Stochastic Modeling and Cost Analysis of some 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 mechanical equipment. A mathematical shape to the word reliability was given later in 1950 with its scientific use for defence purpose. Realizing its importance, the study of reliability theory was developed in western world. The present thesis entitled “Stochastic Modeling and Cost Analysis of Some Industrial Systems” is an attempt to develop the reliability models of the system with varied production capacity depending upon the demand with following objectives: (i) Understanding the process of industries and to create model(s) for the selected industrial system. (ii) To analyse the reliability and availability of industrial system to be considered. (iii) To analyse various other measures like cost-benefit analysis, busy period, mean time to system failure and expected number of visits by repairmen using Semi- Markov process and Regenerative point technique. (iv) To compare the effectiveness of the systems on the basis of the models (to be developed) taking two at a time using Semi-Markov process and Regenerative point technique. Data on failure / repair time and various costs has been collected on visiting Kohinoor Rice Mill. The reliabilities have been developed by considering various situations existing in the mill visited. Mean Time to system Failure and various other measures of system effectiveness have been obtained using Semi-Markov process and Regenerative Point Technique. For calculating measures of system effectiveness programming is done in MATLAB. The graphical study of these measures has been done in ORIGIN. Laplace / Laplace Stieltjes transforms and convolution are used for deriving expressions for these measures of system effectiveness. For solving system of equations Cramer’s rule is used.

The present thesis embodies seven chapters: Chapter 1 is an introductory chapter. It includes fundamental concepts and methodology related to work done. In this chapter, we briefly discuss industrial significance of the reliability and long run availability of industries. A brief summary of the available literature has also been presented in this chapter. This chapter also contains description of the system considered in this thesis. Further, in this chapter the work of the remaining chapters has also been presented. In chapter 2, we discuss the behavioural analysis of a two dissimilar unit standby system working in a rice plant by making one or both units operative depending upon the demand. System consists of following components: Paddy separator, husker, separator, destoner, polisher and colour sorter. Each unit has two types of failure-one due to failure of the component colour sorter which is referred as Type –I failure and the second due to failure of any of the other component(Paddy separator, husker, destoner, polisher) referred as Type – II failure. The processing done on each of the components other than colour sorter is transferable to component of other unit but the processing pending due to failure of colour sorter is completed only on concerned unit after it is repaired. Regenerative point technique has been used to analyse the system. Both failure and repair rates are assumed to follow exponential distribution. Effect of failure rates on availability and MTSF has been carried out. Effect of revenue and cost of busy period on profit has also been discussed. In chapter 3, a standby system is studied which comprises two dissimilar units out of which one is of 8 ton capacity and other is of 4 ton capacity. In this chapter, we have considered the different stages where production is less than demand or at least equal to demand. In case of production less than demand, we have analysed the system with two types of failures and variation in demand by considering the loss of goodwill. Failure time and repair time both are assumed to follow exponential distribution. Repair facility is always available for every failed unit i.e. no unit waits for repair. It is assumed that, in case of production greater than or equal to demand and if one unit is under repair and other is operative, then no other event can take place except decrease in production. Effect of revenue of different capacity on profit has also been discussed along with effect of failure rate on availability of different capacities in both the cases when production is less than demand and when production is at least equal to demand. Chapter 4 is devoted to a stochastic model for a three-unit standby system wherein one, two or all the units may be made operative depending upon the load/demand. The system under consideration is assumed to have two shifts of working. The system to be considered comprises of three units of paddy to rice converters having different capacities. One is of 8 ton capacity and another two are of 4 ton capacity. Priority of operation is given to line of capacity 8 ton instead of 4 ton. Effect of revenue of different capacity on profit, effect of failure rate on MTSF and availability of different capacities has been discussed in this chapter. Graphical study is also carried out. Chapter 5 describes a two similar unit (eight ton capacity) standby system which is analysed with variation of demand and two types of failures. We have considered a single unit of eight ton capacity in place of two similar units of four ton capacity each as in the preceding chapter. Keeping in mind the installation cost of one big unit in place of two small units here, we have analysed a two similar unit standby system with varying demand and two types of failures. We have considered arbitrary distribution for repair rates. Effect of failure rates on availability and MTSF has been carried out. Effect of revenue and cost of busy period on profit has also been discussed. In chapter 6, the comparative study of effectiveness of models discussed in the chapters 3, 4 and 5 with respect to profit evaluation has been discussed. In this chapter, we also analysed the suitability of models discussed in previous chapters in different situations. Chapter 7 is concluding chapter of thesis. The industrial significance along with the limitations and scope of the present work has also been briefly discussed in the summary and conclusion.