Optimal designs of system reliability

Abstract

This study is concerned with economic models in systems reliability, and divided into the following four parts; i) Optimal designs of redundant systems with common mode failures are considered. Parallel, standby, and k-out of-n structures are analyzed. We find the optimal number of redundant units which minimize the expected cost rate. The ase in which the systems are inspected periodically is also studied. When the system fails before a predetermine inspection time, it is replaced by a new one. Otherwise, the failed units in the system are replaced. The expected cost rate is obtained and its behavior is examined. The effect of common mode failures to the optimal number of redundant units is studied numerically. ii) Replacement policies with repair cost limit are considered. In these models, the cost of repair is a random variable and the decision to repair or to replace is based on the cost of repair in relation to predetermined repair cost limit. If the cost of repair is less than the limit, the system is repaired. Otherwise, the system is replaced or overhauled. Repair cost limit replacement policies under minimal repair or imperfect repair are analyzed. In repair cost limit policies, replacement decisions depend only on the cost of single repair. Further cost savings may be possible if replacement decisions are also based on the history of the system. The replacement policies based on the system age and repair cost under minimal repair or imperfect repair are considered. iii) An inspection and replacement policy in redundant systems is discussed. It is assumed that the state of the system is known exactly only by inspection. When the system is inspected, it is replaced only if the number of failed units exceeds a predetermined limit. Otherwise, preventive replacement of a system is delayed to next inspection time. The optimal numbers of redundant units, inspection intervals and replacement limit are obtained. iv) As an economic model related to software...