Reliability Modeling and Analysis of Some Process Industrial Systems

Abstract

The study of operational research started during the second world war and afterwards. With the development of operational research, the study of reliability theory emerged as by product in context of defence studies. The words reliable and reliability are in use from ancient time. In fact these occur frequently in social, political, economical and practical fields to indicate the efficiency of a person or a mechanical equipment. A mathematical shape to the word reliability was given later in 1950 with its scientific use for defense purpose. Realizing its importance, the study of reliability theory was developed in western world. The development of reliability technology in India is an interesting and encouraging history for researchers. The theory of reliability plays an important role, directly or indirectly in almost all of our daily life problems. Some of the systems whose reliability is of immediate concern to the society in general are power, transportation, medical care, steel and communication industries etc. The history of modern engineering reflects that system failures can occur in any field. Industrial accident in Union Carbide, Bhopal in 1984 and power reactor accident in Chernobyl, USSR in 1986 are prime examples of complex system failure. The reliability analysis of an industry can help the management in taking timely decision for its smooth functioning. This can also help the management to understand the effects of increasing/decreasing repair rate of a particular component or sub system. In order, to obtain maximum output it is necessary to run each of the unit in good condition, i.e. each part of the equipment of the unit should run failure free. Therefore, in the present analysis we have focused on the work about reliability, modeling and analysis of some process industrial systems. The present thesis consists of six chapters. Chapter I presents the historical background and development in the field of reliability technology. In this chapter, we briefly discuss industrial significance of the reliability and long run availability of some process industries. The basic concepts of reliability and methodology of solution have been extensively explained. A brief summary of the available literature on the subject have been given in this chapter. Further, in this chapter the work of the remaining chapters has also been presented.

In second chapter, the time dependents and long run availability of polytube manufacturing plant has been analyzed. The plant consists of five sub-systems, namely, mixer, extruder, die, cutter and trifling chute. The failure rate of trifling chute has been found to be very low and assume to have never failed. As per the industry the subsystems cutter and die can work in the reduced state. The transition rates of the all subsystems which lead to the failed state of the system have been assumed to be variable. Behavior analysis of the system has been discussed by assuming that the subsystems cutter and die fail simultaneously. The governing equation determining the reliability of the polytube manufacturing plant has been derived using mnemonic rule from the transition diagram. The equation thus formed is known as Chapman Kolmogorov differential equation consisting of the system of partial differential equations. This partial differential equation has been solved by using Lagrange’s method to obtain the time dependent availability. The effect of failure and repair rates of the subsystems on long run availability has been analyzed taking the real data from the process industry. Chapter III deals with the availability of polytube industry when the subsystems cutter and die fail independently. The governing equations determining the availability of the polytube manufacturing plant has been derived using mnemonic rule from the transition diagram. The Chapman Kolmogrorov differential equations have been thus formed. These partial differential equations are next solved by using Lagrange’s method to obtain the time dependent availability. The long run availability has been analyzed by taking constant failure and repair rates of the subsystems. Certain conclusions based on the study have also been presented in this chapter. In chapter IV the behavioral analysis of time dependent availability and long run availability of rice plant has been discussed. This plant has six units namely: elevator, husking, separator, cleaning, whitening and polishing, all working in series. The concept of pending failed state has been introduced to perform preventive maintenance. This problem has been studied when preventive maintenance of the husk and separator machines are performed. As multi component repairable systems with variable failure and repair rate distribution are difficult to handle mathematically, supplementary variables have been interoduced to change the non markovian character into markovian character. The mathematical formulation for determining the availability of rice plant has been carried out in the form of system of partial differential equations. The partial differential equations thus obtained have been solved by using Lagrange’s method to obtain the state probabilities for various choices of constant failure and repair rates of the subsystems. We have also considered the constant failure and repair rates of the system. With these assumptions the governing partial differential equations reduce to systems of ordinary differential equations. The system thus obtained has finally been solved numerically by using Runge-Kutta fourth order method for suitable choices of constant failure and repair rates. The long run availability of the plant is also computed by solving the equations recursively. The effect of failure and repair rates on availability of the system has been analyzed critically with the help of tables and diagram. The analysis of time dependent and long availability of the main parts of the steel industry having mixed, series and parallel configuration has been studied in chapter V. This industry consists of four subsystems. The first subsystem grinding machine is subjected to major failure and the subsystems descaling mill and the hot steckel mill work in the reduced capacity. The whole system remains operative for a short period of time. The system works under the assumptions that failure and repair rates are variable. The mathematical formulation has next been carried out by using supplementary variable technique. The governing partial differential equations thus formed have been solved by using Lagrange’s method for various combinations of variable failure and repair rates. As a special case again failure and repair rates are taken as constants and the governing differential equations have been reduced to system of ordinary differential equations which have further been solved numerically using the fourth order Runge -Kutta method. The effects of failure and repair rates of the subsystems on long run availability of the system have been studied by taking the real time data obtained from the process industry. Based on the present study of various process industries conclusions have been finally presented in chapter VI. The industrial significance along with the limitations and scope of the present work has also been briefly discussed in this concluding chapter.