Ph.D Thesis
Ph.D Student Shaham Ofer Method for Planning a Binomial Truncated Sequential Test for Reliability Department of Industrial Engineering and Management Professor Dov Ingman Dr. Yefim Haim Michlin

Abstract

The Sequential Probability Ratio Test (SPRT) is widely used in the field of reliability and quality control. In the binomial SPRT is checked the hypothesis that the percentage of defective items does not exceed a specified value.

The procedure for planning the binomial SPRT was published by A. Wald in 1947; however, a proper alternative, for practical use, has not yet been suggested.

The objective of the study is to develop a scientific basis, method and tools for the practical planning of truncated binomial SPRT.

The sample number until the test stops (SN) is a random value and its distribution tails can be extremely long relative to the average SN (ASN). This is not suitable for practical use; therefore, truncation is required, preferable by a pair of lines whose intersection, denoted as the Truncation Apex (TA), determines the maximum SN (maxSN).

The truncation complicates the planning process. Moreover, the discreteness and multidimensionality of the characteristics of such tests prevent their direct comparison and optimization. To remedy these drawbacks, quality features for the test are proposed, one of which - the Relative Efficiency (RE) - represents the ratio of the test's weighted ASN and its counterpart of the non-truncated SPRT. It facilitates a solution of the problems in automatic planning of the test.

The optimality of the test is determined by the minimality of the SN (by means of maxSN and ASN) for a given Operating Characteristic (OC). Presented are formulas and an algorithm for finding the TA and other parameters of the optimal test stopping boundaries. Displacement of the TA from the optimal location results in a drastic increase in ASN. This method also extremely shortens and simplifies the test planning process and will lead to the increased use of the SPRT for practical and research needs.

The proposed method for the binomial test planning, with the incorporated calculation formulas, is applicable without any change to SPRT, intended for checking hypotheses on the exponential distribution parameter.

This study was implemented in the Israeli standard SI-61123. Revisions of international standards IEC 61123 and IEC 61124 (the last is for exponential distributed data), by this study, have been accepted to the work-plan of TC-56 of IEC. For the IEC 61123 revision, TC-56 published a Committee Draft based on this study. The proposed method can be the scientific basis for the improvement of additional standards, for example, in ISO 28591:2017. An actual industrial example and examples of additional reliability and technological applications of the study are also included.