Availability Analysis for the Quasi-Renewal Process

• Published in: IEEE transactions on systems, man and cybernetics. Part A, Systems and humans Vol. 39; no. 1; pp. 272 - 280
• Main Authors: Rehmert, I.J., Nachlas, J.A.
• Format: Journal Article
• Language: English
• Published: IEEE 01-01-2009
• Subjects: Approximation; Availability; Availability functions; Banking; Cybernetics; Degradation; Deterioration; Distribution functions; Laplace equations; Loans and mortgages; Mathematical analysis; Mathematical models; nonhomogeneous point processes; numerical approximations; Numerical models; Performance analysis; Random variables; reliability models; Repair; Stochastic processes
• ISSN: 1083-4427; 1558-2426
• DOI: 10.1109/TSMCA.2008.2007945

Historically, the behaviors of repairable systems were usually modeled under the assumption that repair implied system renewal. Availability functions were then constructed using renewal functions. Often, equipment is not renewed by repair, and for equipment that is not renewed, existing models fail to capture the key features of their behavior-ongoing degradation. More recently, nonrenewal models have been proposed to reflect the fact that equipment is usually not as good as new following maintenance. A wide variety of such models have been defined. They are usually called imperfect repair models. These models have the advantage that they are more realistic but they are also more complicated; therefore, analytical results for the models have been limited. In this paper, one of the nonrenewal models is analyzed, and an approach for obtaining a detailed measure of equipment performance, the point availability, is presented. The ultimate point availability function must be approximated numerically. Nevertheless, the analysis does lead to the time-dependent measure for a variety of possible distribution models. This paper contains two contributions to the study of repairable equipment performance. First, the models analyzed include both stochastic equipment deterioration and stochastically degrading repair performance over multiple operating intervals. Second, the analytical approach to obtaining the point availability function and its approximation is based on the combined analysis of operation-time- and downtime-based formulations of the system availability. This analytical approach to availability computation has not been used previously and is quite effective.