SINGLE AND DOUBLE SAMPLING

By SHIVANI GARG

WHAT IS SAMPLING?Sampling is the act, process, or technique of selecting a suitable sample, or a representative part of a population for the purpose of determining parameters or characteristics of the whole population.

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SINGLE SAMPLING

DOUBLE SAMPLING

SINGLE SAMPLING

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Definition of a Single-Sampling Plan

A single sampling plan is defined by sample size, n, and the acceptance number c. Say there are N total items in a lot. Choose n of the items at random. If at least c of the items are unacceptable, reject the lot.

N = lot size

n = sample size

c = acceptance number

d = observed number of defectives.

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The acceptance or rejection of the lot is based on the results from a single sample - thus a single-sampling plan.

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Conditions of Single-Sampling Plan:-

Acceptance or rejection decision is made after drawing only one sample from the lot.

If the number of defectives, d, does not exceed the acceptance criteria, c, the lot is accepted.

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Single-Sampling PlanLot of N Items

RandomSample of

n ItemsN - n Items

Inspect n Items

d > c d< cReplaceDefectives

n Nondefectives

d Defectives

Found in Sample

Reject Lot Accept Lot

DOUBLE SAMPLING

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Definition of a Double-Sampling Plan

Defined by four parameters:

n1 = sample size for the first sample

c1 = acceptance number of the first sample

n2 = sample size for the second sample

c2 = acceptance number of the second sample

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Conditions of Double-Sampling Plan:-

One small sample is drawn initially.

If the number of defectives is less than or equal to some lower limit, the lot is accepted.

If the number of defectives is greater than some upper limit, the lot is rejected.

If the number of defectives is neither, a second larger sample is drawn.

Lot is either accepted or rejected on the basis of the information from both of the samples.

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Double-Sampling PlanLot of N Items

RandomSample ofn1 ItemsN – n1 Items

Inspect n1 Items

d1 > c2 d1 < c1

ReplaceDefectives

n1 Nondefectives

d1 Defectives

Found in Sample

Reject Lot

Accept Lot

Continue

c1 < d1 < c2

(to next slide)

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(d1+ d2) > c2

Double-Sampling Plan

N – n1 Items

RandomSample ofn2 Items

N – (n1 + n2)Items

Inspect n2 Items

ReplaceDefectives

n2 Nondefectives

d2 Defectives

Found in SampleReject Lot

Accept Lot

Continue

(d1+ d2) < c2

(from previous slide)

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Double sampling plans

AdvantagesCan reduce the total amount of

inspectionAllows the vendor a second

chance

DisadvantagesCan lose the economical

advantageMore record keeping is needed

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