Thesis (Ph.D.) - Cairo University - Institute of Statistical Studies And Research - Department of Mathematical Statistics

A large number of continuous lifetime distributions has been proposed during the last few decades, some of them have been extensively studied and modified. Although few work has been done in discrete reliability, several discrete lifetime distributions have been also proposed. Most reliability studies assume that time is continuous, but sometimes, system lifetimes cannot be measured with calendar time, for example, when an equipment is monitored only once per period and the observation is the number of time periods successfully completed prior to failure, or when an equipment operates in cycles or on demands, and the number of cycles or demands prior to failure is observed. In such situations, system lifetime is a discrete random variable, then, the usual reliability concepts for continuous lifetimes have to be defined again to be adapted to discrete time.Therefore, many discrete analogues of continuous probability distributions were suggested by many researchers using different methods of discretization. In this work, the concept of "Discretization" is studied in detail, four methods of discretization and the corresponding discretized distributions are reviewed, the parameters of two types of the discrete Weibull distributions are estimated, and a new discrete analogue of the finite power function distribution is proposed. Mathcad and microsoft Excel programs are used to simulate data and obtain the parameter estimates for the suggested studied distributions

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