Importance measure on finite time horizon and application to Markovian multistate production systems

Abstract

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 measure, called multi-directional sensitivity measure, defined as the derivative of the system performance in the direction defined by a vector (or matrix) in an appropriate space (e.g. direction of one parameter, of a group of parameters, or generally any direction of the transition rates of a Markov process) is considered. This measure 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 manufacturing, production lines, and power generation, 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 measure 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 1 design parameters.

Importance analysis considering time‐varying parameters and different perturbation occurrence times

“…Obtaining the closed-form solution for Equations (12) and (13) is not possible in most cases, even considering exponential distribution that is an easy distribution to work with. 1 Hence, a simulation approach is proposed to calculate Equations (12) and (13). In this respect, ∫ F τ ð Þdτ=T is the percent of time from zero to T that the system is not working.…”

“…Large difference of the system performance metric in the above two conditions implies large importance of the parameter with respect to its influence on the system performance metric. 11,12 Evidently, for different nominal values of the parameter, different parameter importance values are obtained. Therefore, knowing that in real systems, the parameters values change in time 1,2 and a perturbation can occur to their values at any time during the system mission time, it can be deduced that the amount of change in the value of the performance metric depends on the parameters values perturbation times.…”

From differential to difference importance measures for Markov reliability models

“…This directional derivative is used as an importance measure in reliability and productivity sensitivity analysis in [11] and [9] respectively.…”

Differential importance measure of Markov models using perturbation analysis

“…It is used as an importance measure, namely multi directional importance measure, in reliability sensitivity analysis (Do Van et al 2008c; Do Van et al 2008a),…”