The Maximum Failure Time Distribution

For systems with parallel components, the variable of primary importance is the maximum of the failure times of the different components. In this paper, we study the exact probability distribution of the maximum failure time. Explicit expressions are derived for the cumulative distribution function, probability density function, hazard rate function, moment-generating function, nth moment, variance, skewness, kurtosis, mean deviation, Shannon entropy, and the order statistics. Estimation procedures are derived by the methods of moments and maximum likelihood. We expect that these results could be useful for performance assessment of parallel systems.