scholarly journals Analysis for Xgamma Parameters of Life under Type-II Adaptive Progressively Hybrid Censoring with Applications in Engineering and Chemistry

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2112
Author(s):  
Ahmed Elshahhat ◽  
Berihan R. Elemary
Keyword(s):  
Test Time ◽  
Type Ii ◽  
Bayes Estimators ◽  
Lindley’S Approximation ◽  
Squared Error ◽  
Asymptotic Confidence Intervals ◽  
Credible Intervals ◽  
Life Tests ◽  
Rate Functions ◽  
Chemical Fields

Censoring mechanisms are widely used in various life tests, such as medicine, engineering, biology, etc., as they save (overall) test time and cost. In this context, we consider the problem of estimating the unknown xgamma parameter and some survival characteristics, such as reliability and failure rate functions in the presence of adaptive type-II progressive hybrid censored data. For this purpose, the maximum likelihood and Bayesian inferential approaches are used. Using the observed Fisher information under s-normal approximation, different asymptotic confidence intervals for any function of the unknown parameter were constructed. Using the gamma flexible prior, Bayes estimators against the squared-error loss were developed. Two procedures of Bayesian approximations—Lindley’s approximation and Metropolis–Hastings algorithm—were used to carry out the Bayes estimates and to construct the associated credible intervals. An extensive simulation study was implemented to compare the performance of the different methods. To validate the proposed methodologies of inference—two practical studies using datasets that form engineering and chemical fields are discussed.

scholarly journals Bayesian Estimation and Prediction Based on Constant Stress-Partially Accelerated Life Testing for Topp Leone-Inverted Kumaraswamy Distribution

2021 ◽  
pp. 11-36
Author(s):  
G. R. Al-Dayian ◽  
A. A. El-Helbawy ◽  
R. M. Refaey ◽  
S. M. Behairy
Keyword(s):  
Loss Function ◽  
Accelerated Life Testing ◽  
Constant Stress ◽  
Type Ii ◽  
Life Testing ◽  
Bayes Estimators ◽  
Kumaraswamy Distribution ◽  
Accelerated Life Tests ◽  
Accelerated Life ◽  
Life Tests

Accelerated life testing or partially accelerated life tests is very important in life testing experiments because it saves time and cost. Partially accelerated life tests are used when the data obtained from accelerated life tests cannot be extrapolated to usual conditions. This paper proposes, constant–stress partially accelerated life test using Type II censored samples, assuming that the lifetime of items under usual condition have the Topp Leone-inverted Kumaraswamy distribution. The Bayes estimators for the parameters, acceleration factor, reliability and hazard rate function are obtained. Bayes estimators based on informative priors is derived under the balanced square error loss function as a symmetric loss function and balanced linear exponential loss function as an asymmetric loss function. Also, Bayesian prediction (point and bounds) is considered for a future observation based on Type-II censored under two samples prediction. Numerical studies are given and some interesting comparisons are presented to illustrate the theoretical results. Moreover, the results are applied to real data sets.

scholarly journals Statistical inferences with jointly type-II censored samples from two Pareto distributions

Open Physics ◽  
2017 ◽  
Vol 15 (1) ◽  
pp. 557-565 ◽  
Author(s):  
Hanaa H. Abu-Zinadah
Keyword(s):  
Confidence Intervals ◽  
Life Time ◽  
Model Parameters ◽  
Type Ii ◽  
Time Data ◽  
Data Set ◽  
Censored Samples ◽  
Credible Intervals ◽  
Life Tests ◽  
Censoring Scheme

AbstractIn the several fields of industries the product comes from more than one production line, which is required to work the comparative life tests. This problem requires sampling of the different production lines, then the joint censoring scheme is appeared. In this article we consider the life time Pareto distribution with jointly type-II censoring scheme. The maximum likelihood estimators (MLE) and the corresponding approximate confidence intervals as well as the bootstrap confidence intervals of the model parameters are obtained. Also Bayesian point and credible intervals of the model parameters are presented. The life time data set is analyzed for illustrative purposes. Monte Carlo results from simulation studies are presented to assess the performance of our proposed method.

scholarly journals Bayesian estimation for Dagum distribution based on progressive type I interval censoring

PLoS ONE ◽  
2021 ◽  
Vol 16 (6) ◽  
pp. e0252556
Author(s):  
Refah Alotaibi ◽  
Hoda Rezk ◽  
Sanku Dey ◽  
Hassan Okasha
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimators ◽  
Interval Censoring ◽  
Type I ◽  
Bayes Estimators ◽  
Squared Error Loss ◽  
Squared Error ◽  
Dagum Distribution ◽  
Credible Intervals ◽  
Better Than

In this paper, we consider Dagum distribution which is capable of modeling various shapes of failure rates and aging criteria. Based on progressively type-I interval censoring data, we first obtain the maximum likelihood estimators and the approximate confidence intervals of the unknown parameters of the Dagum distribution. Next, we obtain the Bayes estimators of the parameters of Dagum distribution under the squared error loss (SEL) and balanced squared error loss (BSEL) functions using independent informative gamma and non informative uniform priors for both scale and two shape parameters. A Monte Carlo simulation study is performed to assess the performance of the proposed Bayes estimators with the maximum likelihood estimators. We also compute credible intervals and symmetric 100(1 − τ)% two-sided Bayes probability intervals under the respective approaches. Besides, based on observed samples, Bayes predictive estimates and intervals are obtained using one-and two-sample schemes. Simulation results reveal that the Bayes estimates based on SEL and BSEL performs better than maximum likelihood estimates in terms of bias and MSEs. Besides, credible intervals have smaller interval lengths than confidence interval. Further, predictive estimates based on SEL with informative prior performs better than non-informative prior for both one and two sample schemes. Further, the optimal censoring scheme has been suggested using a optimality criteria. Finally, we analyze a data set to illustrate the results derived.

Data Processing and Technology Application in Bayes and Empirical Bayes Reliability Analysis of Parameter of Ailamujia Distribution

2014 ◽  
Vol 951 ◽  
pp. 249-252
Author(s):  
Hui Zhou
Keyword(s):  
Empirical Bayes ◽  
Bayes Estimators ◽  
Conjugate Prior ◽  
Likelihood Estimator ◽  
Empirical Bayesian ◽  
Technology Application ◽  
Inverse Gamma ◽  
Squared Error ◽  
Linex Loss ◽  
Empirical Bayes Estimators

The estimation of the parameter of the ЭРланга distribution is discussed based on complete samples. Bayes and empirical Bayesian estimators of the parameter of the ЭРланга distribution are obtained under squared error loss and LINEX loss by using conjugate prior inverse Gamma distribution. Finally, a Monte Carlo simulation example is used to compare the Bayes and empirical Bayes estimators with the maximum likelihood estimator.

PLANNING FOR ACCELERATED LIFE TESTS

1999 ◽  
Vol 06 (03) ◽  
pp. 265-275 ◽  
Author(s):  
LOON-CHING TANG
Keyword(s):  
Acceleration Factor ◽  
Test Time ◽  
Initial Sample ◽  
Lower Stress ◽  
Nonlinear Programs ◽  
Accelerated Life Tests ◽  
Accelerated Life ◽  
Stress Levels ◽  
Life Tests ◽  
Sample Allocation

We present two alternative perspectives to the current way of planning for constant-stress accelerated life tests (CSALTs) and step-stress ALT (SSALT). In 3-stress CSALT, we consider test plans that not only optimize the stress levels but also optimize the sample allocation. The resulting allocations also limit the chances of inconsistency when data are plotted on a probability plot. For SSALT, we consider test plans that not only optimize both stress levels and holding times, but also achieve a target acceleration factor that meets the test time constraint with the desirable fraction of failure. The results for both problems suggest that the statistically optimal way to increase acceleration factor in an ALT is to increase lower stress levels and; in the case of CSALT, to decrease their initial sample allocations; in the case of SSALT, to reduce their initial hold times. Both problems are formulated as constrained nonlinear programs.

scholarly journals Bayes Estimation of a Two-Parameter Geometric Distribution under Multiply Type II Censoring

2011 ◽  
Vol 2011 ◽  
pp. 1-10
Author(s):  
J. B. Shah ◽  
M. N. Patel
Keyword(s):  
Geometric Distribution ◽  
Correct Choice ◽  
Bayes Estimation ◽  
Loss Functions ◽  
Type Ii ◽  
Expected Loss ◽  
Bayes Estimators ◽  
Linex Loss ◽  
Type Ii Censored Data ◽  
Two Parameter

We derive Bayes estimators of reliability and the parameters of a two- parameter geometric distribution under the general entropy loss, minimum expected loss and linex loss, functions for a noninformative as well as beta prior from multiply Type II censored data. We have studied the robustness of the estimators using simulation and we observed that the Bayes estimators of reliability and the parameters of a two-parameter geometric distribution under all the above loss functions appear to be robust with respect to the correct choice of the hyperparameters a(b) and a wrong choice of the prior parameters b(a) of the beta prior.

scholarly journals Bayesian Estimation of the Parameter of the p-Dimensional Size-Biased Rayleigh Distribution

2017 ◽  
Vol 56 (1) ◽  
pp. 88-91
Author(s):  
Arun Kumar Rao ◽  
Himanshu Pandey ◽  
Kusum Lata Singh
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Bayesian Estimation ◽  
Density Function ◽  
Rayleigh Distribution ◽  
Survival Model ◽  
Loss Functions ◽  
Bayes Estimators ◽  
Hazard Functions ◽  
Squared Error

In this paper, we have derived the probability density function of the size-biased p-dimensional Rayleigh distribution and studied its properties. Its suitability as a survival model has been discussed by obtaining its survival and hazard functions. We also discussed Bayesian estimation of the parameter of the size-biased p-dimensional Rayleigh distribution. Bayes estimators have been obtained by taking quasi-prior. The loss functions used are squared error and precautionary.

scholarly journals Estimating the Parameters of the Exponential-Geometric distribution based on progressively type-II censored data

2018 ◽  
Vol 6 (1) ◽  
pp. 37
Author(s):  
Aisha Fayomi ◽  
Hamdah Al-Shammari
Keyword(s):  
Censored Data ◽  
Geometric Distribution ◽  
Asymptotic Variance ◽  
Parameters Estimation ◽  
Type Ii ◽  
Progressive Type ◽  
The Em Algorithm ◽  
Asymptotic Confidence Intervals ◽  
Distribution Parameters ◽  
Type Ii Censored Data

This paper deals with the problem of parameters estimation of the Exponential-Geometric (EG) distribution based on progressive type-II censored data. It turns out that the maximum likelihood estimators for the distribution parameters have no closed forms, therefore the EM algorithm are alternatively used. The asymptotic variance of the MLEs of the targeted parameters under progressive type-II censoring is computed along with the asymptotic confidence intervals. Finally, a simple numerical example is given to illustrate the obtained results.

Bayesian Reliability Estmation with a Truncated Normal Prior

1988 ◽  
Vol 37 (3-4) ◽  
pp. 227-231 ◽  
Author(s):  
Samir K. Bhattacharya ◽  
Ravindar K. Tyagi
Keyword(s):  
Bayesian Estimation ◽  
Parameter Space ◽  
Loss Function ◽  
Exponential Model ◽  
Life Testing ◽  
Squared Error Loss Function ◽  
Squared Error Loss ◽  
Squared Error ◽  
Life Tests ◽  
Truncated Normal

Beyesian reliebility estimation for the exponential model. based on life tests that are terminated after a preassigned number of failures, is carried out under the assumption of the squared error loss function and a truncated normal priod density on the parameter space. The Bayesian estimation of reliability for the case of ‘attribute life testing’ is also discussed.

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