Importance Measure on Finite Time Horizon and Application to Markovian Multi-state Production Systems

The sensitivity analysis of complex industrial systems aims at identifying, in a multi-unit structure, which components contribute the most to a variation of the performance criterion. In this paper an importance factor, called multi-directional sensitivity measure, defined as the derivative of the performance in the direction of one parameter, in the direction of a group of parameters (failure and repair rates of components for example), or in any direction of the transition rates of a Markovian system is considered. This importance factor proposed for sensitivity analysis of steady state reliability is developed herein for the transient state. It is also extended and applied to the study of the production capacity of multi-state production systems, such as e.g. manufacturing, production lines, which exhibit performances that can settle on different levels depending on the operative conditions of the constitutive components. A simple numerical example is introduced to show why this factor provides an efficient tool to investigate not only the importance of a given component, but also the importance of a class of components, the importance of the maintenance, and, more generally, the effect of the simultaneous change of several design parameters.