Reliability Engineering Case Study

Chapter (2)
RELIABILITY OF POWER PLANTS

1.1 INTRODUCTION

The importance of reliability in industry is increasing due to factors such as high cost and impact of system failure, increasing complexity and sophistication of systems, and competition. Reliability engineering is implemented by taking structured actions towards maximizing the reliability of systems and minimizing the effects of failures. Generally, three steps are necessary to achieve this objective. These steps are related to the life cycle of the system. In the first stage of the system, which is the design and development stage, it is essential to build maximum reliability into the system. Great care has to be taken into this critical step as it determines the inherent reliability.

Sections 2.3 presents statistical distributions that are commonly uses in reliability applications along with the basic properties of these distributions. Section 2.4 briefly discusses the concept of Markov models. A basic procedure for reliability monitoring is presented in section 2.5.

2.2 RELIABILITY STATISTICS

NIST/SEMATECH (2016) defines reliability as “quality changing over time.” Reliability is measured as the probability that a component/system performs its intended function(s) adequately for a given period of time under certain stated conditions (Dhillon, 2005). Thus, the reliability function of a system is given by

R(t)= P(T>t)= ∫_t^∞▒〖f(u) du〗=1-F(t) (2.1)

In other words, the reliability function R(t) represents the probability that the system’s lifetime, T, is greater than a certain specified period t. The lifetime of a system is treated as a random variable with f(t) as its the probability distribution function (PDF). The complement of the reliability function is the unreliability function, F(t). It is the cumulative distribution function (CDF) of the lifetime random variable T. This function represents the probability failure occurrence during the specified time period t. Thus, it is called the unreliability function. Another important measure of reliability is the mean time to fail (MTTF), which is

This region is often referred to as the useful life of the component. The failures that occur in this interval are chance failures or random failures. They are usually caused by chance events such as accidents, overloading, etc. In the third interval (t_2,∞), the hazard function is increasing. This interval is often called the increasing–failure–rate (IFR) period or the wear-out failure period. The failures that occur in this period are due to wear-out, aging, or serious deterioration of the component. The life of the component is close to its end once entering this period, It should be replaced or scrapped unless there is preventive maintenance or major overhauls to revitalize the component (Kapur and Pecht, 2014; Lie and Xie, 2006; Verma et al., 2016) Figure 2.1 represents a typical bathtub curve; however, different systems and components might have different shapes of the bathtub curve. Electronic components/systems usually have a very long useful life period (CFR period). Computer software generally have a continuously decreasing failure (DFR), as software bugs are detected and fixed, without a wear-out period. While mechanical components/systems usually have a long wear-out failure period (IFR period). In this period, preventive maintenance measures are continuously used to extend the lives of such components/systems. Some examples of bathtub curves with different shapes are shown in Figure 2.2 (Kuo and Zuo,