Bayesian Reliability Analysis of the Power Law Process with Respect to the Higgins-Tsokos Loss Function for Modeling Software Failure Times

Abstract

The Power Law Process, also known as Non-Homogeneous Poisson Process, has been used in various aspects, one of which is the software reliability assessment. Specifically, by using its intensity function to compute the rate of change of a software reliability as time-varying function. Justification of Bayesian analysis applicability to the Power Law Process was shown using real data. The probability distribution that best characterizes the behavior of the key parameter of the intensity function was first identified, then the likelihood-based Bayesian reliability estimate of the Power Law Process under the Higgins-Tsokos loss function was obtained. As a result of a simulation study and using real data, the Bayesian estimate shows an outstanding performance compared to the maximum likelihood estimate using different sample sizes. In addition, a sensitivity analysis was performed, resulting in the Bayesian estimate being sensitive to the prior selection; whether parametric or non-parametric.

Modeling and Simulation of Successive Breakdown Events in Thin Gate Dielectrics Using Standard Reliability Growth Models

“…Notice that both the scale parameter a and shape parameter b depend on the last observed BD time so that they should be strictly treated as unknown random variables. However, as reported in [5], Bayesian estimates using the Higgins-Tsokos loss function can help to overcome this problem. In addition, the Cramér-von Mises goodness statistics can be used to identify whether the system strictly follows PLP or not.…”