| Summary: | 博士 === 國立清華大學 === 工業工程與工程管理學系 === 91 === In this dissertation, a closed form formula is presented first to calculate the performance indices for a series system of unreliable machines with the same production rate and without intermediate buffers. Such indices include the mean and variance of the transient throughput, and the probability that the total outputs will satisfy the demand per processing time. To both fasten computation and be valid under broader conditions than those required under the closed form formula, a sample path method is also proposed. Such two approaches have to rely on the common 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 smallest production rate among machines as the same production rate. Numerical experiments that compare values of these performance indices by different methods are illustrated for a benchmark example, which is a series system of N identical unreliable machines cited from literature for a variable N. The sensitivity of these indices with respect to either MTTF or MTTR is also investigated to see how and how much improvement can be achieved for such a series production system.
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