1. Statistical Process Control and Quality Management
Chapter 19

2. Learning Objectives
LO19-1 Explain the purpose of quality control in production and service operations.
LO19-2 Define the two sources of process variation and explain how they are used to monitor quality.
LO19-3 Explain the use of charts to investigate the sources of process variation.
LO19-4 Compute control limits for mean and range control charts for a variable measure of quality.
LO19-5 Evaluate control charts to determine if a process is out of control.
LO19-6 Compute control limits of control charts for an attribute measure of quality.
LO19-7 Explain the process of acceptance sampling.

3. Control Charts: Are useful tools for monitoring a process.
LO19-1 Explain the purpose of quality control in production and service operations.
Control Charts:
Are useful tools for monitoring a process.
Used to identify sources of variation in a process.
Common Cause
Special Cause
Used to identify when assignable causes of variation have entered the process.
Used to determine that the process being monitored is not in control.
Are analyzed to help determine the sources of variation, which can then be eliminated to bring the process back into control.

4. LO19-1
Six Sigma
Six Sigma is a typical program designed to improve quality and performance throughout a company.
It combines methodology, tools, software, and education to deliver a completely integrated approach to waste elimination and process capability improvement.
The approach requires defining the process function; identifying, collecting, and analyzing data; creating and consolidating information into useful knowledge; and the communication and application of such knowledge to reduce variation.
Six Sigma gets its name from the normal distribution. The term sigma means standard deviation, and “plus or minus” three standard deviations gives a total range of six standard deviations.
So Six Sigma means having no more than 3.4 defects per million opportunities in any process, product, or service.

5. LO19-2 Define the two sources of process variation and explain how they are used to monitor quality.
Causes of Variation
All manufacturing and service processes vary in their performance. The two sources of variation are:

6. LO19-3 Explain the use of charts to investigate the sources of process variation.
Diagnostic Charts
There are a variety of diagnostic techniques available to investigate quality problems.
Two of the more prominent of these techniques are Pareto charts and fishbone diagrams.

7. LO19-3
Pareto Charts
Pareto analysis is a technique for tallying the number and type of service or product defects and investigating the source of the defects. This information is summarized in a Pareto Chart.
The chart is named after a nineteenth-century Italian scientist, Vilfredo Pareto. Pareto’s Principle, often called the 80–20 rule, is that 80 percent variation is explained by 20 percent of the possible causes. In application, quality control efforts should focus on the 20 percent of the causes of the variation that causes poor quality.

8. Pareto Chart - Example LO19-3
The city manager of Grove City, Utah, is concerned with water usage in single family homes. To investigate, she selects a sample of 100 homes and determines the typical daily water usage for various purposes. The sample results are as follows.

9. LO19-3
Fishbone Diagrams
Another diagnostic chart is a cause-and-effect diagram or a fishbone diagram. It is called a cause-and-effect diagram to emphasize the relationship between an effect and a set of possible causes that produce the particular effect.
This diagram is useful to help organize ideas and to identify relationships. It is a tool that encourages open brainstorming for ideas. By identifying these relationships we can determine factors that are the cause of variability in our process.

10. Purpose and Types of Quality Control Charts
LO19-4 Compute control limits for mean and range control charts for a variable measure of quality.
Purpose and Types of Quality Control Charts
The purpose of quality-control charts is to graphically track process variation over time so that we can detect when an assignable cause enters the production system. As “assignable variation”, a manager then investigates and identifies cause and attempts to eliminate the source of the assignable variation.
Types of Quality Control Charts:
Control Charts for Attributes – involves “counting”
Control Charts for Variables – involves “measuring”

11. Mean and Range Chart for Variables
LO19-4
Mean and Range Chart for Variables
A mean or the X-bar chart is designed to monitor process variables such as weight, length, etc. The upper control limit (UCL) and the lower control limit (LCL) are obtained from the equation: A range chart shows the variation in the sample ranges.
Where:
n is the sample size
is the mean of the sample means
is the mean of the ranges
D3 and D4 values are found in Appendix B.10

12. Mean Chart for Variables - Example
LO19-4
Mean Chart for Variables - Example
Statistical Software, Inc., offers a toll-free number that customers can call with problems involving the use of their products from 7 A.M. until 11 P.M. daily. While it is not possible to answer all calls immediately, it is important customers do not wait too long for a person to come on the line. To understand its process, Statistical Software decides to develop a control chart describing the total time from when a call is received until the representative answers the call and resolves the issue raised by the caller. For the 16 hours of operation in one day, five calls were sampled each hour. This information is on the table, in minutes, until the issue was resolved.
Based on this information, develop a control chart for the mean duration of the call. Does there appear to be a trend in the calling times? Is there any period in which it appears that customers wait longer than others?

13. Constructing a Mean Chart
LO19-4
Constructing a Mean Chart .

14. Constructing a Range Chart - Example
LO19-4
Constructing a Range Chart - Example
Develop a control chart for the range. Does it appear that there is any time when there is too much variation in the operation?

15. LO19-4
Range Chart - Example

16. Mean and Range Charts - Minitab
LO19-4
Mean and Range Charts - Minitab

17. LO19-5 Evaluate control charts to determine if a process is out of control.
In-Control Situation

18. Mean Out-of-control, Range in-control
LO19-5
Mean Out-of-control, Range in-control .

19. Mean In-control, Range Out-of-control
LO19-5
Mean In-control, Range Out-of-control

20. Attribute Control Chart: The p-Chart
LO19-6 Compute control limits of control charts for an attribute measure of quality.
Attribute Control Chart: The p-Chart
The percent defective chart is also called a p-chart or the p-bar chart.
It graphically monitors a process by showing the proportion defective over time.

21. Attribute Control Chart: The p-Chart
LO19-6
Attribute Control Chart: The p-Chart

22. LO19-6
p-Chart Example
Jersey Glass Company, Inc., produces small hand mirrors. Each day, the quality assurance department (QA) monitors the quality of the mirrors twice during the day shift and twice during the evening shift. After each four-hour period, QA selects and carefully inspects a random sample of 50 mirrors, classifies each mirror as either acceptable or unacceptable and counts the number of mirrors in the sample that do not conform to quality specifications. Listed below is the result of these checks over the last 10 business days.
Construct a percent defective chart for this process. What are the upper and lower control limits? Interpret the results. Does it appear the process is out of control during the period?

23. Computing the Control Limits
LO19-6
Computing the Control Limits

24. LO19-6
p-Chart using Minitab

25. Attribute Control Chart : The c-Chart
LO19-6
Attribute Control Chart : The c-Chart
The c-chart or the c-bar chart is designed to monitor a process by counting the number of defects per unit. The UCL and LCL are found by:

26. LO19-6
c-Chart Example
The publisher of the Oak Harbor Daily Telegraph is concerned about the number of misspelled words in the daily newspaper. It does not print a paper on Saturday or Sunday. In an effort to control the problem and promote the need for correct spelling, a control chart will be used. The number of misspelled words found in the final edition of the paper for the last 10 days is: 5, 6, 3, 0, 4, 5, 1, 2, 7, and 4. Determine the appropriate control limits and interpret the chart. Were there any days during the period that the number of misspelled words was out of control?

27. LO19-6
c-Chart in Minitab

28. LO19-7 Explain the process of acceptance sampling.
Method of determining whether an incoming lot of a product meets specified standards.
Based on random sampling techniques.
A random sample of n units is obtained from the entire lot.
c is the maximum number of defective units that may be found in the sample for the lot to still be considered acceptable.

29. Acceptance Sampling Procedure
LO19-7
Acceptance Sampling Procedure
Accept shipment or reject shipment?
The usual procedure is to screen the quality of incoming parts by using a statistical sampling plan.
According to this plan, a sample of n units is randomly selected from a lot of N units (the population). This is called acceptance sampling. The inspection will determine the number of defects in the sample. This number is compared with a predetermined number called the critical number or the acceptance number. The acceptance number is usually designated c.
If the number of defects in the sample of size n is less than or equal to c, the lot is accepted.
If the number of defects exceeds c, the lot is rejected and returned to the supplier, or perhaps submitted to 100 percent inspection.

30. Consumer’s Risk vs. Producer’s Risk in Acceptance Sampling
LO19-7
Consumer’s Risk vs. Producer’s Risk in Acceptance Sampling
Type II Error
Type I Error

31. Operating Characteristic Curve
LO19-7
Operating Characteristic Curve
An OC curve, or, operating characteristic curve is developed using the binomial probability distribution in order to determine the probabilities of accepting lots of various quality level .

32. OC Curve - Computation Example
LO19-7
OC Curve - Computation Example
Sims Software purchases DVDs from DVD International. The DVDs are packaged in lots of 1,000 each. Todd Sims, president of Sims Software, has agreed to accept lots with 10 percent or fewer defective DVDs. Todd has directed his inspection department to select a random sample of 20 DVDs and examine them carefully. He will accept the lot if it has two or fewer defectives in the sample.
Develop an OC curve for this inspection plan. What is the probability of accepting a lot that is 10 percent defective?

33. OC Curve - Computation Example
LO19-7
OC Curve - Computation Example
This type of sampling is called attribute sampling because the sampled item, a DVD in this case, is classified as acceptable or unacceptable.
Let  represent the actual proportion defective in the population.
The lot is good if  ≤ .10.
The lot is bad if  > .10.
Let X be the number of defects in the sample. The decision rule is:
Accept the lot if X ≤ 2.
Reject the lot if X ≥ 3.

34. OC Curve - Computation Example
LO19-7
OC Curve - Computation Example
The binomial distribution is used to compute the various values on the OC curve. Recall that the binomial has four requirements:
1. There are only two possible outcomes. Here the DVD is either acceptable or unacceptable.
2. There is a fixed number of trials. In this instance the number of trials is the sample size of 20.
3. There is a constant probability of success. A success is finding a defective DVD. The probability of success is assumed to be .10.
4. The trials are independent. The probability of obtaining a defective DVD on the third one selected is not related to the likelihood of finding a defect on the fourth DVD selected.

35. OC Curve - Computation Example
LO19-7
OC Curve - Computation Example
The table shows six binomial distributions with pi equal to 0.05, 0.10, 0.15, 0.20, 0.25, and The number of trials is the same for all, 20.

36. OC Curve - Computation Example
LO19-7
OC Curve - Computation Example
To begin we determine the probability of accepting a lot that is 5 percent defective. This means that = .05, c = 2, and n = 20. From the Excel output, the likelihood of selecting a sample of 20 items from a shipment that contained 5 percent defective and finding exactly 0 defects is The likelihood of finding exactly 1 defect is .377, and finding 2 is Hence the likelihood of 2 or fewer defects is .924, found by This result is usually written in shorthand notation
P(x≤ 2 |  = .05 and n = 20) = = .924
The likelihood of accepting a lot that is actually 10 percent defective is .677.
P(x≤ 2 |  = .10 and n = 20) = = .677
The complete OC curve in the next slide shows the smoothed curve for all values between 0 and about 30 percent.

37. OC Curve - Computation Example
LO19-7
OC Curve - Computation Example