A reliability and survival model for one and two failure modes system with applications to complete and censored datasets

Abba, Badamasi; Wang, Hong; Bakouch, Hassan S.

doi:10.1016/j.ress.2022.108460

Cited by 14 publications

(14 citation statements)

References 40 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…let 2𝛼 be a positive integer and |(2𝜈 − 𝜃)𝑥| < 1, then, using binomial expansion, we get We complete the proof of Theorem 11 by evaluating and substituting the integral in Equation ( 28) into Equation (26). □…”

Section: Rényi Entropymentioning

confidence: 97%

See 1 more Smart Citation

A two‐parameter parsimonious bathtub model for the analysis of system failure times with illustrations to reliability data

Bakouch,

Abba,

Jónás

et al. 2023

Quality & Reliability Eng

Self Cite

View full text Add to dashboard Cite

In this study, a two‐parameter, upper‐bounded probability distribution called the tau distribution is introduced and its applications in reliability engineering are presented. Each of the parameters of the tau distribution has a clear semantic meaning. Namely, one of them determines the upper bound of the distribution, while the value of the other parameter influences the shape of the cumulative distribution function. A remarkable property of this new probability distribution is that its probability density function, survival function, hazard rate function (HRF), and quantile function can all be expressed in terms of its cumulative distribution function. The HRF of the proposed probability distribution can exhibit an increasing trend and various bathtub shapes with or without a low and long‐flat phase (useful time phase), which makes this new distribution suitable for modeling a wide range of real‐world problems. The constraint maximum likelihood estimation, percentile estimation, approximate Bayesian computation, and approximate quantile estimation computation are proposed to calculate the unknown parameters of the model. The suitability of the estimation methods is verified with the aid of simulation and real‐world data results. The modeling capability of the tau distribution was compared with that of some well‐known two‐ and three‐parameter probability distributions using two data sets known from the literature of reliability engineering: time between failures data of a machining center, and time to failure of data acquisition system cards. Based on empirical results, the new distribution may be viewed as a viable competitor to the Weibull, Gamma, Chen, and modified Weibull distributions.

show abstract

Section: Rényi Entropymentioning

confidence: 97%

“…More recent works that discuss the roles of the TTT plot in model selection are available in the literature (see, e.g., Refs. 26, 27).…”

Section: Applications To Reliability Datamentioning

confidence: 99%

A two‐parameter parsimonious bathtub model for the analysis of system failure times with illustrations to reliability data

Bakouch,

Abba,

Jónás

et al. 2023

Quality & Reliability Eng

Self Cite

View full text Add to dashboard Cite

show abstract

“…This hybrid/compounding technique is the most appropriate for building distributions competent in adequately handling complex failure time datasets, specifically for datasets with bathtub-shaped FRs. 13,17 Besides the series system configuration, other studies focus on models for complex systems with distinct configurations, including multi-component parallel and series-parallel systems, with some recent ones authored by Zhang et al 18 Sadeghi and Roghanian 19 and Chehade et al 20 among others. Though the models mentioned above are illustrated to provide good descriptions of some specific failure time datasets, mostly the two sets of datasets with bathtub-shaped FRs reported by Aarset 4 and Meeker and Escoba.…”

Section: Introductionmentioning

confidence: 99%

“…Though the models mentioned above are illustrated to provide good descriptions of some specific failure time datasets, mostly the two sets of datasets with bathtub-shaped FRs reported by Aarset 4 and Meeker and Escoba. 21 The recent work of Abba et al 17 has revealed the inadequate performance of several of these additive models in modelling other reliability and survival datasets whose distributions of FRs are bathtub-shaped. Their fitted failure rate function (FRF) could not adequately identify the long-flat segment (phase II of Figure 1) and the wear-out change point of the bathtub-shaped FR for the illustrated failure time datasets.…”

Section: Introductionmentioning

confidence: 99%

A new failure times model for one and two failure modes system: A Bayesian study with Hamiltonian Monte Carlo simulation

Abba

Wang

2023

Proceedings of the Institution of Mechanical Engineers, Part O:

Self Cite

View full text Add to dashboard Cite

This paper presents an additive Gompertz-Weibull (AGW) distribution, a four-parameter hybrid probability distribution, and its applications in reliability engineering. The failure rate (FR) function of the proposed model demonstrates an increasing trend and a variety of bathtub shapes with or without a low and yet long-stable segment, making it appropriate for modelling a wide variety of real-world problems. Some relationships between the AGW’s FR and its mean residual life functions are examined. For parameter estimation, maximum likelihood and Bayesian inferences are considered. For posterior simulations, we use Hamiltonian Monte Carlo to evaluate the Bayes estimators of the AGW parameters. We evaluate the performance of the proposed AGW model to that of other recent bathtub distributions constructed following the same approach on three failure time datasets. The first two datasets represent device failure times, while the third represents early cable-joint failure times, all with bathtub FR. For comparison, five parametric and nonparametric evaluation criteria and the fitted FR and mean residual life curves were employed. The results indicated that the AGW model would be the best choice for describing failure times, especially when the bathtub-shaped FR of the presented dataset exhibits its three segments.

show abstract

“…1 In this case, statistical models containing this type of FRF can be applied. Lifetime distributions, such as the exponentiated Weibull, 2 additive Weibull, 3,4 modified Weibull extension, 5 modified Weibull, 6 odd Weibull, 7 beta Weibull, 8 beta modified Weibull, 9 new modified Weibull, 10 exponential-Weibull, 11 Weibull-Dagum, 12 exponentiated additive Weibull, 13 and flexible additive Chen-Gompertz 14 distributions are introduced to cope with the Weibull's limitations.…”

Section: Introductionmentioning

confidence: 99%

Classical and Bayesian estimations of improved Weibull–Weibull distribution for complete and censored failure times data

Wang

Abba

Pan

2022

Appl Stoch Models Bus & Ind

Self Cite

View full text Add to dashboard Cite

In this article, we demonstrate how to enhance the Weibull-Weibull (WW) distribution introduced in the earlier literature into a better form for fitting monotone and non-monotone failure rate data, especially the bathtub-shaped failure rate data with or without a flat region. The model is referred to as an improved WW distribution. The model's flexibility enables it to describe lifetime data with various failure rate functions, including increasing, decreasing, U or V-shaped, and bathtub-shaped with a comparatively low and long-flat segment. We provide a thorough Bayesian analysis of the modified model for complete and right-censored data. Additionally, we developed maximum likelihood estimators for the model's parameters for both complete and right-censored data. The Bayesian credible and asymptotic confidence intervals of the estimators are defined, and simulation results validate the estimators' consistency. To illustrate the applications of the improved distribution with the WW and other generalized distributions, we apply one censored and one uncensored failure times data, each with bathtub-shaped failure rates. The numerical results demonstrate that the improved WW model outperforms the WW distribution and other existing models, as indicated by goodness-of-fit statistics and supported by the fitted models' survival and failure rate curves and P-P plots.

show abstract

A reliability and survival model for one and two failure modes system with applications to complete and censored datasets

Cited by 14 publications

References 40 publications

A two‐parameter parsimonious bathtub model for the analysis of system failure times with illustrations to reliability data

A two‐parameter parsimonious bathtub model for the analysis of system failure times with illustrations to reliability data

A new failure times model for one and two failure modes system: A Bayesian study with Hamiltonian Monte Carlo simulation

Classical and Bayesian estimations of improved Weibull–Weibull distribution for complete and censored failure times data

Contact Info

Product

Resources

About