Estimation of reliability characteristics in a production scheduling model with failures and time-changing parameters described by Gamma and exponential distributions

In the paper a classical model of failures is considered in that successive failure-free times are supposed to have Gamma distributions and are followed by exponentially distributed times of repairs. It is assumed that parameters of these distributions, in general, change with time. Basing on information about the number of failures and failure-free times in a number of periods of the same duration in the past, three different methods of estimation unknown parameters of the model are proposed. Next, predictions of the most important reliability characteristics are found.