waste generation.
Q2. Enlist some commonly used statistical methods in quality engineering.
1) Control charts
2) Sampling plans
3) Designed experiments
4) Regression and correlation analysis
5) Reliability engineering
6) Tolerancing
36. Probability Distribution
• Random variable (X) : variable that assumes values from the outcomes of a random experiment.
It assumes only real values & set of all possible values is known as the range space.
• 2 types:
1. Discrete random variable : that assumes finite no of values
Ex. Number of heads in 3 tosses of a fair coin, number when a die is thrown.
Described using a probability mass function (pmf)
2. Continuous random variable : that assumes infinitely many values OR values in an interval
Ex.Amount of snowfall, weight of sugar bags
Described using a probability density function (pdf)
37. Discrete and Non-Continuous
Distribution
▪ Case : a fair coin is tossed 3 times and random variable may be defined as
the number of tails that we get.
▪ p(x) >= 0 for all values of x
▪ 𝛴𝑝 𝑥 = 1
▪ P(t) = p(X = t)
X 0 1 2 3
P(X) 1/8 3/8 3/8 1/8
0
0
0
1/7
1/5
1/4
2/7
1/3
2/5
0 1 2 3
Probability distribution for no. of tails
in 3 tosses
Binomial
Distribution
Poisson
Distribution
38. 1. Binomial Distribution
• Random variable X has a Binomial distribution with parameters n & p if probability
distribution is given by
P(x) = 𝑛𝐶𝑥 𝑝𝑥
1 − 𝑝 𝑛−𝑥
where x = 0,1,2……n
And 𝑛𝐶𝑥
=
𝑛!
𝑥! 𝑛−𝑥 !
where x <= n
• We use Bi(n , p) notation to indicate x has a binomial distribution.
• x is the number of successes in ‘n’ different independent trials with p being the
probability of success and 1-p is the failure probability in one trial
0<= p <= 1
• Such a trial is called as a Bernoulli trial where a random experiment is carried out with
exactly 2 possible outcomes either a success or a failure and probability of success is
the same every-time the experiment is conducted.
39. Ex. Getting 9 heads when a fair coin is tossed
10 times
• When a fair coin is tossed (random experiment), only 2 possible outcomes – H &T.
• In our case, success is defined as getting a head. p(H) = 0.5 and this is same every-
time. So, this is an example of Bernoulli trial = Bi (10,0.5)
• N = 10, x = 9, p = 0.5,
So, P (9 successes out of 10 trials ) = p(9) = 10C9 (0.5)^9 (1-0.5)^(10-9)
= 10 X (0.5)^10 = 0.0098
= 0.98% < 1%
that we get 9 heads while tossing a fair coin 10 times.
40. Points to remember…
• Binomial distribution curve has a bell shape.
• Binomial distribution never goes below zero.
• As the number of trials (n) increase, the distribution moves away from zero.
• As p increases, there is a shift away from zero in the curve.
• Bernoulli distribution is valid only for independent trials which means that the lot size
>> sample size . Independence of the trials will be lost if the sample is picked from a
small lot without replacement.
• Weighted average (𝜇) = 𝛴 x ∗ 𝑛𝐶𝑥 𝑝𝑥
1 − 𝑝 𝑛−𝑥
= np
• Variance (𝜎2) = 𝛴 𝑥 − 𝜇 2 𝑛𝐶𝑥 𝑝𝑥 1 − 𝑝 𝑛−𝑥 = np(1-p)
41. 2. Poisson Distribution
• If we have an exact probability of an event happening (x out of n times), then random variable is
expressed using a Binomial distribution.
• However, in case we have an “average/ mean probability” of an event happening per unit time,
then the random variable is said to have Poisson distribution given by the mass function
p(x) =
ⅇ−𝜆𝜆𝑥
𝑥!
here x = 0,1,2,3…..
• We use Po (𝜆) notation to indicate x has a poisson distribution.
• Ex : 1. no of pinholes in a galvanised sheet
2. no of blemishes in a fabricated shirt
3. no of accidents per month in a factory
• Poisson distribution has a bell curve that moves away from zero and becomes more symmetric
as the value of lambda increases.
• Poisson distribution never goes below zero.
• Poisson approaches to binomial distribution when n approaches infinity and p approaches zero.
• Weighted average (𝜇) =Variance (𝜎2) = 𝜆
42. Example on Poisson Distribution
• Statement :Typist makes an average 3 mistakes per page.What is the probability that
the page he types now will have not more than one mistake ?
• Because of average 3 number of mistakes, the above statement symbolizes poisson
distribution for the random variable.
• X = no of mistakes per page, X = Po (3) with 𝜆 = 3
• Required probability p(X<= 1) = p(0)+ p(1) =
ⅇ−𝜆𝜆𝑥
𝑥!
= ⅇ−3 30
0!
+
31
1!
= (2.718)^(-3) * (4) = 0.1992
= 19.92 %
43. Continuous Distribution Model
• Described by a probability density
function (pdf)
Ex. f(x) = {0.01 x , 0=< x <= 10
0.01x (20-x) , 10=< x <= 20
0 , otherwise }
Therefore,
✓ f(x) >= 0 for all values of x
✓ 𝛴𝑓 𝑥 = 1
✓p(a <= x <= b) =
𝑎
𝑏
𝑓 𝑥 𝑑𝑥
Normal Distribution
Exponential Distribution
Weibull Distribution
T- Distribution
Chi- squared distribution
F- Distribution
Types
44. Continuous Distribution Models
1. Uniform distribution : probability is same
for all values of x
2. Exponential distribution : f(x) decreases
exponentially with increase in value of x
f(x) f(x)
x x
45. 3. Normal / Gaussian Distribution
• pdf is given by f(x) =
1
𝜎
2𝜋
ⅇ
−
1
2
𝑥−𝜇
𝜎
2
then x is said to have normal distribution
written as X = Nu (𝜇, 𝜎2
)
• Characteristics of a normal distribution curve :
1. It is asymptotic wrt x-axis.
2. Symmetric wrt vertical line x = 𝜇
3. Maxima of the curve occurs at x = 𝜇
4. 2 points of inflexion occur at x =𝜎
• Area under the curve =
𝑎
𝑏
𝑓 𝑥 𝑑𝑥 = 1
• Mean of the distribution =
𝑎
𝑏
𝑥 𝑓 𝑥 𝑑𝑥 = 𝜇
• Variance of the distribution =
𝑎
𝑏
𝑥 − 𝜇 2
𝑓 𝑥 𝑑𝑥 = 𝜎2
f(x)
x
𝜇
𝜎
46. Normal Probability Distribution
• pdf is given by f(x) =
1
𝜎
2𝜋
ⅇ
−
1
2
𝑥−𝜇
𝜎
2
and random variable X = Nu (𝜇, 𝜎2
)
where mu is the mean and sigma square is the variance.
• As distance from 𝜇 increases, the probability decreases.
• As a thumb rule, remember –
1. 2 points of inflexion occur at +/- 1 𝜎
2. +/- 1 𝜎 from mean implies 68.27 % of population
3. +/- 2 𝜎 from mean implies 95.44 % of population
4. +/- 3 𝜎 from mean implies 99.73 % of population
f(x)
x
𝜇
𝜎
47. Cumulative distribution function
• CDF gives us the probability that random variable takes values starting from the
lowest possible value upto and including the given value of x.
• If X is a discrete random variable defined by the probability mass function p(x)
then CDF = F(x) = 𝛴𝑝 𝑥 drawn as a step function.
• If X is a continuous random variable defined by probability density function f(x)
then CDF = F(x) =
𝑎
𝑏
𝑓 𝑥 𝑑𝑥 where a is the smallest possible value and b is the
limit upto which probability estimation is required.
• It is drawn as a continuous curve which is monotonically increasing in nature.
1
1
x
F(x)
x
F(x)
48. Standard Normal Distribution
• If X is any random variable that is normally distributed with 𝜇 =
0 and 𝜎2
= 1, it is called a Standard normal variable denoted by z.
• Probability densify function (PDF) = Ѱ(z) =
1
2𝜋
ⅇ−
1
2
𝑧 2
• Cumulative distribution function (CDF) = F(z) =
−∞
𝑧
Ѱ(t) dt
• Table for CDF for various values of z is known as the NormalTable
which can be read to get the various values of z.
**Relationship between Normal Distribution and Standard
Normal Distribution
If X is normally distributed such that X = Nu (𝜇, 𝜎2
) then
𝑥−𝜇
𝜎
=
Nu (0,1)
which implies z = Nu (0,1)
0 z
Ѱ(z)
1
50. Central LimitTheorem
• Since population measurements are not possible, so samples that are representative
of the population are taken and a parameter X is monitored.The average of X is
calculated daily and all these values will have a normal distribution, a mean value and
a variance. So, ҧ
𝑥 is s.t.b random variable that is normally distributed.
• According to Central limit theorem, if samples of size “n” are repeatedly taken
from a population that is normally distributed and the averages are computed for
parameter X then the averages themselves are random variable which are
normally distributed with mean equal to mean of parent population and variance
smaller than population variance depending upon the sample size.
• If X = Nu (𝜇, 𝜎2
) and samples of size “n” are taken
then averages of sample ҧ
𝑥𝑠 = 𝑁𝑢(𝜇, 𝜎2
/n) is also normally distributed
with mean = population mean and variance = population variance/ sample size (n)
51. What if the population is
not normal ?
Let the population have any
distribution with finite mean 𝜇 and a
finite variance.
According to Central limit theorem,
sample average will be normally
distributed if the sample size is large
enough
with mean of 𝜇 and variance = 𝜎2/n
ҧ
𝑥𝑛 = 𝑁𝑢(𝜇, 𝜎2/n) when n tends to
infinity.
Example 2.
52.
53. What is a business process ??
• A repeatable, coherent, sequence of activities with a clearly defined input, with a certain
material or non- material achievement, output, and internal/ external customers.
• Flow of process consumes time and resources which is often associated with repetitive
tasks.
• Business process in operations typically refers to volume production of goods/services in a
sequence of activities performed by a set of specialized pre-defined resources.
• Advantages of process view –
1. Allows to have a view of activities as a cross –functional flow instead of individual
activities done in isolated silo/ area.
2. Map the activities needed to complete a value- added step.
3. Focus on the customer to meet his expectations (the meet the value addition)
54. SIPOC
• Managing the whole process rather than the individual activities allows “end to end process
improvement.”
• SIPOC is a tool that lists the activities/ components that occur in a process.
• It is a common tool in all 6 sigma projects.
• Why SIPOC ?
1. SIPOC gives high level picture (from supplier to customer) of value added steps in the process.
2. It provides the basis for first discussion of what could be the influencing CTQ parameters.
Supplier Input Process Output Customer
55. Process Mapping
• It is defined as identifying all the steps,
the inputs, output, controls, resources
used in each step, responsibilities for
each step and then mapping them as
they occur.
• It is a visual tool to share knowledge
and build consensus among the team
members.
• Why? –To understand it fully so that it
can be better analysed, improved,
managed and controlled.
• Who is involved? – All the stakeholders
who are involved in daily process
execution.
Start/ End
Process Step
Decision
Transportation
Storage
Inspection
Delay
Standard
symbols used in
making PFD
56. ❑Work on paper
❑Scope of the process and level of detail
❑Just get started : don’t aim for perfect accuracy from the beginning
• Process should be walked and verified
• Editing to be done before it is saved finally
❑Inputs from shop floor operators/ process owners are mandatory
• Hidden Factory
• GEMBA
❑Don’t miss inspection and measurement steps
❑Include rework loops, scrap procedures.
❑Information flow
❑Financial flow can also be included
PROCESS MAPPING PRACTICE
57.
58. • What is a Measurement System ?
A scheme or system including the instruments, equipments,
standards, procedures, software, operators, that are required
to produce a measurement do exist.
• What is Measurement System Analysis (MSA) ?
MSA is the technique of ensuring that the measuring
instruments of adequate capability are available for taking
measurements on the product characteristics and process
variables.
• Why is MSA important in six sigma organisation ?
Six sigma is a data driven methodology, which means that data
measurement is the foundation of any decision making right
from defining the problem to measuring process capability to
final analyse and control (throughout DMAIC)
So, the quality of data is paramount and poor quality data is
not recommended as it will not yield any good results in the
DMAIC process improvement cycle.
• When to carry out MSA ?
Before collecting data from the process.
Some terms for reference –
1. Gage :
any device that is used to obtain
measurement specifically for
devices used on shop floor
2. Standard :
Known reference value with
limits of uncertainty.
59. Measured
value
Observed
variation
(variability)
True
variability/
Inherent
Short term
process
variation
Long term
process
variation
Measurement
variation/
error
Error in
sampling
Measurement
reliability
True value
So, to quantify the variability, it is
important to closely look at the
measurement error.
Measurement should be done carefully
to keep the measurement error low.
With number of experiments going
on, multiple measurements need to
be taken using the measurement
system and evaluate statistical
properties to see at the data
reliability.
Statistical properties include
average of the distribution (mu),
variability (sigma square) and
standard deviation (SD).
Valid for small
time periods or
variation between
the samples due
to machine,
operator
Valid for longer
time periods or
variation between
the samples due to
special causes (shift
change, weather
change, machine
degradation)
60. Bias
• Average value
–True value
Accuracy
• It is opposite to
bias
• Lower is the
bias, greater is
the accuracy
Variability
• The spread in
the data about
the mean
• Factors-
Repeatability &
Reproducibility
Precision
• It is opposite to
variability.
• Lower is the
variability,
higher is the
precision
Linearity
• Refers to how
bias remains
the same over
the range of
possible values
of
measurement
Stability
• Refers to how
precision of
instrument
remains
consistent over
time
Resolution
• Refers to the
smallest
division of unit
that the
instrument is
designed to
measure.
x
𝜇
𝐵𝑖𝑎𝑠
𝜇 x
Variability
decreased implies
high precision
Properties of good
instrument-
1. Near zero bias
2. No linearity problem
3. High precision
4. Stability
5. Adequate resolution
61. Gage R&R study
• It is the study of measurement variability occurring due to repeatability and
reproducibility.
• Repeatability (𝜎𝑒) / EquipmentVariation (EV)- occurs from instrumental hardware
that prevents instrument from giving identical readings when measuring same unit of
product repeatedly by the same operator.
• Reproducibility (𝜎o)/ AppraiserVariation (AV) – occurs when the same unit of product
is measured repeatedly by different operators.
• GRR/ Gage error (𝜎g) = 𝜎𝑒
2
+ 𝜎0
2
• ProcessVariation (𝜎p) = PV = inherent variation of the process
• Overall variation =TV (𝜎 overall) = 𝜎𝑝
2
+ 𝜎𝑔
2
OR 𝑇𝑣2
= 𝐺𝑅𝑅2
+ 𝑃𝑣2
• As a thumb rule,
𝜎𝑔
𝜎𝑃
< 10% is acceptable and measurement is OK.
• If this is greater than 10% but less than 30%, it “can” be accepted on the basis of cost.
However, value >30% is not OK.
62. How to carry out a G R&R study ?
1. Study in detail and make sure that the equipment is calibrated and in good
condition and so are the samples. Appraisers should be aware of measurement
criteria and inspection methods through effective training.
2. Samples should be chosen which cover the spread.
3. Data collection table should be developed with randomized samples between trials
and appraisers.
4. Appraisers perform measurements including multiple trials by everyone.
Measurements done should be descriptive, selective and objective.
5. Data should be shifted to tabular sheet- G R&R
6. Perform calculations to find out the average and R double bar. Use statistical
formulae thereafter.
63. Sampling
• To take measurements, it is very important to select samples that are representative of the
population.This is necessary to save time and cost as measurements on entire population are
not possible.
• To design a sampling plan, we prioritize the input process parameters as well as the o/p to be
measured.
• Goal of measurement needs to be documented.
• Along with the sample size, frequency, data type, hypothesis should be identified.
• Sampling size regulators –
1. If effect is weak, sampling size should be larger.
2. If variability is high, sampling size should be larger.
3. If higher confidence/ precision is needed, sampling size should be larger.
• Quality sampling can either be done from a population where in sample is taken from a fixed
group (no time element) or from a process where in sample is chosen from a flow of items
(time element exists).
64. Quality
sampling
Random
sampling
Simple random – fixed
number of elements is
chosen such that each
element has an equal
chance of being selected
Stratified – population is
divided into different
strata and fixed amount
will be randomly selected
from each strata
Systematic
sampling
Without subgroups –
every nth element will be
measured
With subgroups- fixed
no of elements (n) will be
measured in regular time
interval (m).
POPULATION PROCESS
A
B C
D
65.
66. Process capability Index
• Process capability Index (Cp) is a statistical tool to measure the ability of a
process to produce the output in the designed specification limits.
• 𝐶𝑝 =
𝑣𝑜𝑖𝑐𝑒 𝑜𝑓 𝑐𝑢𝑠𝑡𝑜𝑚𝑒𝑟
𝑣𝑜𝑖𝑐𝑒 𝑜𝑓 𝑝𝑟𝑜𝑐𝑒𝑠𝑠
• Cp =
𝑈𝑆𝐿 −𝐿𝑆𝐿
6𝑠𝑖𝑔𝑚𝑎
• Cp < 1 , incapable process
• Cp > 1, process is called a capable process
• For a process with 6 sigma quality , Cp = 2
• As the value of Cp increases, the process variability decreases provided the
designed specification limits remain constant.
• Therefore, we can conclude that greater is the value of Cp, better is the
quality of process or product.
67. ProcessWith Mean Shift
Cp value speaks only of the process variability / form of the process but does not
tell anything about the target value.
Cp is nowhere connected with the process mean/ mean shift.
Therefore, Cp does not change as the process centre changes.
CONS OF USING CP…
68. Process capability Centering index (Cpk)
• Cpk = distance between process centre and nearest specification / 3 sigma
• Cpk = min
𝜇−𝐿𝑆𝐿
3𝜎
,
𝑈𝑆𝐿−𝜇
3𝜎
• Cpk speaks of the process in terms of both- form/ variability and location/
process centering. So, it is a superior index.
• Cpk < 1 , implies poor centering and the process is NC
• Cpk = 1, border line case
• Cpk > 1, process conforms to specifications
• Cpk = 0, then the mean of process lies on one specification limit.
• Cp >= Cpk and both should be greater than 1.
• If Cp = Cpk then process is perfectly centred.
69.
70. CASE 1 : SW > PW CASE 2 : SW>PW Process
Shift = 1𝛔
71. CASE 3 : SW = PW
CASE 4 : SW = PW, Process
Shift = 1𝜎
72. CASE 5 : SW < PW
CASE 6: SW < PW ,
Process shift= 1𝛔
73. Six Sigma Capability
• When Cp=1, USL-LSL =6𝜎 ,p = 99.73% and as sigma decreases, we can accommodate upto 12𝜎 b/w
LSL and USL.
• According to definition, process has a 𝟔𝝈 capability if defects produced are less than 3.4 defects
per million opportunities.
• P(X occurs b/w +/- 6𝜎 )= 99.9999998 % which implies 0.002 ppm fall outside the spec.
• However, most processes do not have their mean exactly at the target value/ centre of specification
because the process tends to drift off centre.
• According to Motorola six sigma technology, process could be off as far as 1.5 𝜎 from the specification
centre or target such that it has nothing out of spec on lower side and having 3.4 parts per million out
of spec on higher side.
• Implies 99.99966% parts within the spec. Defect rate – 3.4 ppm. Cp = 12𝜎/ 6𝜎 = 2
• Similarly, a +/- 3𝜎 process with 1.5𝜎 mean shift, 93.32 % of our product lies in the specification,
corresponds to 66800 ppm out of spec, Cp = 1.
74. Six Sigma Capability
using discrete data
Key Assessments
1. Confirm of a stable process (control
charts)
2. Measurement of attribute data and
record the no. of defects
3. Calculate DPU, DPMO.
4. Convert to sigma capability
5. Check if the customer requirement
is met ?
Example
75. Tolerancing
• Is the process of determining the allowable variations in product characteristics around
the selected target so that the product can be produced at a competitive cost while
meeting the requirements of the customer.
• For producer, having a tighter tolerance/ lower variability means an increased
production cost.
• Also, tolerancing is an economic issue for both the customer and the producer.The gain
for one may result in a loss for the other.
• Tolerance depends on the manufacturing process – machine, people, environment,
method.
• Tolerancing should be conducted after the final process is selected.
• In general, tolerance is calculated as +/- 3 SD spread (ො
𝜇 + 3 ො
𝜎) where ො
𝜇 & ො
𝜎 are
calculated using n > 50.This reflects the current capability of a process of meeting the
current conditions.These limits are called NaturalTolerance Limits (NTLs).
76. Tolerancing Models
• Traditional tolerancing – fitness of the
product is good only as long as
characteristic is at target or within the
LSL & USL.
Losses from characteristics away from
target are zero according to this model.
• Taguchi Loss function – says that
traditional tolerancing is not true. He
says, you have zero loss when you are
exactly at the target within the
characteristic. Loss will increase (in
parabolic fashion) as we move away from
the target.
LSL USL
Target
Taguchi Loss
function
77. AssemblyTolerancing
• Use Root Sum of Squares (RSS) formula-
Suppose L1, L2, L3 are the measurements of independent
components and assembly given by L = L1 + L2+ L3 ……. Ln
LetT1,T2,T3 be the tolerances of individual measurements, then
tolerance of assembly
T = 𝑇1
2
+ 𝑇2
2
+ 𝑇3
2
… 𝑇𝑛
2
• X1 – Nu (𝜇1, 𝜎1
2
) 𝑎𝑛𝑑 X2 – Nu (𝜇2, 𝜎2
2
) then
X1 + X2 = Nu (𝜇1+ 𝜇2, 𝜎1
2
+ 𝜎2
2
)
X1 – X2 = Nu (𝜇1 - 𝜇2, 𝜎1
2
+ 𝜎2
2
)
78. FMEA
• A technique to investigate all possible weakness in a product/ process design and prioritize the
weakness in terms of their potential to cause the product failure.
• 2 types- Design FMEA (DFMEA) and Process FMEA (PFMEA)
• PFMEA should be performed for –
1. Any new process
2. Current process planned to produce a new product
3. For investigating root cause for defective produced in an existing process.
• How to carry out an FMEA ?
1. Identify possible modes of failure
2. Analyse the possible causes
3. Identify the effects on consumer
4. Rank in terms of Severity, Occurrence, Detection on a scale of 1 (good) to 10 (bad).
5. Calculate Risk Priority Number, RPN = S X O X D
6. Larger the RPN, higher is the risk of failure.
Effect Cause
Severity : S
Occurrence: O
Detection: D
79.
80. Capability index Cpm
• Cpm defined by Chan, Chang & Spiring in 1988 is
defined by Cpm =
𝑈𝑆𝐿 −𝐿𝑆𝐿
6𝜎′
Where 𝜎′ =
𝑥𝑖−𝑇 2
𝑛
andT is the target.
• Cp/ Cpk measures the variability about the mean/
process centre. However, Cpm measures the
variability about the target.
• Cpm index followsTaguchi loss function
philosophy. Maximising Cpm index value follows
amounts to minimising the loss function.
• Cpm max occurs at the target.
• Cpm =
𝑐𝑝
1+𝑣2
where 𝑣 =
𝑇−𝜇
𝜎
• If process is centred, Cp = Cpk =
Cpm
• If process is not centred, Cp>
Cpk & Cpm
• Cpm will never be negative.
• Cpk can be negative if process
centre is outside spec
• Cpk & Cp assume target is at
the centre of spec.
• Cpm does not use specification
limits, but uses specified value
of target.
• When target is not at center,
Cpk and Cpm behave
differently.
Points to Remember…..
