1. Statistical Process Control6
SUPPLEMENT
PowerPoint presentation to accompany
Heizer and Render
Operations Management, Eleventh Edition
Principles of Operations Management, Ninth Edition
PowerPoint slides by Jeff Heyl
© 2014 Pearson Education, Inc.

2. Learning Objectives Apply quality management tools for problem solving
Identify the importance of data in quality management
6S–2

3. Statistical Quality Control
Introduction
Statistical Quality Control
Statistical Process Control (SPC)
Acceptance Sampling (AS)
Statistical process control is a statistical technique that is widely used to ensure that the process meets standards.
Acceptance sampling is used to determine acceptance or rejection of material evaluated by a sample.
6S–3

4. Preparing the clay for throwing
Introduction
Pottery Making Process
Pinching pots
Preparing the clay for throwing
Wedging
Throwing
Painting
Firing
6S–4

5. Introduction
6S–5

6. Statistical Process Control Chart (SPC)
Variability is inherent in every process.
Natural variation – can not be eliminated
Assignable variation -- Deviation that can be traced to a specific reason: machine vibration, tool wear, new worker.
Variation
Natural Variation
Assignable Variation
6S–6

7. Statistical Process Control Chart (SPC)
The essence of SPC is the application of statistical techniques to prevent, detect, and eliminate defective products or services by identifying assignable variation.
6S–7

8. Statistical Process Control Chart (SPC)
A control chart is a time-ordered plot obtained from an ongoing process
Abnormal variation due to assignable sources
Out of control
UCL
LCL
Natural variation due to chance
Mean
Abnormal variation due to assignable sources 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Sample number
6S–8

9. Statistical Process Control Chart (SPC)
Control Charts for Variable Data
Control Charts for Attribute Data
-charts (for controlling central tendency)
R-charts (for controlling variation)
p-charts (for controlling percent defective)
c-charts (for controlling number of defects)
Variable Data (continuous): quantifiable conditions along a scale, such as speed, length, density, etc.
Attribute Data (discrete): qualitative characteristic or condition, such as pass/fail, good/bad, go/no go.
6S–9

10. Statistical Process Control Chart (SPC)
Take random samples
Calculate the upper control limit (UCL) and the lower control limit (LCL)
Plot UCL, LCL and the measured values
If all the measured values fall within the LCL and the UCL, then the process is assumed to be in control and no actions should be taken except continuing to monitor.
If one or more data points fall outside the control limits, then the process is assumed to be out of control and corrective actions need to be taken.

11. x-Charts Upper control limit (UCL) = x + A2R
Lower control limit (LCL) = x - A2R
where R = average range of the samples
A2 = control chart factor from Table S6.1(page 241)
x = average of the sample means
6S–11

12. x-Charts Range=18-13=5 Range=17-14=3 R = (5+3)/2 = 4 Hour 1 Hour 2
Box Weight of Number Oat Flakes
1 17
2 13
3 16
4 18
5 17
6 16
7 15
8 17
9 16
Hour 2
Box Weight of Number Oat Flakes
1 14
2 16
3 15
4 14
5 17
6 15
7 15
8 14
9 17
Range=18-13=5
Range=17-14=3
R = (5+3)/2 = 4
6S–12

13. x-Charts Upper control limit (UCL) = x + A2R
Lower control limit (LCL) = x - A2R
where R = average range of the samples
A2 = control chart factor from Table S6.1 (page241)
x = average of the sample means
6S–13

14. x-Charts x = (16.11+15.22)/2 = 15.665 Hour 1 Hour 2
Box Weight of Number Oat Flakes
1 17
2 13
3 16
4 18
5 17
6 16
7 15
8 17
9 16
Hour 2
Box Weight of Number Oat Flakes
1 14
2 16
3 15
4 14
5 17
6 15
7 15
8 14
9 17
Average=(17+13+…+16)/9=16.11
Average=(14+16+…+17)/9=15.22
x = ( )/2 =
6S–14

15. x-Charts Upper control limit (UCL) = x + A2R
Lower control limit (LCL) = x - A2R
where R = average range of the samples
A2 = control chart factor from Table S6.1 (page241)
x = average of the sample means
6S–15

16. x-Charts Sample Size Mean Factor Upper Range Lower Range n A2 D4 D3
6S–16

17. x-Charts Upper control limit (UCL) = x + A2R
Lower control limit (LCL) = x - A2R
where R = average range of the samples
A2 = control chart factor from Table S6.1 (page241)
x = average of the sample means
6S–17

18. x-Charts
Example S6.1: Eight samples of seven tubes were taken at random intervals. Construct the x-chart with 3- control limit. Is the current process under statistical control? Why or why not? Should any actions be taken?
Sample size = n = 7
A2 = ?
6S–18

19. x-Charts Sample Size Mean Factor Upper Range Lower Range n A2 D4 D3
6S–19

20. x-Charts
Example S6.1: Eight samples of seven tubes were taken at random intervals. Construct the x-chart with 3- control limit. Is the current process under statistical control? Why or why not? Should any actions be taken?
A2 = 0.42
6S–20

21. x-Charts Control Chart for sample of 7 tubes 6.43 = UCL 6.36 = Mean
6.29 = LCL
6.36 = Mean
| | | | | | | | | | | |
Sample number
It is assumed that the central tendency of process is in control with 99.73% confidence. No actions need to be taken except to continuously monitor this process.
6S–21

22. Steps in Creating Charts
Take samples from the population and compute the appropriate sample statistic
Use the sample statistic to calculate control limits
Plot control limits and measured values
Determine the state of the process (in or out of control)
Investigate possible assignable causes and take actions
6S–22

23. R-Charts Upper control limit (UCL) = D4R
Lower control limit (LCL) = D3R
where
R = average range of the samples
D3 and D4 = control chart factors from Table S6.1 (Page 241)
6S–23

24. R-Charts Sample Size Mean Factor Upper Range Lower Range n A2 D4 D3
6S–24

25. R-Charts Example S6.2 Average range R = 5.3 pounds Sample size n = 5
From Table S6.1 D4 = ? D3 = ?
6S–25

26. R-Charts Sample Size Mean Factor Upper Range Lower Range n A2 D4 D3
6S–26

27. R-Charts Example S6.2 Average range R = 5.3 pounds Sample size n = 5
From Table S6.1 D4 = 2.12, D3 = 0
UCL = 11.2
Mean = 5.3
LCL = 0
UCLR = D4R
= (2.12)(5.3)
= 11.2 pounds
LCLR = D3R
= (0)(5.3)
= 0 pounds
6S–27

28. R-Charts
Example S6.3: Refer to Example S6.1. Eight samples of seven tubes were taken at random intervals. Construct the R-chart with 3- control limits. Is the current process under statistical control? Why or why not? Should any actions be taken?
n=7
D3 =? D4 = ?
6S–28

29. R-Charts Sample Size Mean Factor Upper Range Lower Range n A2 D4 D3
6S–29

30. R-Charts
Example S6.3: Refer to Example S6.1. Eight samples of seven tubes were taken at random intervals. Construct the R-chart with 3- control limits. Is the current process under statistical control? Why or why not? Should any actions be taken?
D3 =0.08, D4 = 1.92
6S–30

31. R-Charts Control Chart for sample of 7 tubes 0.33 = UCL 0.17 = R
0.01 = LCL
0.17 = R
| | | | | | | | | | | |
Sample number
The variation of process is in control with 99.73% confidence.
6S–31

32. Mean and Range Charts
(a) The central tendency of process is in control, but its variation is not in control.
R-chart
(R-chart detects increase in dispersion)
UCL
LCL
x-chart
(x-chart does not detect dispersion)
UCL
LCL
6S–32

33. Mean and Range Charts
(b) The variation of process is in control, but its central tendency is not in control.
UCL
(R-chart does not detect changes in mean)
R-chart
LCL
x-chart
(x-chart detects shift in central tendency)
UCL
LCL
6S–33

34. R-Chart and X-Chart
Example S6.4: Seven random samples of four resistors each are taken to establish the quality standards. Develop the R-chart and the x-chart both with 3- control limits for the production process. Is the entire process under statistical control? Why or why not?
n = 4
D3 = 0, and D4 = 2.28
R = ( … + 4)/7 = 3.0
6S–34

35. R-Chart and X-Chart Control Chart for sample of 4 resistors 6.84 = UCL
0 = LCL
| | | | | | | | | | | |
Sample number
The variation of process is in control with 99.73% confidence.
6S–35

36. R-Chart and X-Chart n = 4, A2 = 0.73 R = (3 + 2 + … + 4)/7 = 3.0
6S–36

37. R-Chart and X-Charts Control Chart 101.98 = UCL 99.79 = Mean
97.6 = LCL
| | | | | | | | | | | |
Sample number
The central tendency of process is not in control with 99.73% confidence.
In conclusion, with 99.7% confidence, the entire resistor production process is not in control since its central tendency is out of control although its variation is under control.
6S–37

38. EX 1 in class
A part that connects two levels should have a distance between the two holes of 4”. It has been determined that x-bar chart and R-chart should be set up to determine if the process is in statistical control. The following ten samples of size four were collected. Calculate the control limits, plot the control charts, and determine if the process is in control
No. of Sample
Mean
Range 1
4.01
0.04 2
3.98
0.06 3
4.00
0.02 4
3.99
0.05 5 6
3.97 7
4.02 8 9 10
6S–38

39. R-Chart and X-Chart # of sample Readings of Resistance (ohms) 1 99 100
Example S6.5: Resistors for electronic circuits are manufactured at Omega Corporation in Denton, TX. The head of the firm’s Continuous Improvement Division is concerned about the product quality and sets up production line checks. She takes seven random samples of four resistors each to establish the quality standards. Develop the R-chart and the chart both with 3- control limits for the production process. Is the entire process under statistical control? Why or why not?
# of sample
Readings of Resistance (ohms) 1 99
100
102
101 2
103 3 98 4 5 6 95 97 96 7
6S–39

40. R-Chart and X-Chart D3 =0 D4 = 2.28 n=4 # of Sample 1 2 3 4 5 6 7
Sample range
Sample mean
100.5
101.5
100.0
99.5
99.0
97.0
101.0
D3 =0 D4 = 2.28
n=4
6.84 = UCL
variation of process is in control with 99.73% confidence.
3.0 = R
0 = LCL
| | | | | | | | | | | |
Sample number
6S–40

41. R-Chart and X-Chart A2 =0.73 n=4 X= (100.5 + … + 101.0)/7  99.8
# of Sample 1 2 3 4 5 6 7
Sample range
Sample mean
100.5
101.5
100.0
99.5
99.0
97.0
101.0
X= ( … )/7  99.8
A2 =0.73
n=4
102.0 = UCL
central tendency of process is not in control with 99.73% confidence.
99.8 = X
97.6 = LCL
Thus, entire process is not in control.
| | | | | | | | | | | |
Sample number
6S–41

42. EX 2 in class
A quality analyst wants to construct a sample mean chart for controlling a packaging process. Each day last week, he randomly selected four packages and weighed each. The data from that activity appears below. Set up control charts to determine if the process is in statistical control
Day
Package 1
Package 2
Package 3
Package 4
Monday 23 22 24
Tuesday 21 19
Wednesday 20
Thursday 18
Friday
6S–42

43. Statistical Process Control Chart (SPC)
Control Charts for Variable Data
Control Charts for Attribute Data
-charts (for controlling central tendency)
R-charts (for controlling variation)
p-charts (for controlling percent defective)
c-charts (for controlling number of defects)
Variable Data (continuous): quantifiable conditions along a scale, such as speed, length, density, etc.
Attribute Data (discrete): qualitative characteristic or condition, such as pass/fail, good/bad, go/no go.
6S–43

44. Control Charts for Attribute Data
Categorical variables
Good/bad, yes/no, acceptable/unacceptable
Measurement is typically counting defectives
Charts may measure
Percentage of defects (p-chart)
Number of defects (c-chart)
6S–44

45. P-Charts where p = mean percent defective overall the samples
z = number of standard deviations = 3
n = sample size
6S–45

46. P-Charts
Example S6.6: Data-entry clerks at ARCO key in thousands of insurance records each day. One hundred records entered by each clerk were carefully examined and the number of errors counted. Develop a p-chart with 3- control limits and determine if the process is in control.
Sample Number Percent Sample Number Percent
Number of Errors Defective Number of Errors Defective
Total = 80
6S–46

47. P-Charts n = 100 Because we cannot have a negative percent defective

48. P-Charts Possible assignable causes present
.11 –
.10 –
.09 –
.08 –
.07 –
.06 –
.05 –
.04 –
.03 –
.02 –
.01 –
.00 –
Sample number
Percent defective
UCL= 0.10
LCL= 0.00
p = 0.04
| | | | | | | | | |
Possible good assignable causes present
The process is not in control with 99.73% confidence.
6S–48

49. C-Charts
A c-chart is used when the quality cannot be measured as a percentage.
Number of car accidents per month at a particular intersection
Number of complaints the service center of a hotel receives per week
Number of scratches on a nameplate
Number of dimples found on a metal sheet
6S–49

50. C-Charts UCL = c + 3 c LCL = c - 3 c
where c = mean number defective overall the samples
6S–50

51. C-Charts UCL = c + 3 c = 6 + 3 6 = 13.35 LCL = c - 3 c = 6 - 3 6
Example S6.7: Over 9 weeks, Red Top Cab company received the following numbers of calls from irate passengers: 3, 0, 8, 9, 6, 7, 4, 9, 8, for a total of 54 complaints. Determine the 3-  control limits of a c-Chart. | 1 2 3 4 5 6 7 8 9
Week Number
Number of defect
14 –
12 –
10 –
8 –
6 –
4 –
2 –
0 –
c = 54 / 9 = 6 complaints /week
UCL = 13.35
LCL = 0
c = 6
UCL = c + 3 c =
= 13.35
LCL = c - 3 c =
= => 0
The process is in control with 99.73% confidence.
Because we cannot have the negative number of defective records
6S–51

52. Managing Quality Summary
Effective quality management is data driven
There are multiple tools to identify and prioritize process problems
There are multiple tools to identify the relationships between variables
6S–52