Differential Importance Measure for Components Subjected to Aging Phenomena

Stefano La Rovere,Maria Sperandii,Paolo Vestrucci,Claudia Mandurino

doi:10.1155/2013/945039

Stefano La Rovere, Maria Sperandii + Show 2 more

Open Access

https://doi.org/10.1155/2013/945039

Copy DOI

Abstract

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.

Highlights

Several studies have demonstrated that components do not contribute to system performance in the same way [1, 2]
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
In all cases, we provide analytical equations that allow the estimation of the first-order Differential Importance Measures for components and parameters, on the basis of the Birnbaum measure for components, which only depends on the system function and can be estimated through (4)

Summary

Introduction

Several studies have demonstrated that components do not contribute to system performance in the same way [1, 2]. Importance measures allow the ranking of the input variables of the model which can be the components unavailability and/or the parameters that define their failure and repair probability distributions, according to the contribution of their changes to the model output (system unavailability). The estimation of the “DIM for parameters” provides information about the importance of the random failure, aging phenomena, and corrective and preventive maintenance separately but requires the knowledge of the first-order partial derivatives of the system unavailability with respect to each parameter. We provide some general information about systems made by repairable binary components under aging phenomena and preventive maintenance [5, 7, 8] and about the Differential Importance Measures [9]. We solve some examples taken from paper [8], verify the correctness of the analytical equations, and showing advantages of their use

Background

Techniques and Models

Results and Discussion

Conclusions