Differential Importance Measure for Components Subjected to Aging Phenomena

The paper refers to the evaluation of the unavailability of systems made by repairable binary independent components subjected to aging phenomena. Exponential, exponential-linear, and Weibull distributions are assumed for the components failure times. We assume that components failure rate increases only slightly during the maintenance period, but we recognize the effectiveness of preventive maintenance only in presence of aging phenomena. Importance measures allow the ranking of the input variables. We propose analytical equations that allow the estimation of the first-order Differential Importance Measure (DIM) on the basis of the Birnbaum measures of components, under the hypothesis of uniform percentage changes of parameters. Without further information than that used for the estimation of “DIM for components,” “DIM for parameters” allows considering separately the importance of random failures, aging phenomena, and preventive and corrective maintenance. A two-step process is proposed for the system improvement, by increasing the components reliability and maintainability performance as much as possible (within the applicable technological limits) and then by optimizing preventive maintenance on them. Some examples taken from the scientific literature are solved in order to verify the correctness of the analytical equations and to show their use. 1. Introduction Several studies have demonstrated that components do not contribute to system performance in the same way [1, 2]. Thus, it is essential for analysts to identify “critical" components [3]. Importance measures allow the ranking of input variables of a model [4]. This turns out to be a crucial problem when the model of the system (in a general sense) includes a variety of input variables and structural parameters. This is certainly the case of nuclear power plants and their probabilistic risk assessment [1, 5–11]. In this paper, we are interested in the unavailability of systems made by repairable binary components, under “perfect,” corrective, and preventive maintenance (i.e., components are “as good as new” after maintenance). We assume the exponential distribution for the components repair times. Aging phenomena are introduced into the model through time-dependent failure rates, by assuming the Exponential-linear distribution [5] and the more general Weibull distribution for the components failure times [7]. As in paper [8], we suppose that components failure rate increases only slightly during the “Maintenance period”. It allows referring to constant “effective” failure rate of components.