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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