Economic Reliability Test Plans

Acceptance sampling plan is an essential tool in the Statistical Quality Control. In
most of the statistical quality control experiments, it is not possible to perform 100%
inspection due to various reasons. The acceptance sampling plans are concerned
with accepting or rejecting a submitted lot of a large size of products on the basis of
the quality of the products inspected in a sample taken from the lot. An acceptance
sampling plan is a specified plan that establishes the minimum sample size to be
used for testing. In acceptance sampling plans for a truncated life test, the major
issue is to determine the minimum sample size from a lot under consideration.
Traditionally, when the life test indicates that the mean life of products exceeds the
specified one, the lot of products is accepted, otherwise it is rejected. For the
purpose of reducing the test time and cost, a truncated life test may be conducted to
determine the smallest sample size to ensure a certain mean life time/percentile
lifetime of products when the life test is terminated at a pre-assigned time, and the
number of failures observed does not exceed a given acceptance number c. The
decision is to accept the lot if a pre-determined mean life time/percentile life can be
reached with a pre-determined high probability which provides protection to
consumer. Therefore, the life test is ended at the time the cth failure is observed or at
the pre-assigned time, whichever is earlier. For such a truncated life test and the
associated decision rule, we are interested in obtaining the smallest sample size to
arrive at a decision.