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6. Process or Product Monitoring and Control
6.2. Test Product for Acceptability: Lot Acceptance Sampling


What is Skip Lot Sampling?

Skip Lot Sampling Skip Lot sampling means that only a fraction of the submitted lots are inspected. This mode of sampling is of the cost-saving variety in terms of time and effort. However skip-lot sampling should only be used when it has been demonstrated that the quality of the submitted product is very good.
Implementation of skip-lot sampling plan A skip-lot sampling plan is implemented as follows:
  1. Design a single sampling plan by specifying the alpha and beta risks and the consumer/producer's risks. This plan is called "the reference sampling plan".

  2. Start with normal lot-by-lot inspection, using the reference plan.

  3. When a pre-specified number, \(i\) of consecutive lots are accepted, switch to inspecting only a fraction \(f\) of the lots. The selection of the members of that fraction is done at random.

  4. When a lot is rejected return to normal inspection.
The \(f\) and \(i\) parameters The parameters \(f\) and \(i\) are essential to calculating the probability of acceptance for a skip-lot sampling plan. In this scheme, \(i\), called the clearance number, is a positive integer and the sampling fraction \(f\) is such that \(0 < f < 1\). Hence, when \(f=1\) there is no longer skip-lot sampling. The calculation of the acceptance probability for the skip-lot sampling plan is performed via the following formula $$ P_a(f,i) = \frac{fP + (1-f)P^i}{f + (1-f)P^i} \, ,$$ where \(P\) is the probability of accepting a lot with a given proportion of incoming defectives \(p\), from the OC curve of the single sampling plan.

The following relationships hold:

for a given \(i\), the smaller is \(f\) the greater is \(P_a\),
for a given \(f\), the smaller is \(i\), the greater is \(P_a\).
Illustration of a skip lot sampling plan An illustration of a a skip-lot sampling plan is given below.
Plot illustrating a skip-lot sampling plan for f=0.25 and
ASN of skip-lot sampling plan An important property of skip-lot sampling plans is the average sample number (ASN). The ASN of a skip-lot sampling plan is $$ \mbox{ASN}_{skip-lot} = (F)(\mbox{ASN}_{reference}) \, , $$ where \(F\) is defined by $$ F = \frac{f}{(1-f)P_i + f} \, .$$

Therefore, since \(0 < F < 1\), it follows that the ASN of skip-lot sampling is smaller than the ASN of the reference sampling plan.

In summary, skip-lot sampling is preferred when the quality of the submitted lots is excellent and the supplier can demonstrate a proven track record.

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