RELIABILITY ANALYSIS OF SOME INDUSTRIAL SYSTEMS IN FUZZY ENVIRONMENT

Abstract

An industrial system is consists of numerous components/subsystems and the probability that the system survives, depends directly on each of its constituent components/ subsystems. These components/subsystems are expected to be operational and accessible for the most possible time to maximize pro t and overall production. But failure is nearly unavoidable phenomenon with technological products and systems. Further, age and undesirable operating conditions of production/ manufacturing processes a ect each part of the system di erently. Thus, there is a need to develop a suitable approach for analyzing the performance of these complex systems so that timely actions may be taken for achieving the goal of high production and hence more pro t. The performance analysis includes the study of main reliability attributes such as system reliability, availability, maintainability and risk and safety analysis of the system as well as of its components/units. Generally, system analysts model and analyze the system behavior through various qualitative and quantitative tools/techniques. These techniques require precise knowledge of numerical probabilities and systems'/components' functional dependencies which may be di cult to be obtained in any large-scale system as the data collected or available from the historical records are mostly uncertain, limited and imprecise in nature. In order to predict the behavior of a system, it is necessary to develop mathematical model that deals with the uncertain behavior of the system. With the growing complexity of system, advancement in technology and demand of product quality, the signi cance of reliability and availability becomes very important. Most iii iv of the systems in industry are repairable and it is expected that one should attain maximum pro t from them. Systems always exhibit some kind of uncertainty in their behavior because of the impreciseness of the data associated with these systems. The objective of this thesis is to develop methodology for analyzing performance and behavior of various repairable industrial systems under uncertain environment in di erent forms. The validation of the methodology is also a part of the objective. For that performance and behavior of Butter-Oil Processing Plant (BOPP), Condensate System, Piston manufacturing Plant and Cattle feed plant have been analyzed by using the available information about the systems' primary data. Herein the methodology is based on the amalgamation of techniques: namely, fuzzy set theory (and generalized fuzzy set theory), Runge-Kutta fourth order method and Particle Swarm Optimization. Reliability/Availability has also been studied through the solution of fuzzy di erential equations. System availability in steady state has also been studied in this thesis. The main advantage of the proposed approach is that it provides system analyst a valid range of prediction for all reliability measures by elaborating uncertain data. Through these approaches, system analyst may also optimize the reliability of system. Apart from this analysis, system reliability also has been studied through Intuitionistic fuzzy set theory. Sensitivity analysis has also been carried out for the reliability indices and e ects on system are addressed which will be helpful for the system analyst/ plant maintenance personnel to decide the best suited action and to assign the repair priorities as per the system requirements. The whole work of the thesis is divided into eight chapters and chapter-wise summary of the thesis is as follows: Chapter 1 covers the literature related to evaluation of system reliability/availability, behavior analysis using conventional methods, fuzzy approach based reliability analysis, reliability optimization etc. v Chapter 2 describes preliminaries and terminologies needed for the understanding of overall research work, presented in the subsequent chapters. The concepts of reliability, availability and their measures are discussed. Concepts related to Markov process, Particle Swarm Optimization, Fuzzy Set Theory, Generalized fuzzy and Intuitionistic fuzzy set theory have been described. Chapter 3 formulates a new methodology for behavior analysis of systems through fuzzy Kolmogorov's di erential equations and Particle Swarm Optimization. For handling the uncertainty in data, di erential equations have been formulated by Markov modeling of system in fuzzy environment. Firstly solution of these derived fuzzy Kolmogorov's di erential equations has been found by Runge-Kutta fourth order method and thereafter the solution has been improved by Particle Swarm Optimization. Fuzzy availability is estimated in its transient as well as steady states. Sensitivity analysis has also been performed to nd the relative importance of a particular component of the system. Butter oil processing plant as an industrial system has been studied as a case for application of the proposed approach. Obtained results by the proposed technique have been compared with the results obtained by existed techniques. Chapter 4 is an extension of chapter 3 in the sense that here a technique for solving rst order linear di erential equations with fuzzy constant coe cients and fuzzy initial values is given. It is based again on -cut of a fuzzy set by formulation of optimization model. The approach, named as RKPSO, for solution of fuzzy differential equation is an amalgamation of Runge-Kutta (RK) fourth order method and Particle Swarm Optimization (PSO) technique. Some examples are discussed to illustrate the suggested approach. Furthermore, a concrete example of system of fuzzy di erential equations in more than one dependent variable is taken. The whole process is presented by evaluating the availability of a Piston manufacturing plant, which is a repairable industrial system. Sensitivity analysis of Piston manufacturing plant has also been studied in this chapter, which shows the simultaneous e ects of vi failure and repair rates on the system's steady state availability. Chapter 5 deals with performance analysis of an industrial system having uncertain behavior. In this chapter, reliability/availability has been computed through Markov process. Uncertainty in data has been dealt with generalized fuzzy numbers. Availability of system in transient as well as in steady state has been examined in this chapter. Results have been computed and then compared by performing different arithmetic operations' approaches. For application perspective of proposed approach, butter-oil processing plant has been considered. Impacts of di erent arithmetic approaches in the methodology are re ected by numerical calculations and are depicted through the graphs. Chapter 6 discusses the behavior analysis of a cattle feed plant, which has been investigated by using the approach, proposed through Particle Swarm Optimization and generalized fuzzy methodology. Uncertainties in the data are handled with the help of generalized fuzzy numbers and then behavior of the system has been analyzed in the form of various reliability parameters. In this methodology, availability analysis has been discussed through Markov process having uncertainties in the form of generalized fuzzy numbers in data. Obtained optimization problem, from the proposed approach, has been solved through particle swarm optimization. Application of the method has been shown by the evaluation of the availability of an industrial system. Chapter 7 studies a technique to examine the performance analysis of an industrial system in a more steady and logical manner. In this chapter, we have proposed a structured and methodological framework, to analyze a complex industrial system. In quantitative framework, a set of di erential equations is formulated through Markov modeling of industrial system in intuitionistic fuzzy environment. Intuitionistic fuzzy system availability is estimated in its transient as well as steady states. E ects of variations in failure and repair rates' have been studied for the purpose of sensitivity analysis and to determine the system's most crucial component. To vii study the behavior of the system, availability of the system for di erent ( ; )-cuts has been evaluated. The suggested approach is explained through the study of condensate system of Thermal power plant. Chapter 8 deals with overall summary of this study and brief discussion on the scope for future work.