On the sequential test per MIL-STD-781 and new, more efficient test plans.

Abstract

The sequential probability ratio test is an efficient test procedure compared to the fixed sample size test procedure in the sense that it minimizes the average sample size needed for terminating the experiment at the two specified hypotheses, i.e., at H₀: θ = θ₀ and H₁: θ = θ₁. However, this optimum property does not hold for the values of the testing parameter other than these two hypotheses, especially for those with values between these two. Also the estimation following a sequential test is considered to be difficult, and the usual maximum likelihood estimate is in general biased. The sequential test plans given in MIL-STD-781 do not meet their nominal test risk requirements and the truncation of these test plans is determined by the theory for a fixed sample size test. The contributions of this dissertation are: (1) The distribution of the successive sums of samples from a generalized sequential probability ratio test in the exponential case has been obtained. An exact analysis method for the generalized sequential probability ratio test has been developed as well as its FORTRAN programs based on this distribution. (2) A set of improved sequential probability ratio test plans for testing the mean for the exponential distribution has been established. The improved test plan can meet the test risk requirements exactly and can approximately minimize the maximum average waiting time. (3) The properties of the estimates after a sequential test have been investigated and a bias reduced estimate has been recommended. The general method for constructing the confidence interval after a sequential test has been studied and its existence and uniqueness have been proved in the exponential case. (4) Two modification to the Wald's sequential probability ratio test, the triangular test and the repeated significance test, in the exponential case have been also studied. The results show that the triangular test is very close to the optimal test in terms of minimizing the maximum average sample size, and a method for constructing the triangular test plan has been developed.