University of Calicut

13 August 2020

Birnubaum Joint Importance Measures for Multi-State System

Information about the importance and joint importance of the elements constituting a system, with respect to its reliability, availability, risk and expected performance, is of great practical aid to system designers and managers in fields of power generation, nuclear industry, software industry, telecommunication, transportation etc. Indeed, the identification of which elements or group of elements mostly influence the overall system performance allows one to trace technical system bottlenecks and provides guidelines for effective actions of system improvement. In this sense, importance and joint importance measures are used to quantify the contribution of elements to the system performances. Importance Measures (IMs) were first introduced by Birnubaum (1969). The main objective of an importance ranking is to identify those components of a given system whose improvement may result in the greatest improvement for the system and to provide a checklist for failure diagnosis. Importance measures have received attention since the early times of risk and reliability analysis and have been defined in several ways for binary components in binary systems. Yet, there are far and wide applications for which a multistate modeling is required such as, power generation systems, nuclear systems, software systems, telecommunication systems, gas and oil transportation systems, Gandini (1990). The performance of such systems can settle on different levels (e.g. 100%, 80%, 50% of the nominal capacity), depending on the operative conditions of the constitutive multistate elements. Here the overall system operates at different, discrete, levels of performance so that output provided is a fraction of the normal design capacity. Systems characterized by different levels of performance are referred to as multistate systems. Barlow and Wu (1978) introduced the MSS. Griffith (1979), and El. Neweihi, et al. (1978) have studied the MSS and introduced component importance measures. More details on MSS importance measures can be seen in Bueno (1989) and Kim and Baxter (1987).

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