Some New Discretization Methods with Application in Reliability

Deriving discrete analogues (Discretization) of continuous distributions has drawn attention of researchers, in recent decades. Discretization has been playing a key role in modeling life time data because in real world, most of original life time data are continuous while they are discrete in observation. In this paper, we introduce three new two-stage composite discretization methods to meet the need of fitting discrete-time reliability and survival data sets. All three proposed methods consist of two stages where using construction a new continuous random variable by underlying continuous random variable in the first stage and so based on maintaining hazard rate function in the second stage, discretization do. In the first two methods, hazard rate functions of discrete analogues are decreasing and increasing, respectively, and in the third method with this condition that there is maximum of underlying continuous distribution pdf, hazard rate function of discrete analogue and pdf of its continuous version have the opposite behavior. Therefore hazard rate functions of discrete analogues obtained by this method can be increasing, U-shaped or modified unimodal. Notice that an important advantage of proposed methods is that obtained discrete analogues have monotonic and non-monotonic hazard rate functions. Finally, these proposed methods have been used for approximating the reliability of an important engineering item where exact determination of survival probability is analytically intractable. We then proceed to a comparative study between the discretizing method that retains the form of survival function and ours that indicates our methods are in no way less efficient.