08 Acceptance Sampling Plans_ppm's
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Transcript of 08 Acceptance Sampling Plans_ppm's
Acceptance Sampling
Measure ControlImproveAnalyzeDefineRecognize
Six Sigma Six Sigma Green Belt TrainingGreen Belt Training
2007 American Society for Quality. All Rights Reserved.
2007 American Society for Quality. All Rights Reserved.
ControlImproveAnalyzeMeasureDefineRecognizePage 2 Creating Sampling Plans 2.1
What We Will Learn
1. What is Acceptance Sampling?
2. Definitions of Key Terms.
3. How to create variable data acceptance sampling plans.
4. How to apply variable data acceptance sampling plans.
5. How to create attribute data acceptance sampling plans.
6. How to apply attribute data acceptance sampling plans.
2007 American Society for Quality. All Rights Reserved.
ControlImproveAnalyzeMeasureDefineRecognizePage 3 Creating Sampling Plans 2.1
What is Acceptance Sampling?
The application of specific sampling plans to a designated lot or sequence of lots.
Provides accept/reject criteria for lots of material.
May be used in a program of acceptance control to achieve better quality at lower cost, improved control and increased productivity.
2007 American Society for Quality. All Rights Reserved.
ControlImproveAnalyzeMeasureDefineRecognizePage 4 Creating Sampling Plans 2.1
Definitions
Acceptable Quality Level (AQL)• The poorest level of quality
from a supplier's process that would be considered acceptable as a process average. You want to design a sampling plan that accepts a particular lot of product at the AQL most of the time.
Rejectable Quality Level (RQL)• The poorest level of quality that
the consumer is willing to tolerate in an independent lot. You want to design a sampling plan that rejects a particular lot of product at the RQL most of the time. Also commonly known as lot tolerance percent defective (LTPD) and limiting quality (LQ).
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Lot Percent Defective
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Operating Characteristic (OC) Curve
AQL
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Source: Minitab Help
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ControlImproveAnalyzeMeasureDefineRecognizePage 5 Creating Sampling Plans 2.1
Definitions, Continued
Average outgoing quality (AOQ) curve• Approximates the relationship between
the quality of the incoming material and the quality of the outgoing material, assuming that rejected lots will be 100% inspected and defective items will be reworked and inspected again (rectifying inspection).
Average total inspection (ATI) curve• Approximates the relationship between
the quality of the incoming material and the number of items that need to be inspected, assuming that rejected lots will be 100% inspected and defective items will be reworked and inspected again (rectifying inspection).
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Average Outgoing Quality (AOQ) Curve
Source: Minitab Help
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Lot Percent Defective
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Average Total Inspection (ATI) Curve
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ControlImproveAnalyzeMeasureDefineRecognizePage 6 Creating Sampling Plans 2.1
Acceptance Sampling Plans for Variable Data
We must know:1. Specification limits
2. Acceptable Quality Level
3. Reject Quality Level
Knowledge of the process standard deviation can dramatically reduce the size of the acceptance sample.
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ControlImproveAnalyzeMeasureDefineRecognizePage 7 Creating Sampling Plans 2.1
Example
Pressure Release Valves are specified as 75 ± 10 PSI.AQL = 50 PPM
RQL = 200 PPM
Standard deviation is unknown
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ControlImproveAnalyzeMeasureDefineRecognizePage 8 Creating Sampling Plans 2.1
Creating the Sampling Plan
Stat>Quality Tools>Acceptance Sampling by Variables>Create Compare
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ControlImproveAnalyzeMeasureDefineRecognizePage 9 Creating Sampling Plans 2.1
Creating the Plan
Generated Plan(s)
Sample Size 546
Critical Distance (k Value) 3.69358
Maximum Standard Deviation (MSD) 2.58654
Z.LSL = (mean - lower spec)/standard deviation
Z.USL = (upper spec - mean)/standard deviation
Accept lot if standard deviation <= MSD, Z.LSL >= k and Z.USL >= k; otherwise
reject.
Defectives Probability Probability
Per Million Accepting Rejecting AOQ ATI
50 0.951 0.049 21.6 568.4
200 0.102 0.898 9.3 953.7
Average outgoing quality limit (AOQL) = 27.6 at 85.6 defectives per million.
Copy this number for use in the next step.
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ControlImproveAnalyzeMeasureDefineRecognizePage 10 Creating Sampling Plans 2.1
The Graphs
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Ave
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Operating Characteristic (OC) Curve Acceptance Region Plot
Average Outgoing Quality (AOQ) Curve Average Total Inspection (ATI) Curve
Sample Size = 546, Critical Distance = 3.69358
The maximum compliant
process standard deviation would be 2.587 if the
process is centered on the target. As the process moves from the center the acceptable
standard deviation becomes smaller.
The maximum compliant
process standard deviation would be 2.587 if the
process is centered on the target. As the process moves from the center the acceptable
standard deviation becomes smaller.
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ControlImproveAnalyzeMeasureDefineRecognizePage 11 Creating Sampling Plans 2.1
Making the Decision
Paste the k value here.
Data: Valves.MTW
2007 American Society for Quality. All Rights Reserved.
ControlImproveAnalyzeMeasureDefineRecognizePage 12 Creating Sampling Plans 2.1
Making the Decision
Acceptance Sampling by Variables - Accept/Reject Lot
Make Accept or Reject Decision Using Valves
Sample Size 550
Mean 74.9077
Standard Deviation 2.42923
Lower Specification Limit (LSL) 65
Upper Specification Limit (USL) 85
Z.LSL 4.07853
Z.USL 4.15452
Critical Distance (k Value) 3.69358
Maximum Standard Deviation (MSD) 2.58654
Decision: Accept lot.
2007 American Society for Quality. All Rights Reserved.
ControlImproveAnalyzeMeasureDefineRecognizePage 13 Creating Sampling Plans 2.1
Create a Plan it the Standard Deviation is Known
Pressure Release Valves are specified as 75 ± 10 PSI.
AQL = 50 PPM
RQL = 200 PPM
Historic standard deviation is 2 PSI
2007 American Society for Quality. All Rights Reserved.
ControlImproveAnalyzeMeasureDefineRecognizePage 14 Creating Sampling Plans 2.1
The Graphs
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Lot Defectives Per Million
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Incoming Lot Defectives Per Million
AOQ
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Operating Characteristic (OC) Curve Average Outgoing Quality (AOQ) Curve
Average Total Inspection (ATI) Curve
Sample Size = 70, Critical Distance = 3.69363Note the large decrease in sample size when the standard deviation is known.
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ControlImproveAnalyzeMeasureDefineRecognizePage 15 Creating Sampling Plans 2.1
The Plan
Generated Plan(s)
Sample Size 70
Critical Distance (k Value) 3.69363
Z.LSL = (mean - lower spec)/historical standard deviation
Z.USL = (upper spec - mean)/historical standard deviation
Accept lot if Z.LSL >= k and Z.USL >= k; otherwise reject.
Defectives Probability Probability
Per Million Accepting Rejecting AOQ ATI
50 0.950 0.050 44.2 116.2
200 0.099 0.901 18.5 907.5
Average outgoing quality limit (AOQL) = 56.2 at 84.7 defectives per million.
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ControlImproveAnalyzeMeasureDefineRecognizePage 16 Creating Sampling Plans 2.1
The Decision
Data: Valves
2007 American Society for Quality. All Rights Reserved.
ControlImproveAnalyzeMeasureDefineRecognizePage 17 Creating Sampling Plans 2.1
The Decision
Make Accept or Reject Decision Using Lot 2
Sample Size 70
Mean 75.1323
Historical Standard Deviation 2
Lower Specification Limit (LSL) 65
Upper Specification Limit (USL) 85
Z.LSL 5.06613
Z.USL 4.93387
Critical Distance (k Value) 3.69358
Decision: Accept lot.
2007 American Society for Quality. All Rights Reserved.
ControlImproveAnalyzeMeasureDefineRecognizePage 18 Creating Sampling Plans 2.1
Creating an Attribute Acceptance Sampling Plan
You have been assigned to create sampling plan for non-critical parts that are acquired in lots or 10,000. The Acceptable Quality Level (AQL) is 200 PPM and a reject level at 1,000 PPM.
Sat>Quality Tools>Acceptance Sampling by Attributes
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ControlImproveAnalyzeMeasureDefineRecognizePage 19 Creating Sampling Plans 2.1
The Operation Characteristic (OC) Curves
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Lot Defectives Per Million
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Operating Characteristic (OC) Curve Average Outgoing Quality (AOQ) Curve
Average Total Inspection (ATI) Curve
Sample Size = 6679, Acceptance Number = 3 Note the very large sample size required when attribute data is used.
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ControlImproveAnalyzeMeasureDefineRecognizePage 20 Creating Sampling Plans 2.1
Sampling Plan
Accept lot if defective items in 6679 sampled <= 3; Otherwise reject. Defectives Probability ProbabilityPer Million Accepting Rejecting AOQ ATI 200 0.953 0.047 63.3 6834.2 1000 0.100 0.900 33.2 9667.9
Average outgoing quality limit (AOQL) = 96.6 at 440.9 defectives per million.
Interpretation
If the lots really had 200 PPM defective then 95.3% of lots would be accepted, the AOQ would be 63.3 PPM defective and the average number of parts inspected per lot would be 6834.2.
If the lots had 1,000 PPM defective 10% or the lots would be accepted.
The worst case average PPM for this sampling plan would be 96.6 PPM when the lots actually had 440.9 PPM.
These assume all rejected lots are 100% inspected and that all defective units are reworked or scrapped.
2007 American Society for Quality. All Rights Reserved.
ControlImproveAnalyzeMeasureDefineRecognizePage 21 Creating Sampling Plans 2.1
Your Turn
1. Create acceptance sampling plans for the gross weight of cereal boxes. The specification limits are 12 ounces minimum 12.5 ounces maximum. AQL = 500 RQL = 1000
• First assume the process standard deviation is unknown.
• Then assume the historic process standard deviation is .07 ounces.
2. Create an acceptance plan for attribute data with an AQL of .005 and a RQL of .01
2007 American Society for Quality. All Rights Reserved.
ControlImproveAnalyzeMeasureDefineRecognizePage 22 Creating Sampling Plans 2.1
What We Have Learned
1. What is Acceptance Sampling?
2. Definitions of Key Terms.
3. How to create variable data acceptance sampling plans.
4. How to apply variable data acceptance sampling plans.
5. How to create attribute data acceptance sampling plans.
6. How to apply attribute data acceptance sampling plans.
2007 American Society for Quality. All Rights Reserved.
ControlImproveAnalyzeMeasureDefineRecognizePage 23 Creating Sampling Plans 2.1
Solutions to Student Exercises
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ControlImproveAnalyzeMeasureDefineRecognizePage 24 Creating Sampling Plans 2.1
Creating the Plan Unknown
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ControlImproveAnalyzeMeasureDefineRecognizePage 25 Creating Sampling Plans 2.1
The Plan Unknown
Generated Plan(s)
Sample Size 1292
Critical Distance (k Value) 3.17795
Maximum Standard Deviation (MSD) 0.0741023
Z.LSL = (mean - lower spec)/standard deviation
Z.USL = (upper spec - mean)/standard deviation
Accept lot if standard deviation <= MSD, Z.LSL >= k and Z.USL >= k; otherwise
reject.
Defectives Probability Probability
Per Million Accepting Rejecting
500 0.950 0.050
1000 0.101 0.899
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ControlImproveAnalyzeMeasureDefineRecognizePage 26 Creating Sampling Plans 2.1
Creating the Plan Known
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ControlImproveAnalyzeMeasureDefineRecognizePage 27 Creating Sampling Plans 2.1
The Plan Known
Generated Plan(s)
Sample Size 147
Critical Distance (k Value) 3.19629
Z.LSL = (mean - lower spec)/historical standard deviation
Z.USL = (upper spec - mean)/historical standard deviation
Accept lot if Z.LSL >= k and Z.USL >= k; otherwise reject.
Defectives Probability Probability
Per Million Accepting Rejecting
500 0.950 0.050
1000 0.117 0.883
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ControlImproveAnalyzeMeasureDefineRecognizePage 28 Creating Sampling Plans 2.1
Creating the Attribute Sampling Plan
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ControlImproveAnalyzeMeasureDefineRecognizePage 29 Creating Sampling Plans 2.1
The Attribute Plan
Generated Plan(s)
Sample Size 45
Acceptance Number 0
Accept lot if defective items in 45 sampled <= 0; Otherwise reject.
Proportion Probability Probability
Defective Accepting Rejecting
0.001 0.956 0.044
0.050 0.099 0.901
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ControlImproveAnalyzeMeasureDefineRecognizePage 30 Creating Sampling Plans 2.1
The OC Curve
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Operating Characteristic (OC) Curve
Sample Size = 45, Acceptance Number = 0