Adeyl Khan, Faculty, BBA, NSU
Chapter 10Quality Control
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Phases of Quality Assurance
10-2Figure 10.1
Acceptancesampling
Processcontrol
Continuousimprovement
Inspection of lotsbefore/afterproduction
Inspection andcorrective
action duringproduction
Quality builtinto theprocess
The leastprogressive
The mostprogressive
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Inspection
How Much/How OftenWhere/When Centralized vs. On-site
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Inputs Transformation Outputs
Acceptancesampling
Processcontrol
Acceptancesampling
Figure 10.2
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Inspection Costs
10-4
Co
st
OptimalAmount of Inspection
Cost of inspection
Cost of passingdefectives
Total Cost
Figure 10.3
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Where to Inspect in the Process
Raw materials and purchased partsFinished productsBefore a costly operationBefore an irreversible processBefore a covering process
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Examples of Inspection PointsType ofbusiness
Inspectionpoints
Characteristics
Fast Food CashierCounter areaEating areaBuildingKitchen
AccuracyAppearance, productivityCleanlinessAppearanceHealth regulations
Hotel/motel
Parking lotAccountingBuildingMain desk
Safe, well lightedAccuracy, timelinessAppearance, safetyWaiting times
Supermarket
CashiersDeliveries
Accuracy, courtesyQuality, quantity
10-6Table 10.1
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Statistical Control
Statistical Process Control: Statistical evaluation of the output of a process during production The essence of statistical process control is to assure that the output of a process is random so that future output will be random.
Quality of Conformance :A product or service conforms to specifications
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Control Chart
10-8
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
UCL
LCL
Sample number
Mean
Out ofcontrol
Normal variationdue to chance
Abnormal variationdue to assignable sources
Abnormal variationdue to assignable sources
Figure 10.4
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Control ChartControl Chart
Purpose: to monitor process output to see if it is random
A time ordered plot representative sample statistics obtained from an on going process (e.g. sample means)
Upper and lower control limits define the range of acceptable variation
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• Define• Measure• Compare• Evaluate• Correct• Monitor results
SPC (The Process)
• Random variation• Natural variations in the output of a process, created by countless minor factors
• Assignable variation• A variation whose source can be identified
Variations and Control
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Normal Distribution
10-10
Mean
95.44%
99.74%
Standard deviation
Figure 10.6
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Control Limits: Sampling Distribution & Process Distribution
10-11
Samplingdistribution
Processdistribution
Mean
Lowercontrol
limit
Uppercontrol
limit
Figure 10.7
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SPC Errors
Type I error Concluding a process is not in control when it actually is.
Type II error Concluding a process is in control when it is not.
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In control Out of control
In control No Error Type I error(producers risk)
Out of control Type II Error(consumers risk)
No error
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Type I Error
10-13
Mean
LCL UCL
/2 /2
Probabilityof Type I error
Figure 10.8
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Observations from Sample Distribution
10-14
Sample number
UCL
LCL
1 2 3 4
Figure 10.9
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Control Charts for Variables
10-15
Variables generate data that are measured.Image: http://www.asprova.jp/mrp/glossary/en/cat254/x-r-1.html
Mean control charts
• Used to monitor the central tendency of a process.
• X bar charts
Range control charts
• Used to monitor the process dispersion
• R charts
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Mean and Range Charts
10-16Figure 10.10A
UCL
LCL
UCL
LCL
R-chart
x-Chart Detects shift
Does notdetect shift
(process mean is shifting upward)
SamplingDistribution
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Mean and Range Charts
10-17
x-Chart
UCL
Does notreveal increase
UCL
LCL
LCL
R-chart Reveals increase
Figure 10.10B
(process variability is increasing)SamplingDistribution
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p chartUsed to monitor the proportion of
defectives in a process When observations can be placed into two
categories. Good or bad Pass or fail Operate or don’t operate
When the data consists of multiple samples of several observations each
10-18
Control Chart for AttributesAttributes generate data that are counted
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c Chart
Used to monitor the number of defects per unitAdvantages
Use only when the number of occurrences per unit of measure can be counted; non-occurrences cannot be counted. Scratches, chips, dents, or errors per item Cracks or faults per unit of distance Breaks or Tears per unit of area Bacteria or pollutants per unit of volume Calls, complaints, failures per unit of time
10-19
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Use of Control Charts
At what point in the process to use control chartsWhat size samples to takeWhat type of control chart to use
Variables Attributes
10-20
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Run Tests
Run test – a test for randomnessAny sort of pattern in the data would suggest a non-random processAll points are within the control limits - the process may not be random
10-21
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Nonrandom Patterns in Control charts
TrendCyclesBiasMean shiftToo much dispersion
10-22
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Counting Runs
10-23
Counting Above/Below Median Runs (7 runs)
Counting Up/Down Runs (8 runs)
U U D U D U D U U D
B A A B A B B B A A B
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NonRandom Variation
Managers should have response plans to investigate causeMay be false alarm (Type I error)May be assignable variation
10-24
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Process CapabilityTolerances or specifications
Range of acceptable values established by engineering design or customer requirements
Process variability Natural variability in a process
Process capability Process variability relative to specification
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Process Capability
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LowerSpecification
UpperSpecification
A. Process variability matches specifications
LowerSpecification
UpperSpecification
B. Process variability well within specifications
LowerSpecification
UpperSpecification
C. Process variability exceeds specifications
Figure 10.15
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Process Capability Ratio
3
X-UTLor
3
LTLXmin=C pk
10-27
Process capability ratio, Cp = specification widthprocess width
Upper specification – lower specification6
Cp =
If the process is centered use Cp
If the process is not centered use Cpk
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Limitations of Capability Indexes
Process may not be stableProcess output may not be normally distributedProcess not centered but Cp is used
10-28
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Example 8
MachineStandard Deviation
Machine Capability Cp
A 0.13 0.78 0.80/0.78 = 1.03
B 0.08 0.48 0.80/0.48 = 1.67
C 0.16 0.96 0.80/0.96 = 0.83
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Cp > 1.33 is desirableCp = 1.00 process is barely capableCp < 1.00 process is not capable
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3 Sigma and 6 Sigma Quality
10-30
Processmean
Lowerspecification
Upperspecification
1350 ppm 1350 ppm
1.7 ppm 1.7 ppm
+/- 3 Sigma
+/- 6 Sigma
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Improving Process Capability
SimplifyStandardizeMistake-proofUpgrade equipmentAutomate
10-31
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Taguchi Loss Function
10-32
Cost
TargetLowerspec
Upperspec
Traditionalcost function
Taguchicost function
Figure 10.17
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Learning Objectives
List and briefly explain the elements of the control process. Explain how control charts are used to monitor a process, and the concepts that underlie their use. Use and interpret control charts. Use run tests to check for nonrandomness in process output. Assess process capability.
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