A New Finite Interval Lifetime Distribution Model for Fitting Bathtub-Shaped Failure Rate Curve

Wang, Xiaohong; Yu, Chuang; Li, Yuxiang

doi:10.1155/2015/954327

Cited by 11 publications

(11 citation statements)

References 13 publications

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“…20 A number of studies have been published on modifications, generalizations, and approximations to the Weibull probability distribution with the number of parameters ranging from two to five, with the purpose of enhancing its capability of modeling bathtub-shaped failure rate curves. 4,[21][22][23][24][25] In the last few years, the relevant literature is extremely rich in providing recent results of this area. 9 Cordeiro et al 26 provided a five-parameter extension of the Weibull distribution to model both monotone and nonmonotone failure rates.…”

Section: Introductionmentioning

confidence: 99%

“…However, the Weibull distribution does not provide a reasonable parametric fit for modeling phenomenon with nonmonotone failure rates such as the bathtub‐shaped failure rates . A number of studies have been published on modifications, generalizations, and approximations to the Weibull probability distribution with the number of parameters ranging from two to five, with the purpose of enhancing its capability of modeling bathtub‐shaped failure rate curves . In the last few years, the relevant literature is extremely rich in providing recent results of this area .…”

Section: Introductionmentioning

confidence: 99%

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The omega probability distribution and its applications in reliability theory

Dombi

Jónás

Tóth

et al. 2018

Quality & Reliability Eng

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A new three‐parameter probability distribution called the omega probability distribution is introduced, and its connection with the Weibull distribution is discussed. We show that the asymptotic omega distribution is just the Weibull distribution and point out that the mathematical properties of the novel distribution allow us to model bathtub‐shaped hazard functions in two ways. On the one hand, we demonstrate that the curve of the omega hazard function with special parameter settings is bathtub shaped and so it can be utilized to describe a complete bathtub‐shaped hazard curve. On the other hand, the omega probability distribution can be applied in the same way as the Weibull probability distribution to model each phase of a bathtub‐shaped hazard function. Here, we also propose two approaches for practical statistical estimation of distribution parameters. From a practical perspective, there are two notable properties of the novel distribution, namely, its simplicity and flexibility. Also, both the cumulative distribution function and the hazard function are composed of power functions, which on the basis of the results from analyses of real failure data, can be applied quite effectively in modeling bathtub‐shaped hazard curves.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The omega probability distribution and its applications in reliability theory

Dombi

Jónás

Tóth

et al. 2018

Quality & Reliability Eng

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“…The samples corresponding to both the populations are arranged in ascending order and first (r, r ′ ) observations are considered. For (r, r ′ )= (10,10), (20,20), (30,25) and (40,40), we have computed average values of P and P and their corresponding MSE's and the results are presented in Table 5. Similiarly, we obtain 114 ESTIMATION AND TESTING PROCEDURES UNDER THE CHEN DISTRIBUTION average length and coverage probability of interval estimates which are reported in Table 6.…”

Section: Simulation Based On Estimation Proceduresmentioning

confidence: 99%

“…The data comprise of 50 observations, which represents the quantity of 1000s of cycles to failure for electrical appliances in a life test. The data is presented below: The second data set was used by [20] (initially taken by [6]). It represents the failure data of a 180 ton rear dump truck.…”

Section: Real Data Analysismentioning

confidence: 99%

Estimation and Testing Procedures for the Reliability Characteristics of Chen Distribution Based on Type II Censoring and the Sampling Scheme of Bartholomew

Chaturvedi

Kumar

2020

Stat., optim. inf. comput.

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In this paper, we consider Chen distribution and derive UMVUEs and MLEs of the parameter λ , hazard rate h(t) and the two measures of reliability, namely R(t) = P(X > t), where X denotes the lifetime of an item and P = P(X > Y ), which represents the reliability of an item or system of random strength X subject to random stress Y , under type II censoring scheme and the sampling scheme of Bartholomew . We also develop interval estimates of the reliability measures. Testing procedures for the hypotheses related to different parametric functions have also been developed. A comparative study of different methods of point estimation and average confiddence length has been done through simulation studies. The analysis of a real data set is presented for illustration purpose.

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“…Wang et al (2015) proposed a new four parameter interval life model to describe the bathtub curve. Cordeiro et al (2014) extended the modified Weibull distribution, and established a five-parameter Weibull distribution.…”

Section: Introductionmentioning

confidence: 99%

Piecewise modelling and parameter estimation of repairable system failure rate

2016

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Lifetime failure data usually presents a bathtub-shaped failure rate, and random failure phase dominates its life cycle. Relatively large errors always existed when single distribution model is used for analysis and modelling. Therefore, a bathtub-shaped reliability model based on piecewise intensity function was proposed for repairable system. Parameter estimation was studied by using maximum likelihood method in conjunction with two-stage Weibull process interval estimation and Artificial Bee Colony Algorithm. The proposed model and estimation approach fit the failure rate under bathtub curve very well, adequately reflect the duration of random failure phase, and guarantee the feasibility of quantitative analysis. Moreover, the estimated critical point of bathtub curve could be calculated. At last, the proposed model was applied in the reliability analysis of a repairable Computer Numerical Control system, and the validity of the proposed model and its parameter estimation method were verified.

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A New Finite Interval Lifetime Distribution Model for Fitting Bathtub-Shaped Failure Rate Curve

Cited by 11 publications

References 13 publications

The omega probability distribution and its applications in reliability theory

The omega probability distribution and its applications in reliability theory

Estimation and Testing Procedures for the Reliability Characteristics of Chen Distribution Based on Type II Censoring and the Sampling Scheme of Bartholomew

Piecewise modelling and parameter estimation of repairable system failure rate

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