Planning of sequential binomial tests for various risk ratios

Abstract

AbstractThe Sequential Probability Ratio Test (SPRT) is widely used in the field of reliability and quality control. This paper is a continuation and a significant extension of the authors' earlier paper; it is dedicated to various risk ratios (α/β) and will lead to the increased use of the Sequential Probability Ratio Test for practical and research needs. The sample number (SN) until the test stops 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, usually by a pair of lines whose intersection, denoted as the Truncation Apex (TA), determines the maximum SN (maxSN). The optimality of the test is determined by the minimality of the SN (by means of maxSN and ASN) for a given Operating Characteristic. Presented are formulas and an algorithm for the TA and other parameters of the optimal test stopping boundaries for various α/β. This methodology also shortens the test planning process. Displacement of the TA from the optimal location results in a significant increase in ASN.The study was implemented in the Israeli standard SI‐61123. Revision of IEC 61123 and IEC 61124 (for exponential distributed data), by this study, has been accepted to the work plan of TC‐56 of IEC. The proposed methodology can be the basis for the improvement of additional standards, for example, in ISO 8422:2006.