Phase-type software reliability model: parameter estimation algorithms with grouped data

Okamura, Hiroyuki

doi:10.1007/s10479-015-1870-0

Cited by 23 publications

(13 citation statements)

References 47 publications

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“…It has found a number of interesting applications across various fields. The advantage of working under phase-type distribution is that it allows some analytically tractable results in applications: e.g., in actuarial science (Rolski et al 1998, Albrecher and Asmussen 2010, Lin and Liu 2007, Lee and Lin 2010, option pricing (Asmussen et al 2004, Rolski et al 1998, queueing theory (Badila et al 2014, Chakravarthy and Neuts 2014, Buchholz et al 2014, Breuer and Baum 2005, Asmussen 2003, reliability theory (Assaf andLevikson 1982, Okamura andDohi 2015), and in survival analysis (Aalen 1995, Aalen andGjessing 2001). When jumps distribution of a compound Poisson process is modeled by phase-type distribution, it results in a dense class of Lévy processes, Asmussen et al (2004).…”

Section: Introductionmentioning

confidence: 99%

Distributional Properties of the Mixture of Continuous-Time Absorbing Markov Chains Moving at Different Speeds

Surya

2018

Stochastic Systems

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Abstract. This paper analyses the mixture of two continuous-time Markov chains with absorption on the same state space moving at different speeds, where the mixture occurs at a random time. Variety of associated distributional properties of the Markov mixture process are discussed, for example the transition matrix, the distribution of its lifetime and the corresponding forward intensity. Identities are given explicitly in terms of the Bayesian updates of switching probability and the intensity matrices of the underlying Markov chains despite the fact that the mixture process is not Markovian. They form nonstationary functions of time and duration and have two appealing features: the ability to capture heterogeneity and path dependence when conditioning on the available information (either full or partial) about the past history of the process until current time. In particular, the unconditional lifetime distribution forms a generalized mixture of phase-type distributions. The distribution has dense and closure properties under finite convex mixtures and finite convolutions. When the underlying Markov chains move at the same speed, in which case the mixture process reduces to a simple Markov chain, the heterogeneity and path dependence are removed, and the lifetime has the usual phase-type distribution, Neuts [Neuts MF (1975) Probability distributions of phase-type.

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Section: Introductionmentioning

confidence: 99%

Distributional Properties of the Mixture of Continuous-Time Absorbing Markov Chains Moving at Different Speeds

Surya

2018

Stochastic Systems

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“…In this section, we present the phase-type software reliability model (PH-SRM) proposed by [59,60,63] as an application example of PH fitting in the reliability engineering. The software reliability model (SRM) is a well-known stochastic model for estimating the number of bugs and software reliability quantitatively [46,51,52,74].…”

Section: Phase-type Software Reliability Modelmentioning

confidence: 99%

“…Okamura and Dohi [59,60,63] proposed PH-SRM (phase-type software reliability model) by substituting the PH distribution to the fault detection time distribution in NHPP-based model. Then the p.m.f.…”

Section: Ph-srmmentioning

confidence: 99%

“…We also refer to the numerical tool implemented with the statistical software R. Further, we give two examples of PH fitting; PH estimation for software reliability assessment and PH approximation for dynamic reliability modeling based on a Markov regenerative process (MRGP). We introduce the so-called phase-type software reliability model (PH-SRM) [59,60,63] and mention how to use the PH estimation algorithm to the parameter estimation of PH-SRM. In the second example, we apply the PH approximation (PH expansion) to describe a parallel system with single repair facility by means of the MRGP and evaluate the pointwise availability.…”

Section: Introductionmentioning

confidence: 99%

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Ph Fitting Algorithm and Its Application to Reliability Engineering

Okamura

2016

JORSJ

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This article presents parameter estimation of phase-type (PH) distribution. PH distribution is widely used in model-based performance evaluation such as reliability and queueing system, and is defied by an absorbing continuous-time Markov chain (CTMC). Since non-Markovian model can be approximated by a CTMC by replacing general distributions with PH distributions, the parameter estimation is a challenging issue in stochastic modeling. We focus on the statistical inference algorithms to estimate not only the parameters of PH distribution with grouped, truncated and missing data but also the probability density function, and give two examples of PH fitting in reliability engineering.

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“…Inoue et al [5] developed a bivariate software reliability growth model that considers the uncertainty of the change in the software failure-occurrence phenomenon at the change-point for improved accuracy. Okamura and Dohi [6] introduced a phase-type software reliability model and developed parameter estimation algorithms using grouped data. Song et al [7,8] recently developed an NHPP software reliability model to consider a three-parameter fault detection rate, and applied a Weibull fault detection rate function during the software development process.…”

Section: Introductionmentioning

confidence: 99%

An NHPP Software Reliability Model with S-Shaped Growth Curve Subject to Random Operating Environments and Optimal Release Time

2017

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Abstract:The failure of a computer system because of a software failure can lead to tremendous losses to society; therefore, software reliability is a critical issue in software development. As software has become more prevalent, software reliability has also become a major concern in software development. We need to predict the fluctuations in software reliability and reduce the cost of software testing: therefore, a software development process that considers the release time, cost, reliability, and risk is indispensable. We thus need to develop a model to accurately predict the defects in new software products. In this paper, we propose a new non-homogeneous Poisson process (NHPP) software reliability model, with S-shaped growth curve for use during the software development process, and relate it to a fault detection rate function when considering random operating environments. An explicit mean value function solution for the proposed model is presented. Examples are provided to illustrate the goodness-of-fit of the proposed model, along with several existing NHPP models that are based on two sets of failure data collected from software applications. The results show that the proposed model fits the data more closely than other existing NHPP models to a significant extent. Finally, we propose a model to determine optimal release policies, in which the total software system cost is minimized depending on the given environment.

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Phase-type software reliability model: parameter estimation algorithms with grouped data

Cited by 23 publications

References 47 publications

Distributional Properties of the Mixture of Continuous-Time Absorbing Markov Chains Moving at Different Speeds

Distributional Properties of the Mixture of Continuous-Time Absorbing Markov Chains Moving at Different Speeds

Ph Fitting Algorithm and Its Application to Reliability Engineering

An NHPP Software Reliability Model with S-Shaped Growth Curve Subject to Random Operating Environments and Optimal Release Time

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