An explicit formula for reliability of 1-out-of-n cold standby spare systems with Weibull distribution

Official URL: https://dx.doi.org/10.1142/S0218539322500292

Standby spare systems are particularly important because of their high reliability over other competing systems. A great deal of research has been done in the literature on these systems under various assumptions. Obtaining explicit reliability equations for such systems is achieved only when the failure behavior of their components follows the exponential distribution due to its ease of use. However, in practice, there are many components that their failure behavior does not follow the exponential distribution. In this paper, a closed-form equation is derived for the reliability of the 1-out-of-n cold standby spare system under conditions that the failure of the active component follows the Weibull distribution. The solution method for the system is based on the Maclaurin series and multinomial expansion.