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Reliability Computation Using Logistic and Extreme-Value Distributions

Aliakbar Montazer Haghighi, Mohammed A. Shayib


The estimation of the reliability, R, where R = P(Y less than X), has been considered in the literature in both distribution-free and parametric cases. In particular, when X and Y are assumed to be independent identically distributed (iid) random variables, R has been extensively studied in the literature using various types of distribution functions. In this paper, utilizing the Maximum Likelihood Estimator (MLE), considering logistic and extreme-value type I distributions, estimation of the unknown parameters of these distributions are discussed and estimation of R is given. The effect of sample size and values of ratios of parameters to different estimates of R in different cases is also studied. The MSE analysis is carried on the assumed distributions.


Reliability; Logistic; Extreme-Value; Distributions; MLE

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