The document provides an overview of quality tools and concepts. It defines quality, processes, systems, variation and different quality tools including flowcharts, histograms, Pareto charts, scatter plots, control charts. It explains how to create and interpret these tools. Control charts are discussed in more detail with examples of mean and range control charts showing how to establish control limits and monitor process performance over time. The document serves as an introduction to statistical process control tools for quality improvement.

2. Tools of Quality
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What is Quality

3. Tools of Quality
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What is Quality
In simple words, Quality means
1. Doing things well (create what you intended)
2. Doing things efficiently (waste as little time and materials as
possible)

4. Tools of Quality
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What is Quality
People describe quality with some other definitions
1. A product or service that satisfy stated or implied needs
2. A product or service free of deficiencies
3. A product or service that meets customer expectations
4. A product or service that Exceeds customer expectations
5. Superiority to competitors
6. “I’ll know it when I see it”

5. Tools of Quality
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Statistical
Process Control

6. Tools of Quality
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Statistical
Process Control
(SPC)

7. Tools of Quality
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Red Bead
Experiment

8. Tools of Quality
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Red Bead
Experiment

9. Tools of Quality
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Red Bead
Experiment
Insights
1. All workers perform within a system that is beyond their control.
2. There will always be some workers that are above the average and some
workers that are below the average.
3. Workers should not be ranked because doing so merely represents a ranking
of the effect of the system on the workers.
4. Only management can change the system.

10. Tools of Quality
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Process
A process is a set of interrelated or interacting activities that transform input to
output. For eg. If you own a flower shop, these can be different processes
• Purchase the right flowers from the right suppliers (purchasing);
• Have those flowers delivered at the right time in perfect condition to the
shop (materials management);
• Make sure to have a trained florist on hand to assist customers (knowledge,
labour and production);
• Create the floral arrangements in such a way that they are consistently high
quality and works of art (quality control); and
• Ensure each and every customer is thrilled (customer satisfaction).

11. Tools of Quality
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System
A set of interrelated parts that must work together.
For eg. a flower shop

12. Tools of Quality
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Process
approach to
management
The process management approach is based on:
• The ability of an organization to identify all its processes and recognize
the inputs and outputs of each process
• The documentation of processes so they can be easily implemented
• The identification of the owners of each process
• The implementation of the processes
• The measurement of the outcomes of the implementation
• Continual improvement of the efficiency and effectiveness of the
processes

13. Tools of Quality
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Variation
Difference between designed and expected output of a process
5 Kg Hammer Actual weight –> 4.8 Kg

14. Tools of Quality
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Types of
Variation
Variations can be divided into 2 categories
1. Random or Common variations
Natural variation in the output of a process, created by countless minor
factors. Eg. Older machines generally exhibit a higher degree of natural
variability than newer machines, partly because of worn parts
2. Assignable or Special variation
In process output, a variation whose cause can be identified. A nonrandom
variation. For eg. Tool wear, equipment that needs adjustment, defective
materials, human factors (carelessness, fatigue, noise and other distraction)

15. Tools of Quality
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Special vs
Common
variation
• Special cause variations can usually be detected and removed by the
individuals operating the process first-hand.
• Common cause variations usually require management action to change
some inherent feature of the process.
• 85/15 rule - The management is responsible for providing the necessary
inputs to correct the majority of variation problems, that is, common causes.

16. Tools of Quality
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7 basic tools of
quality
• The seven quality tools were originally developed by Japanese professor of
engineering Kaoru Ishikawa.
• The goal was to implement basic, user-friendly tools that workers from various
backgrounds with varied skill sets could implement without extensive training.
• The 7 basic quality tools are as follows:
1. Flow Chart
2. Histogram
3. Cause-and-Effect Diagram
4. Check Sheet
5. Scatter Diagram
6. Control Charts
7. Pareto Charts

17. Tools of Quality
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7 basic tools of
quality

18. Tools of Quality
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7 basic tools of
quality

19. Tools of Quality
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Flowchart
• A flowchart is simply a graphical representation of
steps.
• a flowchart shows the steps as boxes of various kinds,
and their order by connecting them with arrows
• Flowchart is used for
• Understanding
• Improving
• Communicating
• Documenting the proceess
Emergency Hotline

20. Tools of Quality
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Flowchart
➢ One step in the process
➢ Direction of flow from one step or decision to another.
➢ Decision based on a question.
➢ Delay or wait
➢ Link to another page or another flowchart.
➢ Input or output
➢ Document
➢ Alternate symbols for start and end points

21. Tools of Quality
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Waste
management
Flowchart

22. Tools of Quality
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Flowchart
• A flowchart is simply a graphical representation of
steps.
• a flowchart shows the steps as boxes of various kinds,
and their order by connecting them with arrows.
Emergency Hotline

23. Tools of Quality
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Histogram &
Pareto
• A histogram is an approximate representation of the frequency distribution of
numerical data.
• Pareto charts show the ordered frequency counts of values for the different levels
of a categorical or nominal variable.
Pareto chart
Histogram

24. Tools of Quality
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Histogram
Example
Hammer Head
Hammer Handle
S.No. Weight
1 1.965
2 1.924
3 1.922
4 2.039
5 1.963
6 2.057
7 2.050
8 1.976
9 2.004
10 2.030
11 1.991
12 2.017
13 2.000
14 1.988
15 2.021
16 1.992
17 1.993
18 1.926
19 1.977
20 2.020
Upper Limit = 2.08
Mean = 2
Lower Limit = 1.92

25. Tools of Quality
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When to use
1. Numerical data
2. Analyze the shape of the data’s distribution
3. Analyzing whether a process can meet the customer’s requirements,
4. Analyzing what the output from a supplier’s process looks like

26. Tools of Quality
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Histogram
• A histogram is an approximate representation of the frequency distribution of
numerical data.

27. Tools of Quality
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Histogram
Analysis
Normal Distribution
• Check the mean and variance

28. Tools of Quality
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Histogram
Analysis
Skewed Distribution
• Peak is off center and a tail stretches
• Can be due to the natural limit, Example < 0 or hole punch size from punching
machine .

29. Tools of Quality
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Histogram
Analysis
Double-peaked or bimodal Distribution
• Two peaks
• The outcomes of two processes with different distributions are combined in one
set of data
• For example- Production from a two-shift operation

30. Tools of Quality
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Histogram
Analysis
Plateau Distribution
• Multiple peaks
• Several processes with normal distributions are combined
• For example- Several workers making the same product in batches

31. Tools of Quality
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Histogram
Analysis
Truncated Distribution
• looks like a normal distribution with the tails cut off
• Normal distribution production and then relying on inspection to separate out of
specs outputs
• For example- Products from a suppliers with strict limits

32. Tools of Quality
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Histogram
Analysis
Dog food Distribution
• Normal distribution missing the truncated distribution
• A better quality/ low variance products are used somewhere else
• For example- Products from a suppliers who is selling the low variance products to
someone else

33. Tools of Quality
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Pareto chart
• A Pareto is a diagram that arranges categories from highest to lowest frequency of
occurrence

34. Tools of Quality
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Pareto chart
• 80% of defects are due to only 20% of causes. Therefore, by minimizing 20% of the
causes, we can eliminate 80% of the problems.

35. Tools of Quality
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When to use
1. Analyzing data about the frequency of problems or causes in a process,
2. When there are many problems or causes and you want to focus on the most
significant,

36. Tools of Quality
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Pareto chart
1. Define the measurement scale for the potential causes. (frequency / cost.)
2. Define the time period
3. Collect and tally data for each potential cause.
4. Put root causes on X axis in descending order of value.
5. Label the measurement scale on the vertical (y) axis.

37. Tools of Quality
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Pareto chart
6. Draw one bar for each possible cause to represent the value of the measurement.
7. If desired, add a vertical (y) axis on the right side of the chart to represent
cumulative percentage values.
8. Draw a line to show the cumulative percentage from left to right as each cause is
added to the chart.

38. Tools of Quality
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Scatter plot
A scatter diagram is a chart in which one variable is plotted against another to
determine whether there is a correlation between the two variables. These
diagrams are used to plot the distribution of information in two dimensions.
Coffee Temperature
Customer
rating
80
70
60
1
2
3
4
5

39. Tools of Quality
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When to use
When trying to identify potential root causes of problems
Coffee Temperature
Customer
rating
80
70
60
1
2
3
4
5

40. Tools of Quality
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Control chart
• A control chart is a time-ordered plot of sample statistics.
• Each point is a sample statistics
Lower control
Limit
Upper control
Limit

41. Tools of Quality
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Control chart
• A control chart is a time-ordered plot of sample statistics.
• It is used to distinguish between random variability and nonrandom variability.
• It has upper and lower limits, called control limits, that define the range of
acceptable (i.e., random) variation for the sample statistic.
Lower control Limit
Upper control Limit

42. Tools of Quality
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Mean
Mean is the average of a data set. It is denoted by µ (mu) or ҧ
𝑥
S.no Observation
1 12
2 11
3 10
4 9
5 8
ҧ
𝑥 =
12 + 11 + 10 + 9 + 8
5
ҧ
𝑥 =
50
5
ҧ
𝑥 = 10

43. Tools of Quality
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Standard
Deviation
Standard deviation is a measure of dispersement in statistics. “Dispersement” tells you
how much your data is spread out. It is denoted by 𝜎 (sigma)
S.no Observation
1 12
2 11
3 10
4 9
5 8
(12 − 10)2+(11 − 10)2+(10 − 10)2+(9 − 10)2 +(8 − 10)2
5
=
4+1+0+1+4
5
= 2 = 1.41
S.no Observation
1 14
2 12
3 10
4 8
5 6
(14 − 10)2+(12 − 10)2+(10 − 10)2+(8 − 10)2 +(6 − 10)2
5
=
16+4+0+4+16
5
= 8 = 2.82

44. Statistical Inference
Population &
Sample
Population
10,000 hammers
Sample
50 Hammers

45. Statistical Inference
Population &
Sample
Population parameter –
Numerical measure of interest related to the population
Population Proportion-
Number of elements in the category of interest/ Total
number of elements
Population mean 𝜇
Standard deviation 𝜎
Population proportion p

46. Statistical Inference
Population &
Sample
Population
10,000 Houses
Sample
50 Houses
Sample Mean ҧ
𝑥
Sample Standard
deviation s
Sample Proportion ҧ
𝑝
Sample
Statistics

47. Statistical Inference
Population &
Sample
Sample
50 Houses
Sample Mean ҧ
𝑥 =
σ 𝑥𝑖
𝑛
=
27,64,286
50
= 55285.72
Sample Standard deviation s
=
σ(𝑥𝑖 − ҧ
𝑥)2
𝑛 − 1
= 6069.3
Sample Proportion ҧ
𝑝 =
𝑥
𝑛
=
30
50
= 0.6
𝜇
𝜎
p
*Why (n-1) for sample standard deviation - https://en.wikipedia.org/wiki/Bessel%27s_correction

48. Tools of Quality
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Control chart
• A control chart is a time-ordered plot of sample statistics.
• It is used to distinguish between random variability and nonrandom variability.
• It has upper and lower limits, called control limits, that define the range of
acceptable (i.e., random) variation for the sample statistic.
Lower control Limit
Upper control Limit

49. Tools of Quality
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Mean Control
chart
• Control chart used to monitor the central tendency of a process.
Upper control limit (UCL): =
Lower control limit (LCL): =
Standard deviation of distribution of sample means
Estimate of the process standard deviation
Sample size
The number of standard deviations that control limits are based on
Average of sample means
Observation 1 2 3 4 5
1 12.11 12.15 12.09 12.12 12.09
2 12.1 12.12 12.09 12.1 12.14
3 12.11 12.1 12.11 12.08 12.13
4 12.08 12.11 12.15 12.1 12.12
X-bar 12.1 12.12 12.11 12.1 12.12
Sample

50. Tools of Quality
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Mean Control
chart
• Control chart used to monitor the central tendency of a process.
Upper control limit (UCL): =
Lower control limit (LCL): =
= A factor from table
= Average of sample ranges
Reference:
https://web.mit.edu/2.810/www/files/readings/ControlChartConstantsAndFormulae.pdf
Observation 1 2 3 4 5
1 12.11 12.15 12.09 12.12 12.09
2 12.1 12.12 12.09 12.1 12.14
3 12.11 12.1 12.11 12.08 12.13
4 12.08 12.11 12.15 12.1 12.12
X-bar 12.1 12.12 12.11 12.1 12.12
Range 0.03 0.05 0.06 0.04 0.05
Sample

51. Tools of Quality
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Range Control
chart
• Control chart used to monitor the dispersion of a process.
Observation 1 2 3 4 5
1 12.11 12.16 12.07 12.17 12.03
2 12.1 12.13 12.06 12.13 12.2
3 12.11 12.09 12.14 12.03 12.13
4 12.08 12.1 12.17 12.07 12.12
X-bar 12.1 12.12 12.11 12.1 12.12
Range 0.03 0.07 0.11 0.14 0.17
Sample
Observation 1 2 3 4 5
1 12.11 12.15 12.09 12.12 12.09
2 12.1 12.12 12.09 12.1 12.14
3 12.11 12.1 12.11 12.08 12.13
4 12.08 12.11 12.15 12.1 12.12
X-bar 12.1 12.12 12.11 12.1 12.12
Range 0.03 0.05 0.06 0.04 0.05
Sample

52. Tools of Quality
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Range Control
chart
• Control chart used to monitor the dispersion of a process.
Observation 1 2 3 4 5
1 12.11 12.15 12.09 12.12 12.09
2 12.1 12.12 12.09 12.1 12.14
3 12.11 12.1 12.11 12.08 12.13
4 12.08 12.11 12.15 12.1 12.12
X-bar 12.1 12.12 12.11 12.1 12.12
Range 0.03 0.05 0.06 0.04 0.05
Sample
Mean of sample ranges

53. Tools of Quality
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Control Charts
for Attributes
Used when the process characteristic is counted rather than measured.
1. p-chart is used when the data consist of two categories of items.
a. Good or bad
b. Pass or fail
2. c-chart is used, when the goal is to control the number of occurrences (e.g.,
defects) per unit, For Example
a. Scratches, chips, dents, or errors per item
b. Cracks or faults per unit of distance (e.g., meters, miles)
c. Breaks or tears, per unit of area (e.g., square yard, square meter)
d. Bacteria or pollutants per unit of volume (e.g., gallon, cubic foot, cubic yard)
e. Calls, complaints, failures, equipment breakdowns, or crimes per unit of time

54. Tools of Quality
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p Chart
A p-chart is used to monitor the proportion of defective items generated by a process.
• The centerline on a p-chart is the average fraction defective in the population, p.
• The standard deviation of the sampling distribution when p is known is
• Control limits
• If p is unknown, which is generally the case,
it can be estimated from samples as ത
𝑃

55. Tools of Quality
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c Chart
Control chart for attributes, used to monitor the number of defects per unit.
• The mean number of defects per unit is c.
• the standard deviation is 𝑐
• Control limits
• If the value of c is unknown, as is generally the case, the sample estimate, ҧ
𝑐 , is used
in place of c, using
• ҧ
𝑐 = Number of defects ÷ Number of samples.

56. Tools of Quality
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fishbone
diagram
Also known as cause-and-effect diagram or Ishikawa diagram
The cause-and-effect diagram graphically illustrates the relationship between a given
outcome and all the factors that influence the outcome.

57. Tools of Quality
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Procedure 1. Agree on a problem statement (effect). Write it at the center right of the flipchart or
whiteboard.
2. Brainstorm the major categories of causes of the problem.
3. Brainstorm all the possible causes of the problem. Ask “Why does this happen?”
4. Ask again, “Why does this happen?” about each cause.
5. When the group runs out of ideas, focus attention to places on the fishbone where
ideas are few.

58. Tools of Quality
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Determining the
factors
6 Ms in the manufacturing
1. Manpower - the operational and/or functional labor of people engaged in the
design and delivery of a product
2. Method – a production process and its contributing service delivery
processes.
3. Machine - systems, tools, facilities and equipment used for production.
4. Material - raw materials, components and consumables needed to produce a
desired end product.
5. Mother Nature (Environment) – environmental factors that are unpredictable
and uncontrollable like weather, floods, earthquakes, fire, etc.
6. Measurement – manual or automatic inspections and physical
measurements (distance, volume, temperature, pressure, etc.).

59. Tools of Quality
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Determining the
factors
5 why method
The 5 Whys method, like the fishbone diagram, starts with an underlying problem
statement and then proceeds to ask the question “why?” five times.
1. Why there are large number of rejected cakes? (Under cooking)
2. Why there is an undercooking? (oven was not available)
3. Why oven was not available? (oven stopped working for 30 min)
4. Why oven stopped working? (overheating)
5. Why was there overheating? (temperature gauge was faulty)

60. Tools of Quality
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fishbone
diagram

61. Tools of Quality
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fishbone
diagram When to use
• Determining the factors that cause a positive or negative outcome (or effect)
• Focusing on a specific issue without resorting to complaints and irrelevant discussion
• Determining the root causes of a given effect
• Identifying areas where there is a lack of data

62. Tools of Quality
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fishbone
diagram