1. Statistical Quality Control
Chapter 6
OPS 370

2. Statistical Process/Quality Control at Honda

3. Two Scoops of Raisins in a Box of Kellogg’s Raisin Bran

4. Statistical Quality Control
Ask the students to give examples where they experienced “bad quality” products or services.
For each example, illustrate how quality could be quantified and measured.

5. Illustrations 1. BASF – catalytic cores for pollution control
2. Milliken – industrial fabrics
3. Thermalex – thermal tubing
4. Land’s End – customer service, order fulfillment
5. Hospital pharmacy

6. SQC Categories 1. Statistical Process Control (SPC)
2. Acceptance Sampling

7. Types of Quality Data

8. Variation

9. Sources of Variation

10. Cost of Variation

11. Taguchi Loss Function

12. Taguchi Loss Function

13. SPC Methods-Control Charts

14. Control Charts

15. Developing a Control Chart

16. A Process is “In Control” if
No sample points are outside limits
Most sample points are near the process average
About an equal number of sample points are above and below the average
Sample points appear to be randomly distributed

17. Control Charts for Attributes

18. Control Charts for Attributes

19. Control Chart Z-Value

20. P Chart Calculations

21. P-Chart Example
A Production manager for a tire company has inspected the number of defective tires in five random samples with 20 tires in each sample. The table shows the number of defective tires in each sample of 20 tires. Calculate the proportion defective for each sample, the center line, and control limits using z = 3.00.
Sample
Number of Defective Tires
Number of Tires in each Sample
Proportion Defective 1 3 20 2 4 5
Total 9
100
Calculate the proportion for each sample.

22. P-Chart Example, cont. Have students do the calculations
Then illustrate on paper

23. C-Chart Calculations

24. C-Chart Example
Week
Number of Complaints 1 3 2 4 5 6 7 8 9 10
Total 22
The number of weekly customer complaints are monitored in a large hotel using a c-chart. Develop three sigma control limits using the data table below.

25. C-Chart Example, cont. Have students do the calculations
Then illustrate on paper

26. Control Charts for Variables
1. Control chart for variables are used to monitor characteristics that can be measured, such as length, weight, diameter, time
2. X-bar Chart: Mean
A. Plots sample averages
B. Measures central tendency (location) of the process
3. R Chart: Range
A. Plots sample ranges
B. Measures dispersion (variation) of the process
4. MUST use BOTH charts together to effectively monitor and control variable quality charateristics

27. R-Chart Calculations A2 D3 D4 2 1.88 0.00 3.27 3 1.02 2.57 4 0.73 2.28
Factor for x-Chart A2 D3 D4 2
1.88
0.00
3.27 3
1.02
2.57 4
0.73
2.28 5
0.58
2.11 6
0.48
2.00 7
0.42
0.08
1.92 8
0.37
0.14
1.86 9
0.34
0.18
1.82 10
0.31
0.22
1.78 11
0.29
0.26
1.74 12
0.27
0.28
1.72 13
0.25
1.69 14
0.24
0.33
1.67 15
0.35
1.65
Factors for R-Chart
Sample Size
(n)

28. Example for Variable Control Charts
A quality control inspector at the Cocoa Fizz soft drink company has taken three samples with four observations each of the volume of bottles filled (ounces). Use the data below to develop R and X-bar control charts with three sigma control limits for the 16 oz. bottling operation.
Observation
Sample 1
Sample 2
Sample 3 x1
15.8
16.1
16.0 x2
15.9 x3 x4

29. R-Chart Example Observation Sample 1 Sample 2 Sample 3 x1 15.8 16.1
16.0 x2
15.9 x3 x4
Range
Have the students work out the solution manually on paper and then review it.

30. X-bar Chart Calculations
Factor for x-Chart A2 D3 D4 2
1.88
0.00
3.27 3
1.02
2.57 4
0.73
2.28 5
0.58
2.11 6
0.48
2.00 7
0.42
0.08
1.92 8
0.37
0.14
1.86 9
0.34
0.18
1.82 10
0.31
0.22
1.78 11
0.29
0.26
1.74 12
0.27
0.28
1.72 13
0.25
1.69 14
0.24
0.33
1.67 15
0.35
1.65
Factors for R-Chart
Sample Size
(n)

31. X-bar Chart Example Observation Sample 1 Sample 2 Sample 3 x1 15.8
16.1
16.0 x2
15.9 x3 x4
Sample Mean
Have the students work out the solution manually on paper and then go over it.

32. Interpreting Control Charts
A process is “in control” if all of the following conditions are met.
No sample points are outside limits
Most sample points are near the process average
About an equal number of sample points are above and below the average
Sample points appear to be randomly distributed

33. Control Chart Examples1 2

34. Limits Based on Out of Control Data3 4

35. Process Capability

36. Process Capability

37. Individual Measurements
Specification Limits
Individual Measurements
Control Limits
Sample Means

38. Process Capability Design Specifications Process Design Specifications

39. Process Capability Design Specifications Process Design Specifications

40. Computing Process Capability

41. Cp and Cpk Example
Specifications for a soda bottling process call for a target value of 16.0 oz. with a tolerance of ± 0.2 oz.
Process performance measures are
Mean: µ = 15.9 oz.
Std. Deviation: σ = 0.05 oz.
Compute the Cp value for this bottling process and indicate whether or not it is capable based on the Cp value.
Compute the Cpk value for this bottling process and indicate whether or not it is capable based on the Cpk value.

42. Example Calculations
Have the students compute these numbers, then review and discuss.