Discrete Rayleigh distribution
Using a general approach for discretization of continuous life distributions in the univariate & bivariate situations, we have proposed a discrete Rayleigh distribution. This distribution has been examined in detail with respect to two measures of failure rate. Characterization results have also been studied to establish a direct link between the discrete Rayleigh distribution, and its continuous counterpart. This discretization approach not only expands the scope of reliability modeling, but also provides a method for approximating probability integrals arising out of a continuous setting. As an example, the reliability value of a complex system has been approximated. This discrete approximation in a nonnormal setting can be of practical use & importance, as it can replace the much relied upon simulation method. While the replication required is minimal, the degree of accuracy remains reasonable for our suggested method when compared with the simulation method.
rayleigh distribution life distribution failure rate characterization discrete models reliability approximation second rate of failure