Analysis of the Completion Time for the Job Processed on a Machine Subject to Stochastic Breakdowns

This article addresses the completion time of a job processed on a machine subject to the sequence stochastic breakdowns described by Birge et. al (1990). I present an general analysis on the first and second moments of the completion time. Let r and p denote respectively the starting time and processing time of the job. My contributions can be roughly stated as follows. (A) For the resume case, if r and p possess finite first and second moments, then the completion time has finite second moment. (B) For the repeat case, if r and p possess first and second moments and Pr{U_k ¿ p} > 0, where U_k represents the kth uptime, then the completion time has finite second moment.