Expected Value and Variance of Failure Time in Redundant Systems

Formulas are derived for the mean value and the variance of the distribution of time to system failure for parallel redundant and m out of n systems. A novel approach is used in the derivation which requires only elementary calculus and no explicit integration of specific functions. For the general case component failure times are assumed to be statistically independent and exponentially distributed. In addition, a special case of statistical dependence is treated.