Improving the efficiency of estimation of the dependability indicators of various test plans of homogeneous product

Abstract

Improving the efficiency of comparison of various test plans for homogeneous products is based on the use of the efficiency criterion of biased estimates C( ), where is a certain parameter estimate. The process of selecting efficient biased estimates involves the following: all parameters of the submitted estimates are to be strictly monotone; the estimates with minimal bias A( ) = b2 or close to it are chosen. If, in the process of selection out of the proposed estimates, there is a single unbiased estimate, then the latter is the efficient one. For this estimate to be efficient in the class of unbiased estimates, it is required to prove the Cram r-Rao inequality for such estimate; estimates, for which inequality A = b2 > D is fulfilled, i.e., the bias prevails over the value scatter of such estimate, are excluded; estimates are selected, for which the inequality D/A > 4 is fulfilled, i.e., the estimates, for which the realizations are grouped around the true quantitative value of the estimated parameter from different sides; out of the remaining estimates, the estimate with the minimum bias A( ) = b2 is selected. In case a single estimate with minimum bias A has been selected, such estimate is considered efficient; in case A are equal, the estimate with minimal variance is chosen as the efficient one. As the efficiency criterion of biased estimates, characteristic C( ) = D·b2 is specified. The suggested probability of no-failure (failure) estimates are to be strictly monotone in terms of all parameters and not equal to zero or one.The Aim of the paper. The paper aims to obtain efficient estimates of the probability of no-failure for the binomial test plan and the test plan with limited time and recovery using the efficiency criterion of biased estimates.Methods of research. A bias-efficient estimate was found using integral numerical characteristics of estimation accuracy, i.e., total squared bias of the expected realization of a certain estimate off of the examined parameters of the distribution laws, etc.Conclusions. Bias-efficient estimates were obtained of the probability of no-failure for the binomial test plan and the test plan with limited time and recovery. The obtained probability of no-failure estimates are practically applicable as part of testing and operation of various products not associated with failures.