1. Development and Interpretation of Control Charts
Presented by Dr. Joan Burtner
Certified Quality Engineer
Associate Professor of
Industrial Engineering and Industrial Management

2. Overview Shewhart’s Concept of Control Charts
Common Types of Control Charts
Development of Control Charts
Interpretation of Control Charts
Advanced Topics in Control Charts
Further Reading
IDM 355 Fall 2017
Dr. Joan Burtner, Assoc. Prof. of Industrial Engineering

3. Shewhart’s Concept of Control Charts - 1
“Through the use of the scientific method, extended to take account of modern statistical concepts, it has been found possible to set up limits within which the results of routine effort must lie if they are to be economical. Deviations in the results of a routine process outside such limits indicate that the routine has broken down and will no longer be economical until the cause of trouble is removed..” Devor, Chang, and Sutherland p. 151
IDM 355 Fall 2017
Dr. Joan Burtner, Assoc. Prof. of Industrial Engineering

4. Shewhart’s Concept of Control Charts - 2
“A phenomenon will be said to be controlled when, through the use of past experience, we can predict, at least within limits, how the phenomenon may be expected to vary in the future. Here it is understood that prediction within limits means that we can state, at least approximately, the probability that the observed phenomenon will fall within the given limits.” Devor, Chang, and Sutherland p. 151
IDM 355 Fall 2017
Dr. Joan Burtner, Assoc. Prof. of Industrial Engineering

5. Shewhart’s Concept of Control Charts - 3
“That the quality characteristics of the product fall within the specification limits (derived during engineering design) implies that the customer expectations are being met. That the performance of the process also falls within the statistical limits of variation for routine operation (derived from the observed variation in the process) implies that the customer expectations are being met in an economic fashion.” Devor, Chang, and Sutherland p. 151
IDM 355 Fall 2017
Dr. Joan Burtner, Assoc. Prof. of Industrial Engineering

6. Theory of Variation Common Cause Special Cause
Stable and predictable causes of variation
Inherent in all processes
Managers, not workers, are responsible for common cause variation
Special Cause
Unexpected or abnormal causes of variation
May result in sudden or extreme departures from normal
May also result in gradual shifts (trends)
IDM 355 Fall 2017
Dr. Joan Burtner, Assoc. Prof. of Industrial Engineering

7. Types of Control Charts
Single or multivariate
Track one quality characteristic per chart
Track more than one characteristic on the same chart
Variables or attributes
Variable (measured characteristics)
X-bar, R, S
Attributes (counts)
P (percent non-conforming)
C (count)
U (count per unit)
IDM 355 Fall 2017
Dr. Joan Burtner, Assoc. Prof. of Industrial Engineering

8. Development of Control Charts
Choose quality characteristic to be measured or counted
Collect at least 25 samples
Develop trial control limits
Evaluate for special causes
Determine special causes and remediate
Eliminate out-of-control points
Recalculate control limits
Continue until chart shows process is in control
Monitor process using established control limits
IDM 355 Fall 2017
Dr. Joan Burtner, Assoc. Prof. of Industrial Engineering

9. Interpretation of Control Charts – NIST.GOV
“If a single quality characteristic has been measured or computed from a sample, the control chart shows the value of the quality characteristic versus the sample number or versus time. In general, the chart contains a center line that represents the mean value for the in-control process. Two other horizontal lines, called the upper control limit (UCL) and the lower control limit (LCL), are also shown on the chart. These control limits are chosen so that almost all of the data points will fall within these limits as long as the process remains in-control.”
“Statistical methods to detect sequences or nonrandom patterns can be applied to the interpretation of control charts. To be sure, "in control" implies that all points are between the control limits and they form a random pattern.”
IDM 355 Fall 2017
Dr. Joan Burtner, Assoc. Prof. of Industrial Engineering

10. Interpretation of Control Charts
Look for special cause variation
Points that are outside 3 sigma limits
Series of points that are unusually close to 3 sigma limits
Non-random patterns such as linear trends, oscillation, runs above or below centerline
Textbook tests for special causes differ slightly from Minitab tests
IDM 355 Fall 2017
Dr. Joan Burtner, Assoc. Prof. of Industrial Engineering

11. Control Chart Types Control Charts Example of R Chart:
Variables – based on continuous data
X bar and R (mean and range)
Attributes - based on discrete data
P (proportion)
C (count)
Example of R Chart:
IDM 355 Fall 2017
Dr. Joan Burtner, Assoc. Prof. of Industrial Engineering

12. Control Chart Equations for Variables Charts
Xbar and R Control Chart Constants
Control Chart Calculations n
d 2
A 2
D 3
D 4 2
1.128
1.88
3.267 3
1.693
1.023
2.575 4
2.059
0.729
2.282 5
2.326
0.577
2.115 6
2.534
0.483
2.004 7
2.704
0.419
0.076
1.924
IDM 355 Fall 2017
Dr. Joan Burtner, Assoc. Prof. of Industrial Engineering

13. Partial p Chart Data Data: 30 samples of size 200 each
Inspected
Rejected 1
200 8 2 13 3 7 4 5 6 12 9 27 10 11 14 15 26 28 17 29 30
Data: 30 samples of size 200 each
CL = total defects / total number of samples
Chart built in Excel:
IDM 355 Fall 2017
Dr. Joan Burtner, Assoc. Prof. of Industrial Engineering

14. Control Chart Calculations for Proportion Defective (p)
Chart built in Minitab:
IDM 355 Fall 2017
Dr. Joan Burtner, Assoc. Prof. of Industrial Engineering

15. Control Chart Data for Number of Defects (c)
Sample Number of
Number Defects
1 16
2 14
3 28
4 16
5 12
6 20
7 10
8 12
9 30
10 17
11 9
12 17
13 14
14 16
15 15
16 13
17 14
18 16
19 11
20 20
21 11
22 9
23 16
24 31
25 13
Chart built in Excel:
IDM 355 Fall 2017
Dr. Joan Burtner, Assoc. Prof. of Industrial Engineering

16. Control Chart Equations for Number of Defects (c)
IDM 355 Fall 2017
Dr. Joan Burtner, Assoc. Prof. of Industrial Engineering

17. U Chart Data Data: 21 samples with varying sample sizes
Defects
SampleSize 1 9 90 2 11 3 4 5 15 6 13
100 7 8 10 12 14
115 16 17 18 95 19 20 21
Data: 21 samples with varying sample sizes
CL = total defects / total number of items sampled
UCL and LCL vary with sample size
Chart built in Excel:
IDM 355 Fall 2017
Dr. Joan Burtner, Assoc. Prof. of Industrial Engineering

18. Control Chart Calculations for Number of Defects per Unit (u)
IDM 355 Fall 2017
Dr. Joan Burtner, Assoc. Prof. of Industrial Engineering

19. U Chart Calculations IDM 355 Fall 2017
Dr. Joan Burtner, Assoc. Prof. of Industrial Engineering

20. Further Reading
Christensen, E.H., Coombes-Betz, K.M., and Stein, M.S. (2014). The Certified Quality Process Analyst Handbook. Milwaukee: ASQ Quality Press.
DeVor, R.E., Chang, T., and Sutherland, J.W. (2007). Statistical Quality Design and Control: Contemporary Concepts and Methods (2nd ed.). Upper Saddle River, NJ: Pearson Prentice Hall.
“NIST Information Technology Laboratory” see also: NIST/SEMATECH e-Handbook of Statistical Methods
Westcott, R.T., Ed. (2006). Certified Manager of Quality/Organizational Excellence Handbook (3rd ed.). Milwaukee: ASQ Quality Press.
IDM 355 Fall 2017
Dr. Joan Burtner, Assoc. Prof. of Industrial Engineering

21. Contact Information
US Mail:
Mercer University School of Engineering
1400 Coleman Avenue
Macon, GA
Phone: (478)
IDM 355 Fall 2017
Dr. Joan Burtner, Assoc. Prof. of Industrial Engineering