Differential Importance Measure for Components Subjected to Aging Phenomena

The paper refers to the evaluation of the Unavailability of systems made by repairable binary components subjected to aging phenomena. Exponential, exponential-linear and Weibull distribution 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 used for the estimation of “DIM for components”, “DIM for parameters” allows considering separately the Importance of random failures, aging phenomena, preventive and corrective maintenance. A two-step process is proposed for the system improvement, by increasing the components reliability and maintainability performances as much as possible (within the applicable technological limits) and then by optimizing preventive maintenance on them. Some examples taken from scientific literature are solved in order to verify the correctness of the analytical equations and to show their use.