Pareto analysis for the lifetime performance index of products on the basis of progressively first-failure-censored batches under balanced symmetric and asymmetric loss functions

Ahmadi, Mohammad Vali; Doostparast, Mahdi

doi:10.1080/02664763.2018.1541170

Cited by 13 publications

(7 citation statements)

References 31 publications

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“…After that, the balanced loss function idea appeared in the literature which tried to reflect the desired criteria of two methods (see equation (13)), for example, balanced square error (BSE) loss function [4], balanced general entropy (BGE) loss function [5]), and balanced linear exponential (BLINEX) loss function [6] EL-Sagheer [7] EL-Sagheer [8].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Programming to Determine Best Weighted Coefficient of Balanced LINEX Loss Function Based on Lower Record Values

Al-Duais

Alhagyan

2021

Complexity

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Majority research studies in the literature determine the weighted coefficients of balanced loss function by suggesting some arbitrary values and then conducting comparison study to choose the best. However, this methodology is not efficient because there is no guarantee ensures that one of the chosen values is the best. This encouraged us to look for mathematical method that gives and guarantees the best values of the weighted coefficients. The proposed methodology in this research is to employ the nonlinear programming in determining the weighted coefficients of balanced loss function instead of the unguaranteed old methods. In this research, we consider two balanced loss functions including balanced square error (BSE) loss function and balanced linear exponential (BLINEX) loss function to estimate the parameter and reliability function of inverse Rayleigh distribution (IRD) based on lower record values. Comparisons are made between Bayesian estimators (SE, BSE, LINEX, and BLINEX) and maximum likelihood estimator via Monte Carlo simulation. The evaluation was done based on absolute bias and mean square errors. The outputs of the simulation showed that the balanced linear exponential (BLINEX) loss function has the best performance. Moreover, the simulation verified that the balanced loss functions are always better than corresponding loss function.

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Section: Introductionmentioning

confidence: 99%

Nonlinear Programming to Determine Best Weighted Coefficient of Balanced LINEX Loss Function Based on Lower Record Values

Al-Duais

Alhagyan

2021

Complexity

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“…Then, these estimates have been used to develop some hypothesis testing algorithmic procedures. Recently, Ahmadi and Doostparast 9 studied the statistical inferences about

C_L

on the basis of the progressively first‐failure censored data coming from a Pareto distribution with known scale parameter. Also, see Lee, 10 Wu and Hsieh, 11 Abd El‐Monsef and Hassanein 12 and Mahmoud et al.…”

Section: Introductionmentioning

confidence: 99%

Evaluating the lifetime performance index of products based on progressively Type‐II censored Pareto samples: A new Bayesian approach

Ahmadi

Doostparast

2021

Quality & Reliability Eng

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Process capability indices has been widely applied in industry to assess the performance of industrial processes. For the larger‐the‐better lifetimes of products, the lifetime performance index CL$C_L$ is commonly considered by industrial managers. This paper confines itself to the the Bayesian statistical inferences about CL$C_L$ under the Pareto distribution with the progressively Type‐II censored samples. The Bayesian inferences are based on a conjugate continuous prior for the scale parameter and a discrete prior for the shape parameter of the distribution under consideration. Two illustrative examples are given to demonstrate the sensitivity of results to the prior hyperparameters and the underlying distribution of the observations. Finally, a Monte Carlo simulation study is done to evaluate the behavior of the lifetime performance index CL$C_L$.

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“…Recently, the PFFCS has become quite popular in a life-testing problem and reliability analysis. However, the estimation of parameters of different lifetime models based on PFFCS have been studied by several authors such as [11,20,2,4,1]. In some practical situations, the progressive censoring schemes with random removals are needed.…”

Section: Introductionmentioning

confidence: 99%

“…Figure 1 shows that the profile log-likelihood function is unimodal, so we suggest using α = 0.1 as an initial value to start the iteration to obtain the MLEs. The ordered data of 30 failure times are: 1,3,5,7,11,11,11,12,14,14,14,16,16,20,21,23,42,47,52,62,71,71,87,95,90,120,120,225,246,261. Using this sample, a progressively first-failure censored sample is generated with binomial removals from the real data set with m = 10 and p = 0.5.…”

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confidence: 99%

Inferences for Weibull parameters under progressively first-failure censored data with binomial random removals

Ashour

El-Sheikh

Elshahhat

2020

Stat., optim. inf. comput.

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In this paper, the Bayesian and non-Bayesian estimation of a two-parameter Weibull lifetime model in presence of progressive first-failure censored data with binomial random removals are considered. Based on the s-normal approximation to the asymptotic distribution of maximum likelihood estimators, two-sided approximate confidence intervals for the unknown parameters are constructed. Using gamma conjugate priors, several Bayes estimates and associated credible intervals are obtained relative to the squared error loss function. Proposed estimators cannot be expressed in closed forms and can be evaluated numerically by some suitable iterative procedure. A Bayesian approach is developed using Markov chain Monte Carlo techniques to generate samples from the posterior distributions and in turn computing the Bayes estimates and associated credible intervals. To analyze the performance of the proposed estimators, a Monte Carlo simulation study is conducted. Finally, a real data set is discussed for illustration purposes.

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Pareto analysis for the lifetime performance index of products on the basis of progressively first-failure-censored batches under balanced symmetric and asymmetric loss functions

Cited by 13 publications

References 31 publications

Nonlinear Programming to Determine Best Weighted Coefficient of Balanced LINEX Loss Function Based on Lower Record Values

Nonlinear Programming to Determine Best Weighted Coefficient of Balanced LINEX Loss Function Based on Lower Record Values

Evaluating the lifetime performance index of products based on progressively Type‐II censored Pareto samples: A new Bayesian approach

Inferences for Weibull parameters under progressively first-failure censored data with binomial random removals

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