حساسیت و تجزیه و تحلیل حساسیت از اجزای یک سیستم

In the design of complex systems there is a great interest to know the relative importance of each of their elements. In this paper, we define a new method for measuring the relative importance of each element of the system. We have to specify that this paper concerns only non-repairable systems and components. We present a way of calculating the criticality of each component for a complex system no matter what the random distribution of the life of the component is. The paper also demonstrates a simple way of calculating how the system life improves when the life of a component is improved.

The relative importance of the components of a system has been widely studied. The measures of importance are basically of two kinds: functional importance (that is, importance in relation to the reliability of the system) and structural importance. We consider only non-repairable systems and components. Barlow [1], Boland [2] and Tong [3] have studied the structural importance of the components of a system and more recently Meng [4] and [5] has presented new measures of that kind. Natvig [6] and Bergman [7] propose other measures of the importance of the components of a system. It is also interesting to consult Wall [8], Cheok [9] and Dutuit [10] about measures of importance and some others factors of importance. In this paper a new method is proposed for the importance of components from a functional point of view by studying how the system life improves when the mean life of a component is improved. With this knowledge one can highlight which component (or components) must be given greater attention, when all the components are independent from each other.

In this work, we have defined a new measure of the relative importance of an element of the system for its mean life, when we deal with non-repairable systems and components. The measure of the relative importance of the component is made by means that we have defined as sensitivity for a component, expressed as the partial variation of the mean life of the system in respect to the mean of the component. We have demonstrated that for serial, parallel or complex systems, with the components distributed as exponentially and independents, we obtained the partial variation of the mean life in respect to the component as a product of the probability of criticality and the critical mean life of the component and divided this product by the mean life of that component. This form of obtaining the measure of relative importance of a component has been demonstrated analytically when components follow a uniform distribution. For more general components and forms of the graph of the system, we carried out a demonstration using the Monte Carlo method.