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.

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

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

ASN_skip-lot = (F)(ASN_reference)

where F is defined by

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.