THE CONSTRUCTION OF PROBABILISTIC RELIABILITY MODELS ON THE BASIS OF CURRENT STATUS DATA

In this paper, I consider the problems, which arise in construction of probabilistic lifetime models on the basis of data, obtained from the reliability experiment on one-shot devices. First of all, we are interested in reliability of those one-shot devices, which provide the ability of a spacecraft to perform its functions. In particular, the examples are the devices for fixing and unfixing mobile elements of a spacecraft: solar panels, radar antennas, disclosing bar devices and other equipment. One-shot devices are tested at some predetermined inspection times, and the experiment results in reporting the status of devices instead of an actual failure time. The failure time here is either left censored, if the test outcome is a failure, or right censored, if the test outcome is a success. The obtained sample of left censored and right censored observations (without complete observations), is called a current status sample. For a number of distributions, which are frequently used in reliability theory, I have investigated the ratio of the Fisher information about distribution parameters in a current status sample to the Fisher information in a complete sample of observations. As a result of maximization of the Fisher information, I have obtained the optimal inspection times (from the position of minimal variance of maximum likelihood estimates). I have proposed an algorithm for calculation of nonparametric estimator of lifetime distribution function by current status samples, which provides the maximum of the likelihood function by the values of distribution function at the points of inspection times. I have investigated the statistical properties of obtained nonparametric estimator depending on the sample size and the number of inspection times with Monte Carlo method. For testing adequacy of constructed probabilistic model by current status samples, the author has proposed the goodness-of-fit tests of Kolmogorov, Cramer-von Mises-Smirnov, chi-square and White types. The application of these tests requires the simulation of unknown conditional statistic distributions G ( S|H 0) for applied tests with Monte Carlo method. As the result of comparative analysis of proposed tests by power the chi-square type test can be recommended as the most preferable one.

reliability of one-shot devices, current status samples, maximum likelihood method, nonparametric estimator of distribution function, goodness-of-fit tests, accelerated failure time model, Monte Carlo method