Modern Aspects of Probabilistic Distributions for Reliability Evaluation of Engineering Systems

Abstract

This chapter presents the modern aspects of probabilistic distributions and development of mathematical models of power components and systems for assessment of reliability. The probabilistic models to describe the process of failure follow exponential type, Weibull type, normal and lognormal type probability distribution patterns. These distributions are derived mathematically not empirically therefore termed as theoretical distributions. Among various, the exponential type of distribution is the most important one. Many industrial systems exhibit constant failure rate (CFR) and therefore the simplest exponential distribution is the first choice for comprehensive analysis of these systems. The other probabilistic models of normal, lognormal, and Weibull type distributions have increasing and decreasing hazard rate as a function of operating time, which gives an alternative to exponential failure law. The comprehensive aspects related to above distributions have been described in detail with mathematical models, numerical interpretations, industrial problems, and reliability assessment approaches. © 2024 by The Institute of Electrical and Electronics Engineers, Inc. All right reserved.