McGraw-Hill/Irwin Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.

Statistical Process Control and Quality Management

Chapter 19

19-2

GOALS

1. Discuss the role of quality control in production and service operations.

2. Define and understand the terms chance cause, assignable cause, in control, out of control, attribute, and variable.

3. Construct and interpret a Pareto chart.4. Construct and interpret a fishbone diagram.5. Construct and interpret mean and range charts.6. Construct and interpret percent defective and a c-bar charts.7. Discuss acceptance sampling.8. Construct an operating characteristic curve for various

sampling plans.

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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 VARIATIONAll 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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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.

19-5

Pareto Charts

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.

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.

19-6

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.

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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.

Mean and Range Chart for Variables

RAXLCLandRAXUCL 22

R R 34 DLCLandDUCL

Where: n is the sample size is the mean of the sample means is the mean of the rangesD3 and D4 values are found in Appendix B.8RX

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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?

Mean Chart for Variables - Example

413.916

60.150X 375.6

16

102R

19-9

13.091

37565774139

2

).)((..

RAXUCL

5.735

)375.6)(577(.413.9 2

RAXLCL

Mean Chart for Variables - Example

19-10

13.483

)375.6(115.2

4

RDUCL

Range Chart - Example

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?

375.616

102R

0

)375.6(0 3

RDLCL

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Process In-Control?

YES. Both mean and range charts are in controlNO. Mean is OK but not range

NO. Range is OK but not Mean

19-12

Attribute Control Chart – The p-Chart

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:

samples ofNumber

Defectives ofNumber Totalp

n

pppLCLandUCL

)1(3

EXAMPLEJersey 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?

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Computing the Control Limits

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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:

UCL and LCL c c 3

Attribute Control Chart : The c-Chart

EXAMPLEThe 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? 0 07.277.57.3

47.977.57.3

7.337.3

7.310

37

LCL

UCL

LCLandUCL

c

19-15

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 I Error

Type II Error