08 acceptance sampling plans_ppm's

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Acceptance Sampling Measure Control Improve Analyze Define Recognize Six Sigma Six Sigma Green Belt Training Green Belt Training 2007 American Society for Quality. All Rights Reserved.

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Page 1: 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.

Page 2: 08 Acceptance Sampling Plans_ppm's

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.

Page 3: 08 Acceptance Sampling Plans_ppm's

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.

Page 4: 08 Acceptance Sampling Plans_ppm's

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).

1086420

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Lot Percent Defective

Pro

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Operating Characteristic (OC) Curve

AQL

RQL

Source: Minitab Help

Page 5: 08 Acceptance Sampling Plans_ppm's

2007 American Society for Quality. All Rights Reserved.

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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AOQ (

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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

Page 6: 08 Acceptance Sampling Plans_ppm's

2007 American Society for Quality. All Rights Reserved.

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.

Page 7: 08 Acceptance Sampling Plans_ppm's

2007 American Society for Quality. All Rights Reserved.

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

Page 8: 08 Acceptance Sampling Plans_ppm's

2007 American Society for Quality. All Rights Reserved.

ControlImproveAnalyzeMeasureDefineRecognizePage 8 Creating Sampling Plans 2.1

Creating the Sampling Plan

Stat>Quality Tools>Acceptance Sampling by Variables>Create Compare

Page 9: 08 Acceptance Sampling Plans_ppm's

2007 American Society for Quality. All Rights Reserved.

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.

Page 10: 08 Acceptance Sampling Plans_ppm's

2007 American Society for Quality. All Rights Reserved.

ControlImproveAnalyzeMeasureDefineRecognizePage 10 Creating Sampling Plans 2.1

The Graphs

4003002001000

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Lot Defectives Per Million

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8580757065

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Sample Mean

Sam

ple

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2.587

4003002001000

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Incoming Lot Defectives Per Million

AO

Q (

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on)

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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.

Page 11: 08 Acceptance Sampling Plans_ppm's

2007 American Society for Quality. All Rights Reserved.

ControlImproveAnalyzeMeasureDefineRecognizePage 11 Creating Sampling Plans 2.1

Making the Decision

Paste the k value here.

Data: Valves.MTW

Page 12: 08 Acceptance Sampling Plans_ppm's

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.

Page 13: 08 Acceptance Sampling Plans_ppm's

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

Page 14: 08 Acceptance Sampling Plans_ppm's

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

(D

efec

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Per

Millio

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Lot Defectives Per Million

Aver

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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.

Page 15: 08 Acceptance Sampling Plans_ppm's

2007 American Society for Quality. All Rights Reserved.

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.

Page 16: 08 Acceptance Sampling Plans_ppm's

2007 American Society for Quality. All Rights Reserved.

ControlImproveAnalyzeMeasureDefineRecognizePage 16 Creating Sampling Plans 2.1

The Decision

Data: Valves

Page 17: 08 Acceptance Sampling Plans_ppm's

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.

Page 18: 08 Acceptance Sampling Plans_ppm's

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

Page 19: 08 Acceptance Sampling Plans_ppm's

2007 American Society for Quality. All Rights Reserved.

ControlImproveAnalyzeMeasureDefineRecognizePage 19 Creating Sampling Plans 2.1

The Operation Characteristic (OC) Curves

2000150010005000

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Incoming Lot Defectives Per Million

AOQ

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Aver

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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.

Page 20: 08 Acceptance Sampling Plans_ppm's

2007 American Society for Quality. All Rights Reserved.

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.

Page 21: 08 Acceptance Sampling Plans_ppm's

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

Page 22: 08 Acceptance Sampling Plans_ppm's

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.

Page 23: 08 Acceptance Sampling Plans_ppm's

2007 American Society for Quality. All Rights Reserved.

ControlImproveAnalyzeMeasureDefineRecognizePage 23 Creating Sampling Plans 2.1

Solutions to Student Exercises

Page 24: 08 Acceptance Sampling Plans_ppm's

2007 American Society for Quality. All Rights Reserved.

ControlImproveAnalyzeMeasureDefineRecognizePage 24 Creating Sampling Plans 2.1

Creating the Plan Unknown

Page 25: 08 Acceptance Sampling Plans_ppm's

2007 American Society for Quality. All Rights Reserved.

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

Page 26: 08 Acceptance Sampling Plans_ppm's

2007 American Society for Quality. All Rights Reserved.

ControlImproveAnalyzeMeasureDefineRecognizePage 26 Creating Sampling Plans 2.1

Creating the Plan Known

Page 27: 08 Acceptance Sampling Plans_ppm's

2007 American Society for Quality. All Rights Reserved.

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

Page 28: 08 Acceptance Sampling Plans_ppm's

2007 American Society for Quality. All Rights Reserved.

ControlImproveAnalyzeMeasureDefineRecognizePage 28 Creating Sampling Plans 2.1

Creating the Attribute Sampling Plan

Page 29: 08 Acceptance Sampling Plans_ppm's

2007 American Society for Quality. All Rights Reserved.

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

Page 30: 08 Acceptance Sampling Plans_ppm's

2007 American Society for Quality. All Rights Reserved.

ControlImproveAnalyzeMeasureDefineRecognizePage 30 Creating Sampling Plans 2.1

The OC Curve

0.100.080.060.040.020.00

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Operating Characteristic (OC) Curve

Sample Size = 45, Acceptance Number = 0