A New Reliability Model Based on Lindley Distribution with Application to Failure Data

Norah N Al-Mutairi,Lutfiah I Al-Turk,Sharifah A Al-Rajhi,Emilio Gómez-Déniz

doi:10.1155/2020/4915812

Norah N Al-Mutairi, Lutfiah I Al-Turk + Show 2 more

Open Access

https://doi.org/10.1155/2020/4915812

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Abstract

Software reliability is an important feature that influences systems’ reliability. Software reliability models are a common tool to evaluate software reliability quantitatively. Various reliability models have been suggested based on the NHPP (nonhomogeneous Poisson process). In this article, a new NHPP model based on the Lindley distribution is proposed. The mathematical formulas for its measures of reliability are obtained and graphically illustrated. The proposed model’s parameters are estimated using both the NLSE (nonlinear least squares estimation) and the WNLSE (weighted nonlinear least squares estimation) methods. The model is then validated based on several different reliability datasets. The methods of estimation are evaluated and compared using three different criteria. The performance of the new model is also evaluated and compared, both objectively and subjectively, with three previously suggested models. The application results show that our new model demonstrates good performance in our selected failure data.

Highlights

NHPP Lindley ModelSuppose m(t) denotes the cumulative number of faults discovered at time t, and F(t) is the distribution function of time between two successive failures, the MVF of the NHPP model can be expressed as follows [5]: m(t) aF(t),
Kapur et al [9] proposed a new Software reliability growth models (SRGMs) based on Ito􏽢 type of stochastic differential equation; the proposed model performs comparatively better than the existing NHPP models
We propose a new model that belongs to the NHPP class and based on the Lindley distribution

Summary

NHPP Lindley Model

Suppose m(t) denotes the cumulative number of faults discovered at time t, and F(t) is the distribution function of time between two successive failures, the MVF of the NHPP model can be expressed as follows [5]: m(t) aF(t),. From this figure, we can see that, initially, the faults detected during testing are very high but later on become stable, and larger values of the parameter a give higher MVF form.

Estimation of Model Parameters

Application to Failure Data

Results and Discussion

Conclusions