Acceptance Sampling- A form of inspection

PRESENTED BY : SENARATHNE D.M.U.S | S/09/598

2Outline Introduction Usage Sampling Plans Single, Double and multiple Sampling Plans Operating Characteristic Curve and Acceptance Levels Sampling Risks Average Outgoing Quality Advantages and Disadvantages Conclusion

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3Introduction

A form of inspection applied to lots or batches of

items before or after a process to judge

conformance to predetermined standards

It is a decision making tool by which a conclusion

is reached regarding the acceptability of lot.

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4Acceptance Sampling Used in…

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When testing is destructive When the cost of 100% inspection is extremely high and it

is not technologically feasible When the vendor has an excellent quality history, and some

reduction in inspection from 100% is desired, but the vendor’s process capability is sufficiently low as to make no inspection an unsatisfactory alternative

5Sampling Plans

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Sampling plans

Attribute sampling

Single sampl

ing

Double

Sampling

Multiple

Sampling

Sequential

Sampling

Variable sampling

Sampling Plans specify the lot size, sample size, number of samples and acceptance/rejection criteria. Sampling plans involve

Random sample

Lot

6Single Sampling Plan

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g A representative sample of n items is drawn from a lot size of N items.

Each item in the sample is examined and classified as good/defective

If the number of defective exceeds a specified rejection number (C - cut off point) the whole lot is rejected; otherwise the whole lot is accepted

Random

sample (n

items)

Lot (N items)

Random

sample (n

items)

Lot (N items)

7Double Sampling Plan

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A Double Sampling Plan allows the opportunity to take a second sample if the results of the original sample are inconclusive.

Specifies the lot size, size of the initial sample, the accept/reject/inconclusive criteria for the initial sample (CL - lower level of defectives, CU - upper level of defectives)

Specifies the size of the second sample and the acceptance rejection criteria based on the total number of defective observed in both the first and second sample (CT- total allowable defectives)

It works like the following example

8Double Sampling Plan…acce

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Compare number of defective found in the first random sample to CL and CU and make appropriate decision.

CL CU

Accept Lot Reject Lot

First sample inconclusive, take second sample

First Random sample

Lot

9Double Sampling Plan…acce

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Compare the total number of defective in both samples to CT and make the appropriate decision

Accept Lot Reject Lot

CT

Lot First Random sample

Second Random sample

10Multiple Sampling Plans

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A Multiple Sampling Plan is similar to the double sampling plan in that successive trials are made, each of which has acceptance, rejection and inconclusive options.

Which Plan you choose depends on

Cost and time

Number of samples needed and number of items in each sample

11Operating Characteristic Curve(OCC) An Operating

Characteristic Curve (OCC) is a probability curve for a sampling plan that shows the probabilities of accepting lots with various lot quality levels (%defectives).

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0

0.2

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Lot quality (%defective)

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Under this sampling plan, if the lot has 2% defective . the probability of accepting the lot is 92% . the probability of re-jecting the lot is 8%

If the lot has 10% defective . it has a small proba-bility (11%) of being accepted . the probability of rejecting the lot is 89%

12Customers Acceptance Levels

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Most customers understand that 100% inspection is impractical and are generally willing to accept that a certain level of defectives will be produced.

The Acceptable Quality Level (AQL) is the percentage level of defects at which a customer is willing to accept as lot as “good”.

The Lot Tolerance Percent Defective (LTPD) is the upper limit on the percentage of defectives that a customer is willing to accept.

Customers want lots with quality better than or equal to the AQL but are willing to live with some lots with quality as poor as the LTPD, but prefer not to accept lots with quality levels worse than the LTPD.

13Defining good and bad lot

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Proportion non-conforming

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AQL LTPD

Very Good

Ok! But not great

Very Bad

Instead of good and bad we will define “really good”, “really bad”, “ok, but not great”

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14Customers Acceptance Levels…

Therefore the sampling plan must be designed to assure the customer that they will be receiving the required AQL and LTPD.

The Consumer’s Risk is the probability that an unacceptable lot (e.g. above the LTPD) will be accepted.

The Producer’s Risk is the probability that a “good” lot will be rejected.

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15Sampling Risks

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AQL LTPD

Producer’s Risk = Probability acceptable is rejected

Consumer Risk = Probability unacceptable is accepted

Acceptable lotUnacceptable lot

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16Average Quality Of Inspected LotsThe result of acceptance sampling (assuming rejected lots are 100% inspected) is that the level of inspection automatically adjusts to the quality of the lots being inspected.

The Average Outgoing Quality (AOQ)is the average of rejected lots (100% inspection) and accepted lots ( a sample of items inspected).

AOQ = where;

= Probability of accepting a lot

= Fraction defective

N = Lot size

n = Sample size

The maximum outgoing quality level is referred to as the AOQL

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17Constructing OC Curve

00.10.20.30.40.50.60.70.80.9

1

Proportion non-conforming

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0.677Proportion non-conforming

Probability of acceptance

0 10.01 0.9860.02 0.9220.04 0.6770.06 0.4160.08 0.226

0.1 0.1120.15 0.014

0.2 0.001OC curve for n=50, c=2

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18Advantages It is usually less expensive because there is less

inspection. There is less handling of the product, hence reduced

damage. It is applicable to destructive testing. Fewer personnel are involved in inspection activities. It often greatly reduces the amount of inspection error. The rejection of entire lots are opposed to the sample

return of defectives often provides a stronger motivation to the vendor for quality improvements.

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19Disadvantages

There are risk of accepting “bad” lots and rejecting “good” lots.

Less information is usually generated about the product or about the process that manufactured the product.

Acceptance sampling requires planning and documentation of the acceptance sampling procedure whereas 100% inspection does not.

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20Conclusion Acceptance sampling is a statistical procedure used to

determine whether to accept or reject a production lot of material.

A wide variety of sampling plans are available. Plans have an accepted AQL & a rejected LTPD & an AOQL.

Acceptance sampling tables are there to supply a set of accepted procedures with known properties &verified results.

Sampling provides rational means of verification that a production lot confirms with requirements of technical specifications.

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21

THANK YOU

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