Abstract

In this article, the failure rates of the system's components are functions of time t. We study two cases (i) the mixture of two stages of life time distribution with weibull failure rates, (ii) the mixture of two stages failure rates with weibull distribution. The reliability equivalence factors of some systems with identical components are obtained. Two different methods are used to improve the given systems. Numerical examples are presented to interpret how one can utilize the obtained results. Some special cases are obtained from our results.

Key word: Weibull failure rate distribution, Rayleigh distribution, exponential distribution, mixture distributions, mixture failure rates, hot duplication, reduction method, reliability equivalence factors