1. Statistical Process Control and Quality Management
Chapter 19
McGraw-Hill/Irwin
Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.

2. Learning Objectives
LO1 Explain the purpose of quality control in production and service operations.
LO2 Discuss the two causes of process variation.
LO3 Use a Pareto chart to identify sources of variation.
LO4 Construct and interpret a fishbone diagram.
LO5 Compare an attribute versus a variable measure of quality.
LO6 Compute upper and lower control limits for mean and range charts.
LO7 Compare in-control and out-of-control quality control charts.
LO8 Construct and interpret percent defective and a c-bar charts.
LO9 Explain the process of acceptance sampling.
LO10 Describe an operating characteristic curve for a sampling plan.
Through most of this text we presented many applications of hypothesis testing and confidence interval estimation. In this chapter we present another, somewhat different application of hypothesis testing and confidence interval estimation, called statistical process control or SPC.
Statistical process control is a collection of strategies, techniques, and other actions taken by an organization to ensure it is producing a quality product or providing a quality service. SPC begins at the product planning stage, when we specify the attributes of the product or service. It continues through the production stage. Each attribute throughout the process contributes into the overall quality of the product. To effectively use quality control, measurable attributes and specifications are developed against which the actual attributes of the product or service are compared.
In this chapter we’re going to study control charts and uses in process control and monitoring. We will study the different SPC tools the like the Pareto chart, fishbone diagram, mean and range charts, as well as percent defective and C bar charts. We will discuss acceptance sampling and understand operating characteristic curve for various sampling plans.
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3. Control Charts, Six-Sigma and Variation
LO2 Discuss the two causes of process variation.
Control Charts, Six-Sigma and Variation
Statistical Quality Control emphasizes in-process control with the objective of controlling the quality of a manufacturing process or service operation using sampling techniques.
Statistical sampling techniques are used to aid in the manufacturing of a product to specifications rather than attempt to inspect quality into the product after it is manufactured.
Control Charts are useful for monitoring a process.
SIX SIGMA
Six Sigma is a typical program designed to improve quality and performance throughout the 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.
CAUSES OF VARIATION
All parts produced by a manufacturing process contain variation. The two sources of variation are:
Chance Variation is random in nature and cannot be entirely eliminated unless there is a major change in the techniques, technologies, methods, equipment, or materials used in the process.
Assignable Variation is nonrandom in nature and can be reduced or eliminated by investigating the problem and finding the cause.
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4. LO3 Use a Pareto chart to identify sources of 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.
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5. Pareto Charts LO3 19-5 EXAMPLE
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.
Pareto analysis is a technique for tallying the number and type of defects that happen within a product or service.
The chart is named after a nineteenth-century Italian scientist, Vilfredo Pareto. He noted that most of the “activity” in a process is caused by relatively few of the “factors.”
Pareto’s concept, often called the 80–20 rule, is that 80 percent of the activity is caused by 20 percent of the factors. By concentrating on 20 percent of the factors, managers can attack 80 percent of the problem.
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6. Fishbone Diagrams LO4 Construct and interpret a fishbone diagram. 19-6
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.
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7. Mean and Range Chart for Variables
LO6 Compute upper and lower control limits for mean and range charts.
Mean and Range Chart for Variables
CONTROL CHARTS
The purpose of quality-control charts is to portray graphically when an assignable cause enters the production system so that it can be identified and corrected.
This is accomplished by periodically selecting a random sample from the current production.
A mean or the x-bar chart is designed to control 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.8
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8. Mean Chart for Variables - Example
LO6
Mean Chart for Variables - Example
Statistical Software, Inc., offers a toll-free number where customers can call with problems involving the use of their products from 7 A.M. until 11 P.M. daily. It is impossible to have every call answered immediately by a technical representative, but it is important customers do not wait too long for a person to come on the line. Customers become upset when they hear the message “Your call is important to us. The next available representative will be with you shortly” too many times. 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. Yesterday, for the 16 hours of operation, 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?
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9. Mean Chart for Variables - Example
LO6
Mean Chart for Variables - Example
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10. Range Chart - Example LO6 19-10 EXAMPLE
The length of time customers of Statistical Software, Inc., waited from the time their call was answered until a technical representative answered their question or solved their problem is recorded in Table 19–1.
Develop a control chart for the range. Does it appear that there is any time when there is too much variation in the operation?
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11. Process In-Control?
LO7 Compare in-control and out-of-control quality control charts.
NO. Mean is OK but not range
YES. Both mean and range charts are in control
NO. Range is OK but not Mean
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12. Attribute Control Chart – The p-Chart
LO8 Construct and interpret percent defective and c-bar charts.
Attribute Control Chart – The p-Chart
EXAMPLE
Jersey Glass Company, Inc., produces small hand mirrors. Jersey Glass runs a day and evening shift each weekday. 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. Each mirror is classified as either acceptable or unacceptable. Finally QA counts the number of mirrors in the sample that do not conform to quality specifications. List 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?
The percent defective chart is also called a p-chart or the p-bar chart. It graphically shows the proportion of the production that is not acceptable.
The proportion of defectives is found by:
The UCL and LCL are computed as the mean percent defective plus or minus 3 times the standard error of the percents:
__ _______ _________ _____ __ ____ ______ _ _ _____ __ ___ _ ___ _____ _ ___________ _____ ___ __________ __ ___ __________ ____ __ ___ __________
__ __________ __ __________ __ _____ __
__ ___ ___ ________ __ ___ ____ _______ _________ ____ __ _____ _____ ___ ________ _____ __ ___ ________
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13. Computing the Control Limits
LO8
Computing the Control Limits
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14. Attribute Control Chart : The c-Chart
LO8
Attribute Control Chart : The c-Chart
The c-chart or the c-bar chart is designed to control the number of defects per unit. The UCL and LCL are found by:
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?
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15. Acceptance Sampling LO9 Explain the process of acceptance sampling.
Acceptance sampling is a method of determining whether an incoming lot of a product meets specified standards.
It is 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.
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 the lots 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.
Type II Error
Type I Error
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