The study of a maintenance float model with gamma failure distribution

Abstract

This paper considers an operational system made up of a number of independent and identical units. A given number, N, must be in service and it is supported by a maintenance float. We estimate the float factors using a Taylor series approximation of the gamma distribution for failures and a log normal function for repairs. From the model developed for the gamma case, the exponential, erlang-2 and degenerate cases are obtained. It is shown that the maintenance float factors approach asymptotic values for large N, This paper extends the previous research on maintenance float modelling and shows that the maintenance float factors are independent of N for large values of N. This property is used to obtain a simpler formula for maintenance float factor for the gamma failure distribution. Unlike the formulae obtained for the cases of exponential and Weibull failure distributions, the gamma failure yields a more complex formula. The asymptotic model considerably reduces the computational efforts involved.