Importance Measures in Repairable Multistate Systems With Aging

Abstract

Within the field of reliability multistate systems represent a natural extension of the classical binary approach. For an extensive introduction to this topic, see Natvig (2011b). Repairable multistate systems quickly become too complex for exact analytical calculations. Fortunately, however, such systems can be studied efficiently using discrete event simulations. See Huseby and Natvig (2012). In the binary case importance is usually measured using the approach by Birnbaum (1969). Several authors have extended the notion of importance measures to multi-state systems. See e.g., Zio et al. (2007) and Huseby et al. (2020). In the latter paper the component state processes were modelled as homogenous semi-Markov processes. Such processes typically reach stationary states very quickly. Thus, most properties of the system can be analysed using asymptotic distributions which typically are determined by mean waiting times and the transition matrix of the built-in Markov chain. In the present paper we follow the approach suggested by Huseby et al. (2020). Here, however, we focus on the non-homogenous case. This is relevant in systems subject to e.g., seasonal variations or aging. In order to model this we use an approach similar to Lindqvist et al. (2003). When the component processes are not homogenous, the analysis should cover the entire time frame, not just the asymptotic properties. This makes comparison of importance more complicated. Several numerical examples are included in order to illustrate the methodology.