Transient throughput analysis for a series type system of machines in terms of alternating renewal processes

This paper presents both a closed form and a sample path method to calculate and estimate the performance indices such as the mean and variance of the transient throughput, and the probability that the total outputs will satisfy the demand on time for a series system of unreliable machines with the same production rate and without intermediate buffers. These approaches have to rely on the assumption that each machine is modeled in an alternating renewal process (with Up times and Down times following exponential distributions, respectively, in developing the closed form method). When machines have different production rates, we may treat the system approximately as the one whose machines have the same production rate which is the smallest production rate among machines. Numerical experiments that compare values of these performance indices by different methods are illustrated in terms of such a series system but of identical machines cited from literature. The sensitivity of these indices with respect to either mean time to failure or mean time to repair is also investigated to see how and how much improvement can be achieved in terms of such a system.