Unification of Software Reliability Models Using Markovian Arrival Processes

Abstract

This paper proposes an unified modeling framework of Markov-type software reliability models (SRMs) using Markovian arrival processes (MAPs). The MAP is defined as a point process whose inter-arrival time follows a phase-type distribution incorporating the correlation between successive two arrivals. This paper presents MAP representation of Markov-type SRMs, called MAP-based SRMs. This framework enables us to use generalized formulas for several reliability measures such as the expected number of failures and the software reliability which can be applied to all the Markov-type SRMs. In addition, we discuss the parameter estimation for the MAP-based SRMs from grouped failure data and find maximum likelihood estimates of all the Markov-type SRMs. The resulting MAP-based SRM is a novel approach to unifying the model-based software reliability evaluation using failure data.