1. PROCESS CAPABILTY AND CONTROL CHARTS1

2. Content Introduction Review of basics Process Capability
Types of control Charts
Development and maintenance of control charts
Interpretation of control charts
Practice problem 2

3. Review of basics
Proper strategy for quality control is to Control the process rather than sorting inspection of the product
Variability is a norm but it should be minimized
Two causes of variation
Common causes that are inherent in the process over time
Special causes that are not part of the process all the time but arise because of specific circumstances
Statistics can help identifying the presences of special causes 3

4. Process variation Inherent conflict between two points:
Variation is inevitable
The production is most economical when output is of uniform quality
Source of Variation:
Man, Material, Machine, Mood, Environment etc. ; 4

5. Need for process capability study
A manager is interested in knowing
whether the process is capable of producing the products of desired quality
What proportion of the products produced by process are expected to be accepted/rejected
What changes are needed to improve the capability of the process or to reduce the rejection rate
Process capability study provide answers to all of the above questions 5

6. Process capability
It refers to the performance of the process when it is operating in statistical control.
It is a measure of the uniformity of a process that makes a product
A common measure of process capability is 6-sigma or spread
It makes sense only when the process is in statistical control 6

7. Process capability Definition
It is performance under chronic conditions in which sporadic variation do not exist. 7

8. Process capability analysis?
It is an engineering study to estimate process capability
It may involve estimating the process mean and standard deviation
It might also involve estimating the proportion of nonconforming items 8

9. Benefits Help predicting how well the process will hold the tolerances
Assist in product and process development
Assists in specifying performance requirements for new equipment
Assists in vendor selection
Help in variability reduction and reduces total cost by lowering internal and internal failure costs 9

10. Specification and control limits
Specification Limits (or tolerance limits
Limits that define the conformance boundary for an individual unit
Provided by the designer or the customer for the products for its functioning
Control Limits (or natural tolerance limits)
outcome of the process identifying process variability
Does not apply to an individual units
No relation between specification and control limits 10

11. Specifications and control limits
LSL
USL
LCL
UCL
Process spread=
Specifications and control limits 11

12. Stable and capable process
Stable process
is whose output is influenced only by chance causes and not by special causes
This does not imply that the output will be as per specifications
Capable process
is one that is expected to produce output conforming to the specifications when the process is in control 12

13. Capable and incapable process
LSL
USL
Capable Not Capable
Capable and incapable process 13

14. Control Chart
General theory first proposed by Walter. A. Shewhart of the Bell Telephone Lab in 1920s
A control chart is a graphical tool for monitoring a process
It indicates presence/absence of special cause(s) of variation in the process
It is an on-line quality control tool 14

15. Types of control charts
(Based of type of data)
Attribute control charts
p chart
c chart
Variable control charts
X-bar chart
R chart 15

16. Steps Involved in the construction of Control Charts
Partition the historical data: two distinctly data set- one for the construction and other for reflecting on the performance
Use data to identify 3 sigma limit
Draw the control charts axis. Y axis for variable measurement, X axis for sequence of samples
Plot the most recent average 16

17. Steps Involved in the construction of Control Charts
Interpret (a) in control (b) out of control
( c ) in control but need caution
Update the control charts by discarding the old data and including the recent data 17

20. Type 1, α risk, or producer’s risk:- Probability of concluding that the process is out of control where actually it is in control.
Reduced by 3 sigma limit, Increased by 1 sigma limits
Type 2, β risk, or consumer’s risk:- Probability of concluding that the process is in control where as this is out of control. Risk increases as the limits are widened and reduces as limits are reduced.

21. Comparison of variable and attribute charts
Variables provide more information than attributes
Cost of inspection for obtaining variable data is normally higher than for attributes
Attribute charts more useful at plant level while variable charts at the machine or operator level 21

22. Benefits of control charts
Distinguish special from common causes of variation to guide management action
Can be used by operators for on-line control of a process
Provides predictability for quality and cost
Allow the process to achieve
Higher quality
Lower unit cost
Higher effective capacity 22

23. Steps involved Analyze the product and the process
Define the purpose of using control charts
Select the the characteristic/s for control charting
Select the type of control chart to be used
Analyze the process of measurement
Determine subgroup size and frequency of sampling
Design the format for data recording and charting 23

24. Determine the trial control limits
Plot the points and identify points indicating out of control process
Search for special causes and rectify
Calculate final control limits
Continue the process 24

25. Interpretation of control charts
Process under control
Process whose outcomes are affected by common causes is called stable process or process that is in a state of statistical control
It does not imply that the process is producing the desired quality of products relative to specifications
Let the process continue
Process out of control
Process whose outcomes are affected both by common causes and special causes is called un- stable process or out of control process
Attention required 25

26. Out of control process
A control chart may indicate an out-of- control condition either when one or more points fall beyond the control limits, or when the plotted points exhibit some nonrandom pattern of behavior 26

27. Some Rules for identifying out of control process (Developed at Western Electric)
If a single point plots outside the control limits
Two of three consecutive points outside the warning (2-sigma) on the same side of the center line
Four of five consecutive points beyond the 1- sigma limits.
Eight or more consecutive points fall to one side of the center line
A trend of eight or more points in a row in upward or downward direction 27

28. Some patterns which may be due to out of control process
Change in the level of plotted points
Trend in the plotted pattern
Cyclic behavior in the plotted pattern
Concentration of points near control limits 28

29. Control charts for variables
Used for variable data
Separate chart for each quality characteristic
Two things – mean and spread – must be in control hence two charts are maintained simultaneously
X-bar and R chart
Spread chart is analyzed first and then the chart for mean 29

30. X-bar chart
Details 30

31. Control limits for X-bar and R chart R chart31

32. Charts for attributes Used for attribute data
p chart and np chart for classification data
c chart and u chart for count data
Only one chart is plotted instead of two as in case of charts for variables 32

33. Chart for fraction nonconforming (p Chart)
Used when items are inspected for its conformity or nonconformity to the specifications
Based on Binomial distribution 33

34. Control limits for p chart
Fraction nonconforming in a sample can be found by
Where x in number of nonconforming items and and n is sample size
Where is average of over all the samples 34

35. Chart for number of nonconformities (c chart)
Used to track total number of nonconformities in a sample (of constant size) or the area of opportunities
Based on Poisson distribution 35

36. Control limits for c chart
Where is the average number of nonconformities per sample unit 36

37. Summary
Control charts are tool for SPC which help identifying the presence of assignable causes in the process
Different types of charts for different types of data
Different rules are there for detecting out of control process 37

38. Type of data Continuous data Classification data Count data
A measured value of the quality characteristic is recorded e.g. dimension, weight, specific gravity, cost
Classification data
Quality characteristic is recorded in one of two classes e.g. conforming/nonconforming units, good/bad
Count data
The number of incidences of a particular characteristic is recoded e.g. number of accidents, number of mistakes 38

39. Conceptually, 3-sigma limits for X-bar control charts are
is standard deviation of the sample means and as per central limit theorem where is the s.d. for the individual units
where
is a constant depending on the sample size as
another constant 39

40. Value of the characteristic
Center line
Upper control limit
Sample number
Lower Warning limit
Upper Warning limit
Value of the characteristic
One sigma limit
One sigma limit
Lower control limit 40

41. Value of the characteristicCL
UCL
Sample number
Value of the characteristic
LCL 41

42. Value of the characteristicCL
UCL
Value of the characteristic
LCL
Sample number 42

43. Value of the characteristicCL
UCL
Value of the characteristic
LCL
One sigma limit
One sigma limit 43

44. Value of the characteristicCL
UCL
Value of the characteristic
LCL 44

45. Value of the characteristicCL
UCL
Value of the characteristic
LCL 45

46. Thank You 46

47. Genesis of control charts
Walter A. Shewhart of the Bell Telephone Laboratories issued a memorandum on May 16, 1924 that featured a sketch of a modern control chart. 
Published a book on statistical quality control,
"Economic Control of Quality of Manufactured Product", in 1931, published Van Nostrand in New York. This book set the tone for subsequent applications of statistical methods to process control. 47