Asymptotic and finite-sample properties of a reliability estimator for a competing risks system

Agustin, Marcus A.

doi:10.1080/00949659908811978

Cited by 4 publications

(4 citation statements)

References 7 publications

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“…The failure rate of each software depends on an unknown number of bugs, denoted by B j , where each bug was assumed to form a sample from a gamma distribution with scale and shape parameters denoted by γ j and φ j respectively. In contrast to Agustin (1999), bugs that are observed earlier in the testing period have a higher contribution to the failure of the system. In addition, jobs were assigned to the system where the completion time of a job follows a certain hazard function λ 0 (t; β).…”

Section: Concluding Remarks and Future Directionsmentioning

confidence: 86%

“…Moreover, previous works can be classified into two broad types: those that model times between successive failures, or those that model the number of failures up to a given time (see Singpurwalla and Wilson (1999)). However, such failures could be a result of the software failing to perform assigned tasks with random completion times (see Sun et al (1997), Mok and Chen (1997), Agustin (1999), and Agustin and Peña (1999)). We can then observe failures as well as task completions.…”

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confidence: 99%

“…In this paper, a series system with p softwares is considered where the failure rate of each software follows the Littlewood model. This is in contrast to Agustin (1999) where a series system of p components was considered with each component having a failure rate that follows the Jelinski-Moranda model. Moreover, papers that have considered the Littlewood model tackled only the case of an individual software whereas this paper discusses a system of softwares.…”

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confidence: 99%

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Statistical properties of a system reliability estimator using the Littlewood software reliability model

Agustin

2003

Journal of Applied Probability

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This paper considers a competing risks system with p pieces of software where each piece follows the model by Littlewood (1980) described as follows. The failure rate of a piece of software relies on the residual number of bugs remaining in the software where each bug produces failures at varying rates. In effect, bugs with higher failure rates tend to be observed earlier in the testing period. Tasks are assigned to the system and the task completion times as well as the software failure times are assumed to be independent of each other. The system is observed over a fixed testing period and the system reliability upon test termination is examined. An estimator of the system reliability is presented and its asymptotic properties as well as finite-sample properties are obtained.

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Section: Concluding Remarks and Future Directionsmentioning

confidence: 86%

mentioning

confidence: 99%

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confidence: 99%

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Statistical properties of a system reliability estimator using the Littlewood software reliability model

Agustin

2003

Journal of Applied Probability

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“…For an overview of statistical inference for software reliability, see Singpurwalla and Wilson (1999). Agustin and Peña (1999) and Agustin (1999) consider several systems of components each of which fails according to the EOS model. For an application of the EOS model in estimating a population size for market research, see Basu et al (1995).…”

Section: Introductionmentioning

confidence: 99%

The Lorenz Curve for Model Assessment in Exponential Order Statistic Models

Osborne

Severini

2002

Journal of Statistical Computation and Simulation

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A goodness-of-fit technique for random samples from the exponential distribution based on the sample Lorenz curve is adapted for use in the exponential order statistic (EOS) model. In the EOS model, only those observations in a random sample from the exponential distribution of unknown size N that are less than some known stopping time T are observable. The model is known as the Jelinski-Moranda model in software reliability, where it is used to estimate the number of bugs in software during development. Distributional results are derived for the distance between the sample Lorenz curve and the population Lorenz curve so that it can be used as a goodness-of-fit test statistic. Simulations show that the test has good power against several alternative distributions. Simulations also indicate that in some cases, model misspecification leads to poor parameter estimation. A plotting procedure provides a means of graphical assessment of fit.

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Systems in Series

Agustin

2011

Wiley Encyclopedia of Operations Research and Management Science

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Asymptotic and finite-sample properties of a reliability estimator for a competing risks system

Cited by 4 publications

References 7 publications

Statistical properties of a system reliability estimator using the Littlewood software reliability model

Statistical properties of a system reliability estimator using the Littlewood software reliability model

The Lorenz Curve for Model Assessment in Exponential Order Statistic Models

Systems in Series

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