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CHAPTER 07

ACCEPTANCE SAMPLING PLANS

Professor Mohamed AichouniProfessor Mohamed Aichouni

University of Hail College of Engineering

ME 418 – Quality in ManufacturingISE 320 - Quality Control and Industrial Statistics

Acceptance Sampling

• Acceptance sampling is a method used to accept or reject product based on a random sample of the product.

• The purpose of acceptance sampling is to sentence lots (accept or reject) rather than to estimate the quality of a lot.

• Acceptance sampling plans do not improve quality. The nature of sampling is such that acceptance sampling will accept some lots and reject others even though they are of the same quality.

• The most effective use of acceptance sampling is as an auditing tool to help ensure that the output of a process meets requirements.

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Acceptance Sampling

Producer Consumer

Risk is a ‘good’ lot will be rejected and sent back.

Risk is a ‘bad’ lotwill be accepted.

Take a SampleSize ‘n’,

Accept if ‘c’ or less.

Acceptance Sampling Flow

Chart

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5

Acceptance Sampling

samplingInspect the

sample

Acceptance number

Reject the lotAccept the lot

N

N : sample size

c : عدد القبول

• As mentioned acceptance sampling can reject “good” lots and accept “bad” lots. More formally:

• Producers risk refers to the probability of rejecting a good lot.

• AQL (Acceptable Quality Level) - the numerical definition of a good lot; associated with Producer`s risk.

• The ANSI/ASQC standard describes AQL as “the maximum percentage or proportion of nonconforming items or number of nonconformities in a batch that can be considered satisfactory as a process average”

Terminology

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• Consumers Risk refers to the probability of accepting a bad lot where:

• LTPD (Lot Tolerance Percent Defective) - the numerical definition of a bad or poor lot .

• described by the ANSI/ASQC standard as “the percentage or proportion of nonconforming items or noncomformities in a batch for which the customer wishes the probability of acceptance to be a specified low value.

• Limiting Quality Level - Numerical definition of a ‘poor’ lot, associated with the consumer’s risk.

Terminology

8

Types of Sampling Plans

Sampling Plans by Attributes:

• Single sampling plan by attributes

• Double sampling plan by attributes

• Sequential sampling plan

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Single Sampling

Operating Characteristic (OC) curve

The Operating Characteristic Curve is typically used to represent the four parameters (Producers Risk, Consumers Risk, AQL and LTPD) of the sampling plan.

P on the x axis represents the percent defective in the lot.

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Ideal Operating Characteristics Curve(100% Inspection)

P(Accept Whole Shipment)

100%

0%

Proportion of non Conforming

1 2 3 4 5 6 7 8 9 100

Always Accept Always Reject

P o

f A

ccep

tan

ce

Actual OC Curves

• Are determined by sample size [n] and acceptance number [c].– Accept the lot if ‘c’ or fewer

nonconforming are obtained, reject if more.

• OK to assume Binomial distribution (if lot size is 10x sample size).

• Calculate P accept for range of incoming p levels.

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P(Accept Whole Shipment)

100%

0%

Cut-Off

1 2 3 4 5 6 7 8 9 100

Reject the lot

P < 100 %

Risk to accept bad lot and/or reject a good lot

Actual OC Curves

Proportion of non Conforming

Accept the lot

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Actual OC Curves and the Producer`s Risk and Consumer`s Risk

= 0.05 AQL

Indifference zoneGood

lot

LTPDAQL

0 1 2 3 4 5 6 7 8

10095

75

50

25

10

0

Bad lot

= 0.10

for LTPD Proportion of non conforming

P o

f ac

cep

tan

ce

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Sample problem

• Given a lot size of N=2000, a sample size n=50, and an acceptance number c=2.

• Calculate the OC curve for this plan.

Probability of accepting isobtaining c=2 or less non-conforming items in samples of size n=50.

Vary p from 0 to 0.15(what if p = ….)

16

OC for possible sampling plans

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Vary n and c

Double Sampling

• In an effort to reduce the amount of inspection double (or multiple) sampling is used. Whether or not the sampling effort will be reduced depends on the defective proportions of incoming lots. Typically, four parameters are specified:

n1 = number of units in the first sample

c1 = acceptance number for the first sample

n2 = number of units in the second sample

c2 = acceptance number for both samples

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Procedure• A double sampling plan proceeds as follows:

A random sample of size n1 is drawn from the lot.

If the number of defective units (say d1 ) c1 the lot is accepted.

If d1 c2 the lot is rejected.

If neither of these conditions are satisfied a second sample of size n2 is drawn from the lot.

If the number of defectives in the combined samples (d1 + d2) > c2 the lot is rejected. If not the lot is accepted.

Double Sampling Plan

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Double Sampling Plan

• Application of double sampling requires that a first sample of size n1 is taken at random from the (large) lot. The number of defectives is then counted and compared to the first sample's acceptance number a1 and rejection number r1. Denote the number of defectives in sample 1 by d1 and in sample 2 by d2, then: – If d1<= a1, the lot is accepted.

If d1 >= r1, the lot is rejected. If a1 < d1 < r1, a second sample is taken.

• If a second sample of size n2 is taken, the number of defectives, d2, is counted. The total number of defectives is D2 = d1 + d2. Now this is compared to the acceptance number a2 and the rejection number r2 of sample 2. In double sampling, r2 = a2 + 1 to ensure a decision on the sample. – If D2 <= a2, the lot is accepted.

If D2 >= r2, the lot is rejected. –

Designing Acceptance Plans

• This should be performed on agreement between the producer and the consumer.

• Each party work to reduce the risk, by varying n and c to obtain different OC curves.

• Single and multiple sampling plans can be used.

• Refer to standard published Standards (MIL-STD-105D, Dodge Romig Tables).

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• Minitab perform all the necessary calculations to design acceptance sampling plans.

• http://blog.minitab.com/blog/applying-statistics-in-quality-projects/attribute-acceptance-sampling-for-an-acceptance-number-of-0

•

Acceptance Sampling Plans on Minitab

Examples will be worked out next sessions

International Standards on Sampling Plans

ISO 2859 - 0:1995 Sampling procedures for inspection by attributes -- Part 0: Introduction to the ISO 2859 attribute sampling system

ISO 2859 - 1:1999 Sampling procedures for inspection by attri butes -- Part 1: Sampling schemes indexed by acceptance quality limit

(AQL) for lot - by - lot inspection

ISO 2859 - 1:1999/Cor 1:2001ISO 2859 - 2:1985

Sampling procedures for inspection by attributes -- Part 2: Sampling plans indexed by limiting quality (LQ) for isolated

lot i nspection

ISO 2859 - 3:1991 Sampling procedures for inspection by attributes -- Part 3: Skip - lot sampling procedures

ISO 2859 - 4:2002 Sampling procedures for inspection by attributes -- Part 4: Procedures for assessment of declared quality levels

ISO 3951:1989 Sampling procedures and charts for inspection by variables for percent nonconforming

ISO 8422:1991 Sequential sampling plans for inspection by attributes

ISO 8422:1991/Cor 1:1993ISO 8423:1991

Sequential sampling plans for inspection by variables for percent nonconforming (known stan dard deviation)

ISO 8423:1991/Cor 1:1993ISO/TR 8550:1994

Guide for the selection of an acceptance sampling system, scheme or plan for inspection of discrete items in lots

ISO 10725:2000 Acceptance sampling plans and procedures for the inspection of bulk materials

ISO 11648 - 1:2003 Statistical aspects of sampling from bulk materials -- Part 1: General principles

ISO 11648 - 2:2001 Statistical aspects of sampling from bulk materials -- Part 2: Sampling of particulate materials

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Conclusion

"Quality control truly begins and endswith education",

K. Ishikawa (1990).

Lecture Finished

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CHAPTER 06 – PART 2

ACCEPTANCE SAMPLING PLANS

EXAMPLES ON MINITAB

Professor Mohamed AichouniProfessor Mohamed Aichouni

University of Hail College of Engineering

ME 418 – Quality in ManufacturingISE 320 - Quality Control and Industrial Statistics

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• http://blog.minitab.com/blog/applying-statistics-in-quality-projects/attribute-acceptance-sampling-for-an-acceptance-number-of-0

Acceptance Sampling Plans on Minitab

Acceptance Sampling Plans on Minitab

This graph represents the probability to accept a batch for a given proportion of defectives.

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Acceptance Sampling Plans on Minitab

Acceptance Sampling Plans on Minitab

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Acceptance Sampling Plans on Minitab