6.2.7. What is Skip Lot Sampling?

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

6.2.7. 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.. 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 calculate 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

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

An important property of skip-lot sampling plans is the average sample number (ASN). The ASN of a skip-lot sampling plan is

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 an proven track record..