# Sequential Sampling Plan

**Sequential Sampling Plan**

Sequential sampling is similar to multiple sampling except that the sequential sampling can theoretically continue indefinitely. In practice the plan is truncated after the number inspected is equal to three times the number inspected by a corresponding single sampling plan. Sequential sampling, which is used for cortely or destructive tests, usually has a subgroup size of 1, thereby making it an item-by-item plan.

Item-by-item sequential sampling is based on the concept of the sequential probability ratio test, (SPRT). Figure illustrates the sampling plan technique. The “stepped” line shows the number detective for the total number inspected and is updated with the inspection results of each item. If the cummulative results equal or are greater than the upper line, the lot is rejected. If the cummulative results equal or are less than the lower line, the lot is accepted. If neither decision is possible, another item is inspected. Thus, if the 20th sample is found to be defective, the cummulative number of defective will be five. Since the five defectives exceeds the rejection line for 20 inspections, the lot is rejected, as shown by the dashed line in figure.

The sequential sampling plan is defined by the producer’s risk, α and its process quality Pα, and by the consumer’s risk, β, and its process quality, Pβ, Using these requirements, the equations (slope intercept form) can be determined for the acceptance line and rejection line using the following formulae.

where

S = Slope of the lines

hr = Intercept for the rejection line

ha = Intercept for the acceptance line

Pβ = Fraction defective for consumer’s risk

Pα = Fraction defective for producer’s risk

β = Consumer’s risk

α = Producer’s risk

da = number of defection for acceptance

dr = number of defection for rejection

n = number of units inspected.