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17- 1
Chapter
Seventeen
McGraw-Hill/Irwin
© 2005 The McGraw-Hill Companies, Inc., All Rights Reserved.
17- 2
Chapter Seventeen
Statistical Quality
ControlGOALSWhen you have completed this chapter, you will be able to:ONEDiscuss the role of quality control in production and service operations.
TWO Define and understand the terms chance causes, assignable cause, in control and out of control, and variable.
THREEConstruct and interpret a Pareto chart.
FOURConstruct and interpret a Fishbone diagram.
Goals
17- 3
Chapter Seventeen continued
Statistical Quality ControlStatistical Quality ControlGOALSWhen you have completed this chapter, you will be able to:
FIVEConstruct and interpret a mean chart and a range chart.
SIX Construct and interpret a percent defective chart and a c-bar chart.
SEVENDiscuss acceptance sampling.
EIGHTConstruct an operating characteristic curve for various sampling plans.
Goals
17- 4
Statistical Process Control
A collection of strategies, techniques, and actions taken by an organization to ensure they
are producing a quality product or providing a quality service
Statistical Process Control Statistical Process Control
17- 5
Causes of Variation
Assignable VariationAssignable Variation is not random in nature and can be reduced or eliminated by investigating the problem and finding the cause.
There is variation in all parts produced by a manufacturing process.
Sources of VariationSources of Variation
Chance VariationChance Variation is random in nature and cannot be entirely eliminated.
17- 6
A technique for tallying the number and type of defects that happen within a product or service
Produce a vertical bar chart to display data.
Diagnostic Charts: Pareto Chart
Pareto AnalysisPareto Analysis
Steps in pareto analysisSteps in pareto analysis
Tally the type of defects.
Rank the defects in terms of frequency of occurrence from largest to smallest.
17- 7The accounting department of a large organization is spending significant time correcting travel vouchers submitted by employees from its numerous locations. Accounting staff noted that typical errors included wrong travel codes, incorrect employee identification numbers, inaccurate math, placing expenses on the wrong lines of the form, and failure to include proper documentation of expenses. Example 1
Department staff pulled a sample of 100 vouchers and tallied errors in the various categories.
17- 8
Error Type Number found
Wrong codes 60
Incorrect employee identification number
25
Inaccurate math 23
Inaccurate form placement
80
Incomplete documentation
42
Example 1 continued
17- 9
Error Type Number Percent
Wrong codes 60 26
Incorrect employee identification number
25 11
Inaccurate math 23 10
Inaccurate form placement
80 35
Incomplete documentation
42 18
Total 330 100
Example 1 Pareto table
17- 10
Pareto Chart for Voucher Errors
0
10
20
30
40
50
60
70
80
90
Inaccurate formplacement
Wrong codes Incompletedocumentation
Incorrect employeeid
Inaccurate math
Defect
Cou
nt
-
10
20
30
40
50
60
70
80
90
100
Cum
ulat
ive P
erce
ntEXCEL
Example 1 Pareto Chart
17- 11
Major causes listed on left-hand
side of diagram
Diagnostic Fishbone ChartDiagnostic Fishbone Chart
Also called cause-and-effect diagramcause-and-effect diagram
Helps organize ideas and identify
relationships
Identifies factors that
cause variability
Usually considers four problem areas: methods, materials,
equipment, and personnel
Problem or effect is head of fish
Fishbone chart
17- 12
Suppose a family restaurant, such as those found along an interstate highway, has recently been experiencing complaints from customers that the food being served is cold.
Example 2
In the following fishbone diagram, notice each of the subcauses are listed as assumptions. Each of these subcauses must be investigated to find the real problem regarding the cold food.
17- 13
Methods
Equipment Personnel
Materials
Complaintsof cold
food
Food placed underheating lights
Food heated tocorrect temperature Food at correct
starting tem perature
Packaging insulatesenough
Thermostatworking properly
Heating lights atcorrect height
Em ployees operatingequipm ent correctly
Servers deliverfood quickly
Example 2
17- 14
Purpose of Quality Control Charts
Portray graphically when an assignable cause enters the production system so that it can be identified and corrected
Monitoring accomplished by periodically selecting a random sample from the current production.
Purpose of Quality-Control Charts
17- 15
Types of Quality Control Charts-Variables
Xwhere is the mean of the sample means
Mean (Mean (xx-bar) Chart-bar) Chart
Designed to control variables such as weight or length
Limits How much variation can be expected for a given sample size
UCL: upper control limitLCL: lower control limit
U C L = X + 3 s
nL C L = X - 3
s
n
17- 16
UCL X A R and LCL X A R 2 2
is the mean of the sample rangesR
Xwhere is the mean of the sample means
Shortcut method for UCL and LCL
A2 is a constant used in computing the
upper and lower control limits, factors found in Appendix B.
Shortcut method
17- 17
Types of Quality Control Charts-Variables
UCL D R and LCL D R 4 3
Designed to show whether the overall range of measurements is in or out of control
Range ChartRange Chart
17- 18
Example 3
Hour #mm. #mm. #mm. #mm.
1 23 24 26 28
2 26 24 30 27
3 24 32 26 27
4 24 28 31 26
5 25 24 25 27
A manufacturer of chair wheels wishes to maintain the quality of the manufacturing process. Every 15 minutes, for a five hour period, a wheel is selected and the diameter measured. Given are the diameters (in mm.) of the wheels.
17- 19
EXAMPLE 3 continued
Hour X R1 25.3 52 26.8 63 27.3 84 27.3 75 25.3 3
Mean and Range Table
Grand Mean (25.25+26.75+...+25.25)
5 = 26.35
Mean Range
(5+6+...+3)
5
=5.8
UCL and LCL for MeanUCL=26.35+.729(5.8)=30.58LCL=26.35-.729(5.8)=22.12
UCL and LCL for the range diameter UCL=2.282(5.8) = 13.24
LCL=2.282(0) = 0
17- 20
UCL = 30.58
Mean Chart for Diameters
20
22
24
26
28
30
1 2 3 4 5Hours
Sa
mp
le M
ea
ns
Mean=26.35
LCL=22.12
UCL=30.58
Example 3 continued
No points outside limits: Process in control
17- 21
Range Charts for Diameters
0
2
4
6
8
10
12
14
1 2 3 4 5
Hour
Sa
mp
le R
an
ge
UCL = 13.24
Mean =5.8
LCL = 0
Example 3 continued
No points outside limits: Process in control
17- 22
Types of Quality Control Charts-Attributes
samplesofNumber
defectivespercenttheofSump
Percent Defective ChartPercent Defective Chart((pp-chart or -chart or pp-bar chart)-bar chart)
Graphically shows the proportion of the production that is not acceptable (p)
The UCLUCL and LCLLCL computed as the mean percent defective plus or minus 3 times the standard error of the percents
n
pppLCLandUCL
)1(3
17- 23
Example 4
.. ( . )
. .
08 308 1 08
40008 041
A manufacturer of running shoes wants to establish control limits for the percent defective. Ten samples of 400 shoes revealed the mean percent defective was 8.0% Where should the manufacturer set the control limits?
17- 24
Types of Quality Control Charts-Attributes
UCL and LCL c c 3
CC-chart (-chart (cc-bar chart) -bar chart)
UCL and LCL found byDesigned to monitor the number of defects per
unit
17- 25
Example 5
84.46.2
6.236.2
6.210/26
LCLandUCL
c
A manufacturer of computer circuit boards tested 10 after they were manufactured. The number of defects obtained per circuit board were: 5, 3, 4, 0, 2, 2, 1, 4, 3, and 2. Construct the appropriate control limits.
17- 26
c-bar chart for Number of Defects per Circuit Board
012345678
1 2 3 4 5 6 7 8 9 10
Sample Number
Sa
mp
le C
ou
nt
UCL = 7.44
c = 2.6
LCL = 0
Example 5
17- 27
Acceptance Sampling
c is the maximum number of defective units that may be found in the
sample for the lot to still be considered acceptable.
Acceptance samplingAcceptance sampling
A 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.
17- 28
736.387.349.)10.,10/1(
914.315.599.)05.,10/1(
nXP
nXP
Suppose a manufacturer and a supplier agree on a sampling plan with n=10 and acceptance number of 1. What is the probability of accepting a lot with 5% defective? A lot with 10% defective?
Uses binomial probability distribution to determine the probabilities of accepting lots of various quality levels
Operating Characteristic Curve
Short form OC
17- 29
OC Curve for Sampling Plan (n=20,c=2)
0
0.2
0.4
0.6
0.8
1
1.2
0 10 20 30 40
Incoming lot percent defective
Pro
ba
bili
ty o
f a
cc
ep
tin
g lo
tProbability of
accepting a lot that is 10%
defectiveis .677
Example 6