Sequential testing for two exponential distributions at arbitrary risks

Abstract

Purpose

This paper aims to propose a methodology for planning of a truncated sequential probability ratio test (SPRT) in which two systems with exponentially distributed times between failures (TBFs) are compared. The study is concerned with tests with arbitrary probabilities of I‐ and II‐type errors.

Design/methodology/approach

The study methodology, based on the proposed optimality criteria for these tests, permitted comparison of different modes of truncation and obviated the drawbacks of discreteness and multidimensionality of their characteristics.

Findings

The solution permits planning of a heavily‐truncated test with an average sample number exceeding its counterpart for the optimal (non‐truncated) test by at most a specified percentage. Relationships are outlined for optimal selection of the truncated test boundaries. So are optimality estimation criteria for the constructed test. The superiority of the SPRTs, truncated by the proposed methodology, over their counterparts, processed according to current practices, is demonstrated.

Research limitations/implications

The solution refers to the case where the compared systems have exponentially distributed TBFs (or times to failure (TTFs) for non‐repairable cases).

Practical implications

The proposed algorithm and relationships for planning the tests in question can be used by developers of tests for reliability. A planning example from the semiconductor industry is given.

Originality/value

This paper presents a novel approach to planning of truncated SPRTs with arbitrary probabilities of I‐ and II‐type errors. The methodology is also applicable for truncated binomial SPRTs.

Citation

Michlin, Y.H., Kaplunov, V. and Ingman, D. (2012), "Sequential testing for two exponential distributions at arbitrary risks", International Journal of Quality & Reliability Management, Vol. 29 No. 4, pp. 451-468. https://doi.org/10.1108/02656711211224884