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

TL;DR

This paper applies Bayesian methods to the Power Law Process for software failure modeling, demonstrating improved reliability estimates over traditional methods through simulation and real data analysis.

Contribution

It introduces a Bayesian reliability estimation framework for the Power Law Process using the Higgins-Tsokos loss function, with validation via simulation and real data.

Findings

Bayesian estimates outperform maximum likelihood estimates in accuracy.

Bayesian estimates are sensitive to prior choices.

The approach is validated with real software failure data.

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.