LINEX Loss Function Research Articles

Integration of Bayesian Adaptive Exponentially Weighted Moving Average Control Chart and Paired Ranked-Based Sampling for Enhanced Semiconductor Manufacturing Process Monitoring

Exponentially weighted moving average (EWMA) and Shewhart control charts are commonly utilized to detect the small to moderate and large shifts in the process mean, respectively. This article introduces a novel Bayesian AEWMA control chart that employs various loss functions (LFs), including square error loss function (SELF) and LINEX loss function (LLF). The control chart incorporates an informative prior for posterior and posterior predictive distributions. Additionally, the control chart utilizes various paired ranked set sampling (PRSS) schemes to improve its accuracy and effectiveness. The average run length (ARL) and standard deviation of run length (SDRL) are used to evaluate the performance of the suggested control chart. Monte Carlo simulations are conducted to compare the performance of the proposed approach to other control charts. The results show that the proposed method outperforms in identifying out-of-control signals, particularly under PRSS schemes compared to simple random sampling (SRS). The proposed CCs effectiveness was validated using a real-life semiconductor manufacturing application, utilizing different PRSS schemes. The performance of the Bayesian AEWMA CC was evaluated, demonstrating its superiority in detecting out-of-control signs compared to existing CCs. This study introduces an innovative method incorporating various LFs and PRSS schemes, providing an enhanced and efficient approach for identifying shifts in the process mean.

Symmetric LINEX loss twin support vector machine for robust classification and its fast iterative algorithm

Twin support vector machine (TSVM) is a practical machine learning algorithm, whereas traditional TSVM can be limited for data with outliers or noises. To address this problem, we propose a novel TSVM with the symmetric LINEX loss function (SLTSVM) for robust classification. There are several advantages of our method: (1) The performance of the proposed SLTSVM for data with outliers or noise can be improved by using the symmetric LINEX loss function. (2) The introduction of regularization term can effectively improve the generalization ability of our model. (3) An efficient iterative algorithm is developed to solve the optimization problems of our SLTSVM. (4) The convergence and time complexity of the iterative algorithm are analyzed in detail. Furthermore, our model does not involve loss function parameter, which makes our method more competitive. Experimental results on synthetic, benchmark and image datasets with label noises and feature noises demonstrate that our proposed method slightly outperforms other state-of-the-art methods on most datasets.

PERBANDINGAN METODE MLE BAYESIAN LOSS FUNCTION DALAM PENDUGAAN PARAMETER DISTRIBUSI INVERS RAYLEIGH

The purposes of this study are to estimate the scale parameter of invers Rayleigh distribution under MLE, Bayesian Generalized square error loss function (SELF), and Bayesian LINEX loss function . The posterior distribution is considered to use two types of prior, namely Jeffrey’s prior and exponential distribution. The proposed methods are then employed in the real data. Several criteria AIC, AICc, and BIC for the selection model are considered in order to identify the method which results in a suitable value of parameter estimated. This study found that Bayesian Generalized SELF at first polynomial and Bayesian LINEX loss function under exponential distribution yielded better estimation values than MLE based on AIC, AICc, and BIC

Bayesian analysis of single server Markovian queueing model with balking under asymmetric loss functions

The aim of this article is to obtain the Bayesian estimates of traffic intensity () in an M/M/1 queueing model with balking. Balking is a behavior of impatient customers in which upon arrival, customer decides not to enter the queue and leave the system without getting served. In this article, we considered balking probability as a function of the number of customers present in the system. We obtained the Bayesian estimates of for the model under study by using various asymmetric loss functions such as modified quadratic loss function (M/QLF), entropy loss function (ELF), De’groot loss function (DLF), and linex loss function (LLF). Also, we provide some simulation results for supporting our findings for different sample sizes and parametric values. Further, a numerical application, for the better understanding of the model, will also be analyzed.

Multi-view cost-sensitive kernel learning for imbalanced classification problem

Multi-view imbalanced learning concentrates on recognizing valuable patterns from multi-view imbalanced data. There are numerous algorithm-level multi-view imbalanced learning methods including multi-view ensemble learning methods and multi-view cost-sensitive learning methods. However, these approaches have two drawbacks. Firstly, from the multi-view representation perspective, they either ignore the agreement among different views, or fail to fully exploit the complementarity information contained in multi-view data. Secondly, from the class-imbalanced perspective, multi-view ensemble learning first needs to design a specific data pre-processing scheme to generate views and then fuses the local and global information with multi-view ensemble schemes. Such models are closely related to practical problems and lack universality. In contrast, multi-view cost-sensitive learning methods possess concise formulations. But the success of such methods depends on imposing appropriate misclassification cost to the majority and minority classes. Inspired by elegant merits of asymmetric LINEX loss function, we propose a multi-view cost-sensitive kernel learning method with LINEX loss termed as MVCSKL. It not only fully exploits the consensus and complementary information of multiple views, but also adaptively learns and adjusts the misclassification cost of different classes through the asymmetric LINEX loss function. Besides, the introduction of the kernel function enables the MVCSKL model to handle complex nonlinear problem and further guarantees its prediction performance. Furthermore, we adopt the alternating direction method of multipliers and gradient descent algorithm to solve MVCSKL. Based on the Rademacher complexity, we analyze the generalization capability of MVCSKL. Extensive experiments are conducted to verify the effectiveness of the proposed model.

Bayesian and non-Bayesian inference for a general family of distributions based on simple step-stress life test using TRV model under type II censoring

In this article, we consider the parametric inference, using Type II censored data, based on the tampered random variable (TRV) model for simple step-stress life testing (SSLT). We have taken the members of the Lehmann family of distributions as the baseline lifetimes of the experimental units under normal stress conditions. Based on Type II censored data and a simple SSLT framework, we obtain the maximum likelihood estimator (MLE) and the Bayes estimators of the model parameters. Further, we obtain asymptotic confidence intervals of the unknown model parameters using the observed Fisher information matrix. Moreover, bootstrap confidence intervals were constructed. The Bayes estimators are computed using the Markov chain Monte Carlo (MCMC) method under the squared error loss function and the LINEX loss function. We also construct the highest posterior density (HPD) credible intervals of the unknown model parameters. Extensive simulation studies are performed to investigate the finite sample properties of the proposed estimators. Finally, the proposed methods are illustrated with the analysis of a real data set.

Adaptive EWMA control chart using Bayesian approach under ranked set sampling schemes with application to Hard Bake process

The memory-type control charts, such as cumulative sum (CUSUM) and exponentially weighted moving average control chart, are more desirable for detecting a small or moderate shift in the production process of a location parameter. In this article, a novel Bayesian adaptive EWMA (AEWMA) control chat utilizing ranked set sampling (RSS) designs is proposed under two different loss functions, i.e., square error loss function (SELF) and linex loss function (LLF), and with informative prior distribution to monitor the mean shift of the normally distributed process. The extensive Monte Carlo simulation method is used to check the performance of the suggested Bayesian-AEWMA control chart using RSS schemes. The effectiveness of the proposed AEWMA control chart is evaluated through the average run length (ARL) and standard deviation of run length (SDRL). The results indicate that the proposed Bayesian control chart applying RSS schemes is more sensitive in detecting mean shifts than the existing Bayesian AEWAM control chart based on simple random sampling (SRS). Finally, to demonstrate the effectiveness of the proposed Bayesian-AEWMA control chart under different RSS schemes, we present a numerical example involving the hard-bake process in semiconductor fabrication. Our results show that the Bayesian-AEWMA control chart using RSS schemes outperforms the EWMA and AEWMA control charts utilizing the Bayesian approach under simple random sampling in detecting out-of-control signals.

Estimation for two Gompertz populations under a balanced joint progressive Type-II censoring scheme

Comparative lifetime experiments are remarkable when the study is to ascertain the relative merits of two competing products regarding the duration of their service life. This paper considers the comparative lifetime experiments of two Gompertz populations under a balanced joint progressive Type-II censoring scheme. The lifetime distributions of the units are assumed to follow the Gompertz distribution with a common shape but different scale parameters. The maximum likelihood estimates of the unknown parameters are derived. The existence of the maximum likelihood estimates is proved. Expectation-maximization and stochastic expectation-maximization algorithms are provided to calculate the estimates. The bootstrap-p, bootstrap-t, and approximate confidence intervals are established. To obtain the Bayesian estimates, it is assumed that the prior of scale parameters is a Beta-Gamma distribution and the prior of the common shape parameter is an independent Gamma distribution. Under squared error loss and LINEX loss functions, the Metropolis-Hastings algorithm is provided to compute the Bayes estimates and the credible intervals. Further, the statistical inferences with order restriction are studied when it is known a priori that the expectation of the lifespan of one population is shorter than that of the other population. A wide range of simulation experiments is conducted to evaluate the performance of the proposed methods. Finally, the lifetimes of white organic light-emitting diodes and the breaking strengths of jute fiber of gauge lengths are analyzed to illustrate the practical application of the proposed model and methods.

Bayes Estimation of Pareto Distribution Based on Type II Censored Data under the Weighted LINEX Loss Function

Bayes Estimation of Pareto Distribution Based on Type II Censored Data under the Weighted LINEX Loss Function

Reliability analysis of bathtub-shaped distribution using empirical Bayesian and E-Bayesian estimations under progressive Type-II censoring

This paper investigates the performance of empirical Bayesian and E-Bayesian estimation of the bathtub-shaped distribution based on the progressive Type-II censored samples. These two estimations overcome the selection of hyperparameters in the Bayesian method. The empirical Bayesian analysis employs the classical approach to determine the hyperparameters. The E-Bayesian estimation uses the prior distribution of hyperparameters to derive the expectation of Bayesian estimates. The estimates of parameters are derived under the squared error loss and LINEX loss functions. The extensive simulations show the results of the empirical Bayesian estimates and the E-Bayesain estimates. Further, the empirical Bayesian estimation is also presented to analyze the parameters of bathtub-shaped distribution based on the general progressive Type-II censored samples. The two datasets from the electromechanical field and medical survival analysis are analyzed using the empirical Bayesian and E-Bayesian methods.

On Statistical Modeling Using a New Version of the Flexible Weibull Model: Bayesian, Maximum Likelihood Estimates, and Distributional Properties with Applications in the Actuarial and Engineering Fields

In this article, we present a new statistical modification of the Weibull model for updating the flexibility, called the generalized Weibull-Weibull distribution. The new modification of the Weibull model is defined and studied in detail. Some mathematical and statistical functions are studied, such as the quantile function, moments, the information generating measure, the Shannon entropy and the information energy. The joint distribution functions of the two marginal univariate models via the Copula model are provided. The unknown parameters are estimated using the maximum likelihood method and Bayesian method via Monte Carlo simulations. The Bayesian approach is discussed using three different loss functions: the quadratic error loss function, the LINEX loss function, and the general entropy loss function. We perform some numerical simulations to show how interesting the theoretical results are. Finally, the practical application of the proposed model is illustrated by analyzing two applications in the actuarial and engineering fields using corporate data to show the elasticity and advantage of the proposed generalized Weibull-Weibull model. The practical applications show that proposed model is very suitable for modeling actuarial and technical data sets and other related fields.

Bayesian estimation of Marshall Olkin extended inverse Weibull under progressive type II censoring

AbstractThe estimations of parameters and percentiles for a three‐parameter Marshall Olkin extended inverse Weibull distribution based on progressively type‐II censored sample are concerned. The Bayesian, least‐squares, maximum likelihood and percentiles estimate methods for the model parameters have been developed. Comparing all estimate methods, the least‐squares, maximum likelihood and percentiles estimate methods are shown not stable due to the identification problem in the extended parametric space. Therefore, the Bayes estimate methods are focused. Three Bayesian estimations of the distribution parameters andppercentiles for 2.5, 50 and 97.5 under the squared error loss, absolute error loss and LINEX loss functions are respectively calculated by using the Markov chain Monte Carlo sampling procedure. Moreover, two real data sets are presented for the application illustration. Finally, concluding remarks are addressed.

Double-objective economic statistical design of () control chart using Linex loss function

PurposeThe purpose of this paper is to develop a double-objective economic statistical design (ESD) of () control chart under Weibull failure properties with the Linex asymmetric loss function. The authors have expressed the probability of type II error (β) as the statistical objective and the expected cost as the economic objective.Design/methodology/approachThe design used in this study is based on a double-objective economic statistical design of () control chart with Weibull shock model via applying Banerjee and Rahim's model for non-uniform and uniform schemes with Linex asymmetric loss function. The results in the least average cost and β in uniform and non-uniform schemes by Linex loss function, compared with the same schemes without loss function.FindingsNumerical results indicate that it is not possible to reduce the second type of error and costs at the same time, which means that by reducing the second type of error, the cost increases, and by reducing the cost, the second type of error increases, both of which are very important. Obtained based on the needs of the industry and which one has more priority has the right to choose. These designs define a Pareto optimal front of solutions that increase the flexibility and adaptability of the control chart in practice. When the authors use non-uniform schemes instead of uniform schemes, the average cost per unit time decreases by an average and when the authors apply loss function, the average cost per unit time increases by an average. Also, this quantity for double-objective schemes with loss function compared to without loss function schemes in cases uniform and non-uniform increases. The reason for this result is that the model underestimated the costs before using the loss function.Practical implicationsThis research adds to the body of knowledge related to flexibility in process quality control. This article may be of interest to quality systems experts in factories where the choice between cost reduction and statistical factor reduction can affect the production process.Originality/valueThe cost functions for double-objective uniform and non-uniform sampling schemes with the Weibull shock model based on the Linex loss function are presented for the first time.

Statistical inference of the stress-strength reliability for inverse Weibull distribution under an adaptive progressive type-Ⅱ censored sample

<abstract><p>In this paper, we investigate classical and Bayesian estimation of stress-strength reliability $\delta = P(X > Y)$ under an adaptive progressive type-Ⅱ censored sample. Assume that $X$ and $Y$ are independent random variables that follow inverse Weibull distribution with the same shape but different scale parameters. In classical estimation, the maximum likelihood estimator and asymptotic confidence interval are deduced. An approximate maximum likelihood estimator approach is used to obtain the explicit form. In Bayesian estimation, the Bayesian estimators are derived based on symmetric entropy loss function and LINEX loss function. Due to the complexity of integrals, we proposed Lindley's approximation to get the approximate Bayesian estimates. To compare the different estimators, we performed Monte Carlo simulations. Under gamma prior, the approximate maximum likelihood estimator performs better than Bayesian estimators. Under non-informative prior, the approximate maximum likelihood estimator has the same behavior as Bayesian estimators. In the end, two data sets are used to prove the effectiveness of the proposed methods.</p></abstract>

E-Bayesian estimation and E-posterior risk of failure probability under different loss functions and its applications in reliability analysis

This paper, based on the E-Bayesian estimation (expected Bayesian estimation), introduced the definition of E-posterior risk (expected posterior risk); we will derive the expressions of E-Bayesian estimation and their E-posterior risk for failure probability under the compound symmetric LINEX loss function, and will compare the results with the corresponding results under the square loss function. Monte Carlo simulations compared the performances of the proposed the estimation method, and compared the results on the basis of E-posterior risk. Finally, combined with the life testing data from a type of aero engine, the calculation and reliability analysis are performed, with E-Bayesian estimation and hierarchical Bayesian estimation, respectively (also using the MCMC method). When considering evaluating the E-Bayesian estimations under different loss functions, in this paper the E-posterior risk as an the evaluation standard is proposed.

Statistical Inference for Gumbel Type-II Distribution Under Simple Step-Stress Life Test Using Type-II Censoring

In this paper, we focus on the parametric inference based on the Tampered Random Variable (TRV) model for simple step-stress life testing (SSLT) using Type-II censored data. The baseline lifetime of the experimental units, under normal stress conditions, follows the Gumbel Type-II distribution with $\alpha$ and $\lambda$ being the shape and scale parameters, respectively. Maximum likelihood estimator (MLE) and Bayes estimator of the model parameters are derived based on Type-II censored samples. We obtain asymptotic intervals of the unknown parameters using the observed Fisher information matrix. Bayes estimators are obtained using Markov Chain Monte Carlo (MCMC) method under squared error loss and LINEX loss functions. We also construct highest posterior density (HPD) intervals of the unknown model parameters. Extensive simulation studies are performed to investigate the finite sample properties of the proposed estimators. Three different optimality criteria have been considered to determine the optimal censoring plans. Finally, the methods are illustrated with the analysis of two real data sets.

Bayesian and MLE of R=P(Y>X) for Exponential Distribution Based on Varied L Ranked Set Sampling

The ranked set sampling (RSS) is an effective scheme popularly used to produce more precisely estimators. Despite its popularity, RSS suffers from some drawbacks which includes high sensitivity to outliers and it cannot sometimes be applicable when the population is relatively small. To overcome these limitations, varied L ranked set sampling (VLRSS) is recently introduced. It is shown that VLRSS scheme enjoys with many interesting properties over RSS and also encompasses several existing RSS schemes. In addition, it is also helpful for providing precise estimates of several population parameters. To fill this gap, this article extends the work and address the estimation of based ℛ on VLRSS when the strength and stress both follow exponential distribution. Maximum likelihood approach as well as Bayesian method are considered for estimating ℛ. The Bayes estimators are obtained by using gamma distribution under general entropy loss function and LINEX loss function. The performance of the estimators based on VLRSS are investigated by a simulation study as well as a real dataset relevant to industrial field. The results reveal that the proposed estimators are more efficient relative to their analogues estimators under L ranked set sampling given that the quality of ranking is fairly good.

Statistical Inference for Competing Risks Model with Adaptive Progressively Type-II Censored Gompertz Life Data Using Industrial and Medical Applications

This study uses the adaptive Type-II progressively censored competing risks model to estimate the unknown parameters and the survival function of the Gompertz distribution. Where the lifetime for each failure is considered independent, and each follows a unique Gompertz distribution with different shape parameters. First, the Newton-Raphson method is used to derive the maximum likelihood estimators (MLEs), and the existence and uniqueness of the estimators are also demonstrated. We used the stochastic expectation maximization (SEM) method to construct MLEs for unknown parameters, which simplified and facilitated computation. Based on the asymptotic normality of the MLEs and SEM methods, we create the corresponding confidence intervals for unknown parameters, and the delta approach is utilized to obtain the interval estimation of the reliability function. Additionally, using two bootstrap techniques, the approximative interval estimators for all unknowns are created. Furthermore, we computed the Bayes estimates of unknown parameters as well as the survival function using the Markov chain Monte Carlo (MCMC) method in the presence of square error and LINEX loss functions. Finally, we look into two real data sets and create a simulation study to evaluate the efficacy of the established approaches.

E–Bayesian Estimation for the Inverted Topp – Leone Distribution Based on Type-II Censored Data

The objective of this paper is to estimate the unknown parameter for inverted Topp – Leone (ITL) distribution using the E-Bayesian estimation method under type-II censored sampling. The squared error loss function and the LINEX loss function are used to estimate the unknown parameter. The effectiveness of the E-Bayesian estimators in comparison to the Bayesian and maximum likelihood estimators based on mean square error is investigated using a Monte Carlo simulation.

Statistical inference for Gompertz distribution under adaptive type-II progressive hybrid censoring

Gompertz distribution is a significant and commonly used lifetime distribution, which plays an important role in reliability engineering. In this paper, we study the statistical inference of Gompertz distribution based on adaptive Type-II hybrid progressive censored schemes. From the perspective of frequentist, we derive the point estimations through the method of maximum likelihood estimation (MLE) and the existence of MLE is proved. Besides MLE, we propose the stochastic EM algorithm to reduce complexity and simplify computing. We also apply the method of Bootstraps (Bootstrap-p and Bootstrap-t) to construct confidence intervals. From Bayesian aspect, the Bayes estimates of the unknown parameters are evaluated by applying the MCMC method, the average length and coverage rate of credible intervals are also carried out. The Bayes inference is based on the squared error loss function and LINEX loss function. Furthermore, a numerical simulation is conducted to assess the performance of the proposed methods. Finally, a real-life example is considered to illustrate the application and development of the inference methods. In summary, the Bayesian method seems to perform the best among all approaches, while other approaches also present different advantages.