Basic probabilistic and statistical concepts for maintenance of parts and systems

Mathematical models are presented which are useful for determining when replacement or maintenance is needed. In addition, techniques for assessing the efficacy of maintenance and/or overhaul are discussed. Since the underlying concepts and techniques for nonrepairable items are relatively well known, attention is focused on repairable items. Moreover, great emphasis is placed on the major differences between the concepts, probabilistic models, and statistical analysis techniques appropriate for nonrepairable and repairable items respectively. Such emphasis is still required because the superficial similarities between nonrepairable and repairable items have contributed to the widespread use of poor terminology and notation which, in turn, make the similarities appear to be substantive, rather than just superficial. This vicious circle-which is still evident in most current reliability texts and standards-must be broken, and this paper is intended to contribute to this campaign. It is also stressed that, even to the very limited extent that repairable systems concepts and techniques are discussed in the literature, excessive emphasis is placed on reliability growth or improvement. This has resulted in even less understanding of basic notions of repairable-systems deterioration, i.e. of basic concepts associated with systems maintenance. This paper focuses on concepts connected with systems maintenance to help rectify this imbalance. Nonetheless, it is also stressed that the same models (with different parameters) can often be used for both situations.