Interval Estimation for the Two-Parameter Bathtub-Shaped Lifetime Distribution Based on Records

Asgharzadeh, A.; Abdi, M.; Wu, Shuo‐Jye

doi:10.15672/hjms.2014177468

Cited by 6 publications

(10 citation statements)

References 22 publications

(19 reference statements)

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“…General entropy loss function (GLF) is an asymmetric function and suggested by Calabria and Pulcini [16]. Dey and Liao [17] studied with Bayes estimation under GLF.…”

Section: Bayesian Estimationmentioning

confidence: 99%

Comparison of estimators under different loss functions for two-parameter bathtub - shaped lifetime distribution

Gencer

2020

Cumhuriyet Science Journal

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Chen is suggested a two-parameter distribution. This distribution can have increasing failure rate function or a bathtub-shaped that allows it to fit real lifetime data sets. The ML (Maximum Likelihood) and Bayes estimates of the parameters of Chen's distribution are constituted in this paper. The approximate values of Bayesian estimates are obtained by using the Tierney-Kadane approach. Two-parameter bathtub-shaped distribution's estimations are derived using Jeffrey's extension prior under General entropy, Squared and Linex loss functions. Besides, performances of ML and Bayes estimates are compared concerning MSE's (Mean Square Error) by using Monte Carlo simulation. As a result, it has been seen that approximate Bayes estimates obtained under linex loss function are better than others. Moreover, real data analysis for his distribution is presented.

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“…General entropy loss function (GLF) is an asymmetric function and suggested by Calabria and Pulcini [16]. Dey and Liao [17] studied with Bayes estimation under GLF.…”

Section: Bayesian Estimationmentioning

confidence: 99%

Comparison of estimators under different loss functions for two-parameter bathtub - shaped lifetime distribution

Gencer

2020

Cumhuriyet Science Journal

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“…We consider two cases separately to draw inference on R, namely when the common first shape parameter α is unknown and known. In both cases we generate the upper record values with the sample sizes; (n, m) = (5, 5), (8,8), (10,10), (12,12), (15,15) from the Burr Type XII distribution and different values of n and m, given in Table 1, are considered.…”

Section: Simulation Studymentioning

confidence: 99%

“…Moreover, for this example it is recommended to compare the Burr Type XII distribution with common distributions such as Weibull and two-parameter bathtub-shaped based on the goodness-of-fit test. The Weibull distribution is considered by Baklizi [11] based on upper records for the reliability problem and the two-parameter bathtub-shaped distribution is considered by Selim [42] and Asgharzadeh et al [8] based on upper records for the parameter and interval estimation problems. The Weibull distribution parameters have the unique ML estimates.…”

Section: Real Life Examplesmentioning

confidence: 99%

“…R when α is unknown and (n,m)=(8vs. R when α is unknown and (n,m)=(10,12) vs. R when α is unknown and (n,m)=(10,12) vs. R when α is unknown and (n,m)=(10,15) vs. R when α is unknown and (n,m)=(10,15) vs. R when α is unknown and (n,m)=(12,8) vs. R when α is unknown and (n,m)=(12,8) vs. R when α is unknown and (n,m)=(15,12) vs. R when α is unknown and (n,m)=(15,12) R Bias MLE Bias Lindley SEL Lind. LINEX v=−1 Lind.…”

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confidence: 99%

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Statistical inference of P(X Y ) for the Burr Type XII distribution based on records

Kızılaslan¹,

Nadar²

2015

HJMS

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In this paper, the maximum likelihood and Bayesian approaches have been used to obtain the estimates of the stress-strength reliability R = P (X < Y) based on upper record values for the two-parameter Burr Type XII distribution. A necessary and sufficient condition is studied for the existence and uniqueness of the maximum likelihood estimates of the parameters. When the first shape parameter of X and Y is common and unknown, the maximum likelihood (ML) estimate and asymptotic confidence interval of R are obtained. In this case, the Bayes estimate of R has been developed by using Lindley's approximation and the Markov Chain Monte Carlo (MCMC) method due to lack of explicit forms under the squared error (SE) and linear-exponential (LINEX) loss functions for informative prior. The MCMC method has been also used to construct the highest posterior density (HPD) credible interval. When the first shape parameter of X and Y is common and known, the ML, uniformly minimum variance unbiased (UMVU) and Bayes estimates, Bayesian and HPD credible as well as exact and approximate intervals of R are obtained. The comparison of the derived estimates is carried out by using Monte Carlo simulations. Two real life data sets are analysed for the illustration purposes.

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“…In the proposed models, the system degradation was assumed to follow the gamma processes [6]. Asgharzadeh et al presented a method for two-parameter bathtub-shaped lifetime distribution estimation based on upper record values by constructing exact confidence intervals and exact joint confidence regions of parameters [7]. Furthermore, confidence intervals were estimated via the asymptotic normality of the maximumlikelihood estimators.…”

Section: Introductionmentioning

confidence: 99%

Reliability-Based Analytic Models for Fatigue Lifetime Distribution Estimation of Series Mechanical Systems under Random Load considering Strength Degradation Path Dependence

Gao

Xie

2017

Mathematical Problems in Engineering

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Time-dependent statistical characteristics of load process and strength degradation process are critical to lifetime distribution of series mechanical systems. Conventional rain-flow counting method for lifetime distribution estimation has limited practical application due to its strict requirement for statistical properties of load process. Besides, dynamic interaction between load process and strength degradation process results in strength degradation path dependence (SDPD). SDPD and failure dependence of components jointly bring considerable difficulties in prediction of system lifetime distribution and system residual lifetime distribution. To address these problems, reliability-based analytic models for estimation of whole lifetime distribution and residual lifetime distribution of series mechanical systems under random load are developed in this paper, which take the time-dependent statistical parameters of load process and strength degradation process as the input of the models. Furthermore, SDPD and failure dependence of components are taken into account in the proposed models in an explicit mathematical expression. The results show that SDPD, failure dependence of components, and initial strength dispersion have significant influences on system lifetime distribution.

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Interval Estimation for the Two-Parameter Bathtub-Shaped Lifetime Distribution Based on Records

Cited by 6 publications

References 22 publications

Comparison of estimators under different loss functions for two-parameter bathtub - shaped lifetime distribution

Comparison of estimators under different loss functions for two-parameter bathtub - shaped lifetime distribution

Statistical inference of P(X Y ) for the Burr Type XII distribution based on records

Reliability-Based Analytic Models for Fatigue Lifetime Distribution Estimation of Series Mechanical Systems under Random Load considering Strength Degradation Path Dependence

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