 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".

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.

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. 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. 