Estimates of Reliability Indicators for Failure-Free Tests Conducted According to the Binomial Plan

Abstract

The purpose of the work is to construct estimates close in their effectiveness to effective estimates of the binomial test plan, but devoid of their shortcomings in failure-free tests. Reliability function and mean time to failure are selected as indicators of reliability. Methods. To find an effective estimate, integral numerical characteristics of the estimation accuracy were used, namely: the total squared of the offset (deviation) of the expected implementation of a certain variant of the estimate from all possible parameters of the binomial test plan. Results and Conclusions. The estimate of failure probability ${\hat P_3}$ should be recognized more effective in comparison with the proposed ones, as having a minimum displacement and close to the minimum variation of its values. The constructed composite estimate of failure probability ${\hat P_3}$ allows escaping from the incident, when we assess the situation as a reliable event in failure-free tests. At the same time, when failures occur, the ${\hat P_3}$ estimate fully coincides with the absolutely effective estimate $\hat P = 1 - R/N$, which, in this case, allows using it for any results (R>0) of the binomial tests instead of the estimate $\hat P$. The MTTF estimate ${\hat T_4}$ should be recognized more effective in comparison with the proposed ones, as having a minimum displacement and a minimum variation. The constructed estimate ${\hat T_4}$ allows estimating the MTTF with a finite value in case of failure-free tests conducted according to the binomial plan. However, the estimate ${\hat T_4}$ is constructed on the assumption that time to failure has an exponential distribution. If the distribution of time to failure is not known, the non-parametric estimate ${\hat T_0}$ has an advantage in its efficiency