Exact computation for some sequential tests

Abstract

Assume that the probability density function for the lifetime of a newly designed product has the form: , for some known H(·). The Exponential ε(θ), Rayleigh, and Pareto Pdf's are special cases. A class of continuous-time sequential tests based on the transformed total time on test and the total number of failures is proposed. The use of Steck's (1971) recursions for rectangle probabilities of uniform order statistics simplifies the exact computation for the operating characteristic, the average sample number, and the average failure number. Applications are given to Epstein and Sobel's (1955) continuous-time sequential probability ratio tests (SPRT), Anderson (1960) type of modification to the SPRT, a Bayesian sequential reliability demonstration test (BSRDT) and a predictive sequentila reliability demonstration test (PSRDT). Jeffreys’ prior appears inappropriate for both BSRDT's and PSRDT's. An ad hoc noninformative prior is used for BSRDT's and PSRDT's. Relationship between BSRDT's and PSRDT's is discussed. Numerical examples are given for illustrating the recursion formulas for the OC and ASN functions.

Keywords:

• Exponential distribution
• Sequential probability ratio test
• Bayesian sequential test
• Reliability demonstration test
• Producer's risk
• Consumer's risk
• Average sample number
• Average failure number
• Operating characteristic