In probability theory and statistics, the moment-generating function (UMGF) of a random variable is an alternative specification of its probability distribution. Thus, it provides the basis of an alternative route to analytical results compared with working directly with probability density functions or cumulative distribution functions. There are particularly simple results for the moment-generating functions of distributions defined by the weighted sums of random variables. Note, however, that not all random variables have moment-generating functions. The moment-generating function does not always exist even for real-valued arguments, unlike the characteristic function. There are relations between the behavior of the moment-generating function of a distribution and properties of the distribution, such as the existence of moments.
Published in Chapter:
A Comparison for Optimal Allocation of a Reliability Algorithms Production System
Abdelkader Zeblah (University of Sidi Bel Abbes, Algeria), Abdelkader Rami (University of Sidi Bel Abbes, Algeria), and Eric Châtelet (University of Technology of Troyes, France)
Copyright: © 2015
|Pages: 30
DOI: 10.4018/978-1-4666-7258-1.ch018
Abstract
The most important phase in many industrial power applications is the design problem. Usually the demand increases randomly with time in the form of a cumulative demand curve. To adapt the power system capacity to the demand, new power architecture is predicted. To build this latter, the reliability optimization plays an important role to find the realizable power system architecture. This chapter describes and uses different meta-heuristics optimization methods to solve the redundancy optimization problem for multi-state series-parallel power systems. The authors consider the case where redundant power components are chosen to achieve a desirable level of reliability. The power components of the system are characterized by their cost, capacity, and reliability. The proposed meta-heuristics seek the optimal architectures of series-parallel power systems in which a multiple choice of components are allowed from a list of products available in the market. The approach has the advantage of allowing power components with different parameters to be allocated in power systems. To allow fast reliability estimation, a Moment Generating Function (MGF) method is applied. An illustrative example is presented.