1. An Integrated Goods and Services Approach
OPERATIONS MANAGEMENT
An Integrated Goods and Services Approach
Statistical Process Control
CHAPTER 16
JAMES R. EVANS
AND
DAVID A. COLLIER
Operations Management/Ch. 16 Statistical Process Control
©2007 Thomson South-Western

2. Chapter 16 Learning Objectives
To understand the elements of good control systems, variation in processes, the difference between common and special causes of variation, quality control metrics, and the design of quality control systems.
To understand variation in manufacturing and service processes and the role of control charts and statistical process control methods in helping managers control variation.
To be able to construct and interpret simple control charts for both continuous and discrete data.
To understand the concept of process capability and be able to analyze process capability data, compute process capability indexes, and interpret the results.

3. Chapter 16 Statistical Process Control
Quality Control Systems
Quality control is to ensure that a good
or service conforms to specifications and
meets customer requirements by
monitoring and measuring processes and
making any necessary adjustments to
maintain a specified level of performance.

4. Chapter 16 Statistical Process Control
Quality Control Systems
Quality Control Systems have three components
A performance standard or goal,
A means of measuring actual performance,
Comparison of actual performance with the standard to form the basis for corrective action.

5. Exhibit 16.1
Economic Implications of the 1:10:100 Rule
1:10:100: Rule: if a defect or service error is identified and corrected in the design stage, it might cost $1 to fix. If it is detected during the production process, it might cost $10 to fix. However, if the defect is not discovered until it reaches the customer, it might cost $100 to correct.

6. Exhibit 16.1
Economic Implications of the 1:10:100 Rule

7. Chapter 16 Statistical Process Control
Quality at the Source: the people responsible for the work control the quality of their processes by identifying and correcting any defects or errors when they first are recognized or occur.

8. Chapter 16 Statistical Process Control
Quality Control Practices in Manufacturing
Acceptance Sampling: the process of making decisions on whether to accept or reject a group of items purchased from some external supplier based on specified quality characteristics.
Producer’s Risk: the probability of rejecting a lot of good quality.
Customer’s Risk: the probability of accepting a lot of poor quality.

9. Chapter 16 Statistical Process Control
Quality Control Practices in Manufacturing
Incoming control and acceptance sampling: ensure conformance to requirements before value-adding operations begin.
In-process control: ensure that defective outputs do not leave the process an prevent defects in the first place.
Finished goods control: verifying that product meets customer requirements.

10. Chapter 16 Statistical Process Control
Quality Control Practices in Services
Prevent sources of errors in the first place by using poka-yoke approaches.
Customer satisfaction measurement with actionable results (responses that are tied directly to key business processes).
Many quality control tools and practices apply to both goods and services.

11. Chapter 16 Statistical Process Control
Quality Control Practices in Services
However, the seven differences between goods and services described in Chapter 1 do create major differences in how to apply and use quality concepts and tools such as:
Customers participate in creating the service, and therefore, introduce more uncertainty into the service process than in goods-producing processes.
Customers have a personality that can be difficult for the service-provider to accommodate while physical goods have no personality.

12. Exhibit 16.3
Skilled Care’s Customer Grade Card Scoring System – Benchmarked from Baldrige Winner
Skilled Care Pharmacy, located in Mason, Ohio, is a $25 million dollar privately held regional provider of pharmaceutical products delivered within the long term care, assisted living, hospice, and group home environments.
The Grade Card uses a school-like A-B-C-D scoring system shown in Exhibit The scores from the four questions covering Quality, Responsiveness, Delivery, and Communication are converted from letters to numbers and averaged.
“Delivery” performance was dramatically improved.

13. Chapter 16 Statistical Process Control
Foundations of Statistical Process Control
Statistical process control (SPC): a methodology for monitoring quality of manufacturing and service delivery processes to help identify and eliminate unwanted causes of variation.

14. Chapter 16 Statistical Process Control
Foundations of Statistical Process Control
Common cause variation: result of complex interactions of variations in materials, tools, machines, information, workers, and the environment.
Common cause variation accounts for 80 to 95 percent of observed variation.
Only management has the power to change systems and infrastructure that cause common cause variation.

15. Chapter 16 Statistical Process Control
Foundations of Statistical Process Control
Special (assignable) cause variation: arises from external sources that are not inherent in the process, appear sporadically, and disrupt the random pattern of common causes.
Special cause variation accounts for 15 to 20 percent of observed variation.
Front line employees and supervisors have the power to identify and solve specific causes of variation.

16. Chapter 16 Statistical Process Control
Foundations of Statistical Process Control
Stable system: a system governed only by common causes.
In control: if no special causes affect the output of the process.
Out of control: when special causes are present in the process.

17. Chapter 16 Statistical Process Control
Foundations of Statistical Process Control
Discrete metric: one that is calculated from data that are counted (often called attribute type data).
Continuous metric: one that is calculate from data that are measured as the degree of conformance on a continuous scale of measurement (often called variable type data).

18. Exhibit 16.4
Examples of Service Quality Metrics

19. Chapter 16 Statistical Process Control
Foundations of Statistical Process Control
SPC uses control charts: a run chart to which two horizontal lines, called control limits, are added; the upper control limit (UCL) and lower control limit (LCL).
Control limits are chosen statistically to provide a high probability (generally greater that 0.99) that points will fall between these limits if the process is in control.

20. Chapter 16 Statistical Process Control
Foundations of Statistical Process Control
As a problem-solving tool, control charts allow employees to identify quality problems as they occur. Of course, control charts alone cannot determine the source of the problem.
The general structure of a control chart is shown in Exhibit 16.5 (next slide).

21. Exhibit 16.5
Structure of a Control Chart

22. Chapter 16 Statistical Process Control
DOW Chemical Company’s Use of SPC and Control Charts
Earliest successful applications of SQC (statistical quality control) techniques were in the chemical-process areas.
Exhibit 16.6 shows before- and after- X-bar charts on dryer analysis after SQC and retraining were implemented.
Use of control charts in the control room made operators realize that their attempts to fine-tune the process introduced unwanted variation; see before and after range charts in Exhibit 16.7.
Dow Chemical exerted tighter control of chemical neutralization operation with control charts, as shown in Exhibit 16.8.

23. Exhibit 16.6
Before-and-After x-Charts of Dow Dryer Analysis

24. Exhibit 7.7
Exhibit 16.7
Before-and-After R-Charts on Dow Dryer Analysis

25. Exhibit 16.8
x- and R-Charts on Dow’s Neutralizer Excess Alkalinity Before and After SQC (OM: Spotlight)

26. Chapter 16 Statistical Process Control
SPC General Methodology
Steps 1 through 4 focus on setting up an initial
chart; in step 5, the charts are used for
ongoing monitoring; and finally, in step 6, the
data are used for process capability analysis.
1. Preparation
a. Choose the metric to be monitored.
b. Determine the basis, size, and frequency of sampling.
c. Set up the control chart.

27. Chapter 16 Statistical Process Control
SPC General Methodology
2. Data collection
a. Record the data.
b. Calculate relevant statistics: averages, ranges, proportions, and so on.
c. Plot the statistics on the chart.
3. Determination of trial control limits
a. Draw the center line (process average) on the chart.
b. Compute the upper and lower control limits.

28. Chapter 16 Statistical Process Control
SPC General Methodology
4. Analysis and interpretation
a. Investigate the chart for lack of control (sometimes called root cause analysis).
b. Eliminate out-of-control points.
c. Recompute control limits if necessary.
5. Use as a problem-solving tool
a. Continue data collection and plotting.
b. Identify out-of-control situations and take corrective action.
6. Determination of process capability using the control chart data

29. Chapter 16 Constructing X-bar and R-Charts

30. Chapter 16 Statistical Process Control
Goodman Tire and Rubber Company SPC Example
Goodman Tire periodically tests its tires for tread wear under simulated road conditions using x-bar and R-charts.
Company collects twenty samples, each containing three radial tires from different shifts and several days of operations (see Exhibit 16.9 for data).
X-bar Control Limits:
UCL = (10.8) = 42.9
LCL = – 1.02(10.8) = 20.8

31. Exhibit 16.9
Excel Template for Goodman Tire x- and R-Charts

32. Exhibit 16.10
R-Chart for Goodman Tire Example

33. Exhibit 16.11
x-Chart for Goodman Tire Example

34. Chapter 16 Statistical Process Control
Interpreting Patterns in Control Charts
A process is said to be “in control” when it has the
following characteristics:
No points are outside the control limits – the traditional and most popular SPC chart guideline,
The number of points above and below the center line is about the same,
The points seem to fall randomly above and below the center line,
Most points, but not all, are near the center line, and only a few are close to the control limits.

35. Exhibit 16.12
Samples in a Controlled Process from a Normal Distribution

36. Chapter 16 Statistical Process Control
Interpreting Patterns in Control Charts
A more in-depth understanding of SPC charts includes
evaluating the “patterns in the sample data” using guidelines
such as:
Eight points in a row above or below the center line
10 of 11 consecutive points above or below the center line
12 of 14 consecutive points above or below the center line
Two of three consecutive points in the outer one-third region between the center line and one of the control limits
Four of five consecutive points in the outer two-thirds region between the center line and one of the control limits.

37. Exhibit 16.13
Illustration of Some Rules for Identifying Out-of-Control Conditions

38. Chapter 16 Constructing p-charts

39. Exhibit 16.14
Data and Calculations for p-Chart Example

40. p-Chart for ZIP Code Reader Example with Constant Sample Size
Exhibit 16.15

41. Exhibit 16.16
Data Calculations for Variable Sample Size Example

42. Exhibit 16.17
p-Chart for Variable Sample Size Example

43. Exhibit 16.18
p-Chart Using Average Sample Size

44. Chapter 16 Constructing c- and u-charts
Where p-chart monitors the proportion of nonconforming items, a c-chart or a u-chart monitor the “number of nonconformances” per unit (i.e., a count of the number of defects, errors, failures, etc.)
Example: one customer’s purchase order may have several errors, such as wrong items, order quantity, or wrong price.

45. Exhibit 16.24
Choosing the Right Control Chart

46. Chapter 16 Constructing c- and u-charts
These charts are used extensively in service organizations.
To use a c-chart the size of the sampling unit or the number of opportunities for errors remains constant.
To use a u-chart the size of the sampling unit or the number of opportunities for errors may vary.

47. Chapter 16 Constructing c- and u-charts
Example c-chart applications: a fender or windshield on a certain automobile model, ceramic coffee cups all of same size and shape, etc.
Example u-chart applications: a carpet, paper or textile production run, packing slips for different order mixes/sizes, etc.

48. Exhibit 16.24
Choosing the Right Control Chart

49. Exhibit 16.19
Machine Failure Data for c-Chart
The number of machine failures over a 25-day period.

50. Exhibit 16.20
c-Chart for Machine Failures

51. Exhibit 16.21
Data and Calculations for u-Chart Example
The number of defects (wrong purchase order numbers, wrong quantities, etc.) in packing slips each day.

52. Exhibit 16.22
Example of u-Chart

53. Summary of Control Chart Formulas
Exhibit 16.23
Summary of Control Chart Formulas
The chart below summarizes the formulas needed for various types of control charts discussed in this chapter. Exhibit provides a simple set of guidelines for choosing the proper chart.

54. Exhibit 16.24
Choosing the Right Control Chart

55. Chapter 16 Control Chart Design
Sample size: small sample size keeps costs lower; however large sample sizes provide greater degrees of statistical accuracy in eliminating the true state of control.
Sampling frequency: samples should be close enough to provide an opportunity to detect changes in process characteristics as soon as possible and reduce the chances of producing a large amount of nonconforming output.

56. Chapter 16 Control Chart Design
Tightness of control limits: standard control limits are based on 3 standard deviation ranges about the mean, providing a low risk for Type I error. The wider the control limits, the greater risk for a Type II error.

57. Chapter 16 Statistical Process Control
Other Practical Issues in SPC Implementation
SPC is a useful methodology for processes that operate at a low sigma level (less than or equal to three sigma).
However, when the rate of defects is extremely low, standard control limits are not so effective.
For processes with a high sigma level (greater than 3 sigma), few defectives will be discovered even with large sample sizes.

58. Chapter 16 Statistical Process Control
Process Capability
Process capability is the natural variation in a process that results from common causes.
Cp = (UTL – LTL)/6 s
where
UTL = upper tolerance limit
LTL = lower tolerance limit
s = standard deviation of the process (or an estimate based on the sample standard deviation, s)

59. Chapter 16 Statistical Process Control
Process Capability
Process capability is the natural variation in a process that results from common causes.
When Cp = 1, the natural variation is the same as the design tolerance as in Exhibit 16.27(b).
When Cp < 1, a significant percentage of output will not conform to the specifications as in Exhibit (a).

60. Exhibit 16.27
Process Capability Versus Design Specifications

61. Chapter 16 Statistical Process Control
Process Capability
When Cp > 1, indicates good capability as in Exhibit (c); in fact, many firms require Cp values of 1.66 or greater from their suppliers, which equates to a tolerance range of about 10 standard deviations.
The value of Cp does not depend on the mean of the process; thus, a process may be off-center such as in Exhibit 16.27(d) and still show an acceptable value of Cp.

62. Exhibit 16.27
Process Capability Versus Design Specifications

63. Exhibit 16.26
Capability Versus Control (arrows indicate the direction of appropriate management action)

64. Chapter 16 Statistical Process Control
One-sided capability indices that consider off centering
Cpu = (UTL – û)/3s
Cpl = (û – LTL)/3s
Cpk = Min (Cpl, Cpu)
where
UTL = upper tolerance limit
LTL = lower tolerance limit
û = the mean performance of the process
s = standard deviation of the process (or an estimate based on the sample standard deviation, s)

65. Chapter 16 Solved Problem #1
A production process, sampled 30 times with a sample size of 8, yielded an overall mean of 28.5 and an average range of 1.6.
Construct R- and x-charts for this process.
From Appendix B with n = 8, we have A2 = .37, D3 = .14, and D4 = 1.86.
For the x-chart: UCL= (1.6) =
LCL= (1.6)=27.908
For the R-chart: UCL= 1.86(1.6) = 2.976
LCL=0.14(1.6)= 0.224

66. Chapter 16 Solved Problem #1
b. At a later stage, six samples produced these sample means: , 28.25, 29.13, 28.72, 28.9, Is the process in control?
The sample is above the UCL, signifying an out-of-control condition.
c. Do the following sequence of sample means indicate that the process is out of control: 28.3, 28.7, 28.1, 28.9, 28.01, 29.01? Why or why not?
All points are within the control limits, and there do not appear to be any shifts or trends evident in the new data.

67. Chapter 16 Solved Problem #2
Over several weeks, 20 samples of 50 packages of synthetic-gut tennis strings were tested for breaking strength; 38 packages failed to conform to the manufacturer’s specifications. Compute control limits for a p-chart.
Solution
p = 38/1000 = and the standard deviation is (0.038)(0.962)/50 = 0.027
Control limits: UCL = (0.27) =
LCL (.027) = so set LCL = 0.

68. Chapter 16 Solved Problem #3
A controlled process shows an overall mean of 2.50 and
an average range of Samples of size 4 were used
to construct the control charts.
Part A: What is the process capability?
From Appendix B, d2 = 2.059, s = R/d2 = 0.42/2.059 = 0.20.
Thus, the process capability is 2.50  3(.020), or 1.90 to 3.10.
Part B: If specifications are 2.60 ± 0.25, how well can
This process meet them?
Because the specification range is 2.35 to 2.85 with a target of
2.60, we may conclude that the observed natural variation
exceeds the specifications by a large amount. In addition, the
process is off-center (see Exhibit 16.29).

69. Exhibit 16.29
Comparison of Observed Variation and Design Specifications for Solved Problem # 3