International Journal of Computer Applications (0975 – 8887) Volume 86 – No 10, January 2014 35 Reliability Analysis of a Discrete Life Time Model Sandeep kumar Hindu College University of Delhi Birjesh Kumar, Ph.D J.P Institute of Engg.& Technology, Meerut Alka Chaudhary, Ph.D Meerut College, Meerut C.C.S. University, Meerut ABSTRACT Several studies deals with life testing of various systems with respect to Reliability characteristics. The life testing generally considered a continuous life time Distribution. However, there are situations when life times are recorded on discrete scale. In life testing, Geometric distribution has an important role in such type of analysis. A vast literature on the life testing plans in the Bayesian framework is also available where the parameter of basic life time distribution is considered as a random variable. The present study deals with the development of the methodology for life testing in terms of classical, modified classical and Bayes Reliability. Keywords Classical Component Reliability ( CCR),Modified Classical Component Reliability(CCR*), Bayes Component Reliability(B C R). 1. INTRODUCTION Reliability theory a branch of statistical science, has an effective role in the rapid advancement in human amenities, such as modern electronic computers, televisions, washing machines, electronic locomotives, refrigerators, mobile and cell phones, etc. When a manufacturer floats a new brand of light bulb in the market, he would like his customers to have some information about the average life of his product. Life testing experiments are designed to measure the average life of the component or to answer such questions as “what is the probability that the item will fail in the time interval [ 0 t , 0 t t  ] given that it was working at time 0 t ”. In simple life testing experiments a number of items are subject to tests and the data consist of the recorded lives of all or some of the items. Studies in life testing generally consider a continuous lifetime distribution. However, there are situations when lifetimes are recorded on a discrete scale. For example, the lifetime of light bulb lights up whenever a paper enters the machine i.e. the bulb functions at discrete time epochs and can fail after providing a certain number of prints. In this case, the lifetime is defined as the number of successful operation of a device before failure. Obviously, the geometric distribution has an important place in such analysis. Life testing is a costly and time consuming phenomenon, and, therefore, it should be recognized that the parameters, characterizing reliability characteristics, in a life time distribution are bound to follow some random variations due to environmental changes. So it is a factor which should be considered with experimental data for analyzing the reliability characteristics of the systems. Obviously, the Bayesian analysis of the various reliability characteristics of systems becomes important. A comparative study in this regard is by Martz and Walher [1982]. Bhattacharya [1967] presented the Bayesian analysis of the system reliability using many prior distributions. Studies like Brush [1986], Brush et, al [1981], and Sharma et., Al.[1992, 1993, 1994, 2005]are also efforts in the same direction following the concepts, posterior analysis of some other reliability characteristics like availability, hazard functions, MTSF etc. of certain complex static system will be considered in the study. 2. NOTATIONS MTSF : Mean time to system failure    Rt PX t   : Reliability of Independent and identical components for a mission time t. CCR : Classical Component Reliability. CCR* : Modified Classical Component Reliability. BCR : Bayes Component Reliability .  km R t : Classical reliability of a k-out of m system. R* km (t) : Modified Classical Reliability of a k-out of m. BR km (t) : Bayes Reliability of a k-out of m system. R S (t) : Classical Reliability of a series system. R* S (t): Modified Classical Reliability of a series system. BR S (t) : Bayes Reliability of a series system. R P (t) : Classical Reliability of a parallel system. R* P (t) :Modified Classical Reliability of a parallel system. B P (t) : Bayes Reliability of a parallel system. 3. STATISTICAL BACKGROUND For developing the procedure, it is assume that- (a) Suppose a lot of N items, is to be tested with a life testing operation. Let the life time distribution of each items be geometric with p.m.f.     , 1 . ; x f X      x = 0, 1, 2 ... 0 1    …. (1) With MTSF= E[X] = (1 )    ; V[X] = 2 (1 )   