Fuzzy Set-Based Reliability Estimation

Introduction

The term “reliability” refers to a system's ability to function without fail. It can be described as a quantitative measure in the sense of probability. To put it another way, a system's reliability is the probability that it will work properly within a predetermined time interval. Time can be continuous or discrete. Most researches have done Reliability Estimation on discrete time (Cheung RC, 1980; Hsu, C. J., & Huang, C.Y.,2011; Gokhale, S. S., &Trivedi, K. S.,2002). The reliability of software is usually calculated in terms of a time unit. The failure probability is calculated as: PR (f) = 1 – pr. (If the whole probability of an event=1and pr= probability of success of an event as probability always range of 0 to 1). Now a days, Component-Based Software Engineering (CBSE) is rapidly used in every organization. The only approach to deal with the size and complexity of software components is to reuse them rather than re-implement them. CBSE is used in large scale which points an issue on component’s reliability and system’s reliability acquired by gathering the components. Reliability estimation for the whole system in component based approach is achieved by considering the reliability estimation of individual components associated with the system as well as transition probabilities associated between any two connected components within the system. An architecture-based reliability model for estimating the system reliability is presented in this paper.

In traditional reliability theory, components and structures are thought to have only two states, correct or incorrect. This means that success and failure are clearly defined and there are no intermediate states between them. However, in some cases, the above statement may not be correct. In addition to structural factors, other factors such as performance, quality, cost, and so on may influence the failure or success criterion. This leads to a broad concept of success and failure. The traditional system reliability problem is difficult to address when the components have distinct probability density functions (pdf). The conventional probability's weakness is in accounting for data uncertainty. As a result, instead of using the pdf of the components, we used fuzzy set theory and the membership functions to obtain the system reliability. In real world problem, we cannot say that the whole system is fully success or fully failure. Thus, uncertainty can be found almost everywhere. When we speak about uncertainty; we normally use a vague or everyday phrase like 'not quite certain’. In the early stage to estimate the reliability, most of the metrics are bias in nature. This paradigm focuses on the fuzzy inference system to deal with the lack of relevant data and uncertainty. Data uncertainty occurs due to a variety of reasons such as user’s inaccurate perception of failures, incorrect measurement, imprecise collections of reliability data etc. Fuzzy sets, fuzzy estimation and fuzzy probability theories are important tools to describe and analyze the uncertain values.

Motivation: It is important to acquire a high degree of reliability while building the software for application domains. This is a really difficult issue for the software industry nowadays. Software presently is expected to be self-adaptive, and as a result, it is frequently more complex. The optimization of a multi-objective problem in different areas is required to provide reliability for a complex system. To improve reliability estimation in component-based systems, several reliability models are proposed. But none of them operate optimally across several projects.

Objectives: The fuzzy logic technique is better than the statistical methods to estimate overall system reliability. The fuzzy concept refers to imprecision, approximation, uncertainty, and a chaotic environment.