Sahinoglu-Libby (SL) probability density function-component reliability applications in integrated networks

Abstract

The forced outage ratio of a hardware (or a software) component is defined as the failure rate divided by the sum of the failure and the repair rates. The probability density function (PDF) of the FOR is a three-parameter beta distribution (G3B), renamed to be the Sahinoglu-Libby (SL) probability distribution that was pioneered in 1981. The failure and repair rates are assumed to be the generalized gamma variables where the corresponding shape and scale parameters, respectively, are unequal. A three-parameter beta or G3B PDF, equivalent to an FOR PDF, renamed to be the SL, is shown to default to an ordinary two-parameter beta PDF when the shape parameters are identical. Furthermore, the authors will present a wide perspective of the usability and limitations of the said PDF in theoretical and practical terms, also referring to work done by some other authors in the area. In the new era of quality and reliability, the usage of the SL will assist studies in correctly formulating the PDF of the unavailability or availability random variables to estimate the network reliability and quality indices for engineering and utility considerations. Bayesian methodology is employed to compute small-sample estimators by using informative and noninformative priors for the component failure and repair rates in terms of loss functions, as opposed to the uncontested and erroneous usage of the mle, regardless of the inadequacy of the historical data. Case studies illustrate a phenomenon of overestimation of the availability index in safety and time critical components as well as in systems, when mle is conventionally employed. This work assists the network planners, and analysts, like those of Internet Service Providers, providing a targeted reliability measure of their integrated computer network in a quality-conscious environment under the pressure of an ever-expanding demand and a risk, that needs to be mitigated.