An Innovative Method to Hypothesis Testing for System Safety Assessment

Abstract

The way forward in system safety engineering will be quantitative, and this paper proposes an innovative method for generating a uniform way to understand the composite of testing and experience. In recent years, new approaches to exact hypothesis testing have been developed without a Gaussian probability distribution for success or failure rates. These techniques eliminate errors introduced by the Gaussian assumption, which is important for the small failure rates that are common in modern systems development, and offer considerable promise as a basis for the new direction.
 This paper presents a theory for exact hypothesis testing and combines two 18th-century theorems to derive an equation for the probability distribution of failure rate employing only the number of tests and the observed count of failures. The concept is expanded to demonstrate the combination of operational experience and expert opinion to update test results. The objective in this work is to derive the general likelihood distribution of failure rate given any set of test results, and then to examine the implications regarding testing requirements, design and interpretation. The particular application considered here is safety assessment for a military weapons system. While the theory developed is for deriving the exact failure rate distribution for system safety applications, it is equally valid for investigating success rates and/or for interpreting performance evaluation tests.