Reliability Analysis of a 1-out-of-n Cold Standby Redundant System under the Generalized Lindley Distribution

Cold standby 1-out-of-n redundant systems are well-established models in system reliability engineering. To date, reliability analyses of such systems have predominantly assumed exponential, Erlang, or Weibull failure distributions for their components. The Lindley distribution and its generalizations represent a significant class of statistical distributions in reliability engineering. Certain generalized Lindley distributions, due to the appealing characteristics of their hazard functions, can serve as suitable alternatives to other well-known lifetime distributions like the Weibull. This study investigates the reliability of a 1-out-of-n cold standby redundant system with perfect and imperfect switching, assuming that the active component failure times follow the Generalized Lindley distribution. We derive a closed-form expression for the system reliability. To achieve this, the distribution of the sum of n independent and identically distributed random variables following the Generalized Lindley distribution is first determined using the moment-generating function approach.