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Effective packaging solutions are pivotal in addressing sustainability challenges associated with food consumption. Sustainable packaging must not only reduce ecological impact but also ensure food quality preservation, minimize the risk of foodborne diseases, and contribute to mitigating the accumulation of plastic waste. While paper-based food packaging is environmentally friendly, it is susceptible to mold growth when exposed to specific humidity and temperatures, potentially leading to spoilage and safety concerns. This study introduces an innovative modeling approach employing survival analysis to estimate time to visible mold growth on paper-based materials used in food-contact packaging under varying environmental conditions. The objective is to establish an alternative statistical framework for assessing the impact of relative humidity and temperature on mold proliferation. This approach is particularly relevant to novel sustainable packaging materials in the food industry, especially when dealing with censored data. Survival heatmaps are developed to simplify the visualization of spoilage likelihood, measured by time to visible growth at a given confidence level. Although the survival model is proposed for paper-based materials, there are no theoretical limitations to its extension for use with other materials within and beyond the food industry. • Proposed survival heatmaps to simplify spoilage likelihood visualization. • Investigated spoilage characteristics of novel paper-based packaging. • Addressed challenges of censored data in mold growth modeling. • Proposed a conservative predictive model to assess spoilage timelines. [ABSTRACT FROM AUTHOR]

This paper is concerned with applying the Bayesian and E-Bayesian approaches to estimating the unknown parameters of the modified Topp–Leone–Chen distribution under a progressive Type-II censored sample plan. The paper explores the complexities of different estimating methods and investigates the behavior of the estimates through some computations. The Bayes and E-Bayes estimators are obtained under two distinct loss functions, the balanced squared error loss function, as a symmetric loss function, and the balanced linear exponential loss function, as an asymmetric loss function. The estimators are derived using gamma prior and uniform hyperprior distributions. A numerical illustration is given to examine the theoretical results through using the Metropolis–Hastings algorithm of the Markov chain Monte Carlo method of simulation by the R programming language. Finally, real-life data sets are applied to prove the flexibility and applicability of the model. [ABSTRACT FROM AUTHOR]

In quality engineering, process capability indices play a crucial role in assessing the capability of a given process. Among the widely recognized indices are Cp, Cpk, Cpm, and Cpmk, all of which presuppose the normality of the product lifetime. However, Maiti et al. (2010) proposed a more versatile process capability index, denoted as Cpyk, which does not rely on distributional assumptions. The study is currently investigating statistical inferences for the Cpyk index within the context of progressively type-II censored samples, marking the first exploration of this aspect in the research. This paper investigates maximum likelihood and Bayesian inference for the Cpyk when the underlying distribution follows the inverse Rayleigh distribution. Additionally, the study explores Bayesian credible intervals and the highest posterior density intervals using the Markov Chain Monte Carlo procedure. Various types of bootstrap confidence intervals are also taken into consideration. To assess the performance of these intervals, a Monte Carlo simulation is executed, comparing their coverage probabilities and mean lengths. The paper concludes with an illustrative example utilizing real data, providing a practical application of the discussed methodologies. [ABSTRACT FROM AUTHOR]

The complementary risk is common and important in the engineering field. However, there is not much research about it because of its complex derivation compared with the competing risk model. In this paper, we concentrate on inference of step-stress partially accelerated life test in the presence of complementary risks under progressive type-II censoring scheme. The Weibull distribution is chosen as the baseline lifetime of the model. The tampered random variable model is adopted as the statistical acceleration model in the accelerated test. We apply both the classical and Bayesian methods to obtain the estimation of lifetime parameters and acceleration factors. The reliability and reversed hazard rate are estimated based on the parametric estimates. The computational formulae of expected total test time are creatively derived under the step-stress and censored setting. The theoretical calculations are compared with simulated values to verify the derivation. Also, numerical studies including the simulation study and real-data analysis in engineering background are conducted to compare and illustrate the performance of the approaches proposed in the paper. Some conclusions and suggestions for actual production are given at the end of the paper. [ABSTRACT FROM AUTHOR]

Model averaging has become a crucial statistical methodology, especially in situations where numerous models vie to elucidate a phenomenon. Over the past two decades, there has been substantial advancement in the theory of model averaging. However, a gap remains in the field regarding model averaging in the presence of missing censoring indicators. Therefore, in this paper, we present a new model-averaging method for accelerated failure time models with right censored data when censoring indicators are missing. The model-averaging weights are determined by minimizing the Mallows criterion. Under mild conditions, the calculated weights exhibit asymptotic optimality, leading to the model-averaging estimator achieving the lowest squared error asymptotically. Monte Carlo simulations demonstrate that the method proposed in this paper has lower mean squared errors compared to other model-selection and model-averaging methods. Finally, we conducted an empirical analysis using the real-world Acute Myeloid Leukemia (AML) dataset. The results of the empirical analysis demonstrate that the method proposed in this paper outperforms existing approaches in terms of predictive performance. [ABSTRACT FROM AUTHOR]

The lifetime performance index (LPI) is an important metric for evaluating product quality, and research on the statistical inference of the LPI is of great significance. This paper discusses both the classical and Bayesian estimations of the LPI under an adaptive progressive type-II censored lifetime test, assuming that the product's lifetime follows a generalized inverse Lindley distribution. At first, the maximum likelihood estimator of the LPI is derived, and the Newton–Raphson iterative method is adopted to solve the numerical solution due to the log-likelihood equations having no analytical solutions. If the exact distribution of the LPI is not available, then the asymptotic confidence interval and bootstrap confidence interval of the LPI are constructed. For the Bayesian estimation, the Bayesian estimators of the LPI are derived under three different loss functions. Due to the complex multiple integrals involved in these estimators, the MCMC method is used to draw samples and further construct the HPD credible interval of the LPI. Finally, Monte Carlo simulations are used to observe the performance of these estimators in terms of the average bias and mean squared error, and two practical examples are used to illustrate the application of the proposed estimation method. [ABSTRACT FROM AUTHOR]

The paper introduces a nonparametric estimator for the regression function of left truncated and right censored data, achieved through minimising the mean squared relative error. Under α-mixing condition, strong uniform convergence of the estimator is established with a rate over a compact set. An extensive simulation study is conducted to assess the estimator's performance, comparing its efficiency to that of the classical regression estimator for finite samples across various scenarios. Moreover, a real world application is presented to demonstrate the practical utility of the proposed estimator. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the inferential procedures within both classical and Bayesian frameworks for the generalized logistic distribution under a random censoring model. For randomly censored data, our main goals were to develop maximum likelihood estimators and construct confidence intervals using the Fisher information matrix for the unknown parameters. Additionally, we developed Bayes estimators with gamma priors, addressing both squared error and general entropy loss functions. We also calculated Bayesian credible intervals for the parameters. These methods were applied to two real datasets with random censoring to provide valuable insights. Finally, we conducted a simulation analysis to assess the effectiveness of the estimated values. [ABSTRACT FROM AUTHOR]

Consider the semiparametric linear regression estimation problem with right-censored data. Under right censoring, the Buckley–James estimator (BJE) is the standard extension of the least squares estimator. Moreover, an iterative algorithm for the BJE has been implemented in R package called rms. We show that it often does not yield a solution, even if a consistent BJE exists. Yu and Wong (J Stat Comput Simul 72:451–460, 2002) proposed another algorithm to find all possible BJEs. The latter algorithm is modified in this paper so that it indeed finds all BJEs when the underlying regression parameter vector is identifiable. We show that some of these BJE's can be inconsistent. Thus it is important to decide how to select a proper BJE such that it is consistent if the parameter is identifiable. We suggest either choose one close to the modified semi-parametric maximum likelihood estimator (Yu and Wong in Technometrics 47:34–42, 2005) or a finite boundary point if there are infinitely many BJEs. [ABSTRACT FROM AUTHOR]

As a common semiparametric mode, the partially linear additive model has flexible structures, and it has been widely used in practice. In this paper, we study the quantile regression estimation of the model when its responses are censored. In particular, we consider a more general censoring framework, which allows different types of censoring (left, right, double, or interval censoring) simultaneously. Based on the general principles of data augmentation, we propose a unified iterative algorithm, where the censored data is imputed by sampling data from the quantile process, and regression parameters are refitted by using bootstrap samples. Monte Carlo simulations are conducted to verify the finite-sample properties of the method, and the results show its good performance. The application to Boston housing price data further illustrates the advantages of this method in practice. [ABSTRACT FROM AUTHOR]

Diverse methods to evaluate the prediction model of a time to event have been proposed in the context of right censored data where all subjects are subject to be susceptible. A time-dependent AUC (area under curve) measures the predictive ability of a marker based on case group and control one which are varying over time. When a substantial portion of subjects are event-free, a population consists of a susceptible group and a cured one. An uncertain curability of censored subjects makes it difficult to define both case group and control one. In this paper, our goal is to propose a time-dependent AUC for a cure rate model when a censoring distribution is related with covariates. A class of inverse probability of censoring weighted (IPCW) AUC estimators is proposed to adjust the possible sampling bias. We evaluate the finite sample performance of the suggested methods with diverse simulation schemes and the application to the melanoma dataset is presented to compare with other methods. [ABSTRACT FROM AUTHOR]

An improved adaptive Type-II progressive censoring scheme was recently introduced to ensure that the examination duration will not surpass a specified threshold span. Employing this plan, this paper aimed to investigate statistical inference using Weibull constant-stress accelerated life tests. Two classical setups, namely maximum likelihood and maximum product of spacings, were explored to estimate the scale, shape, and reliability index under normal use conditions as well as their asymptotic confidence intervals. Through the same suggested classical setups, the Bayesian estimation methodology via the Markov chain Monte Carlo technique based on the squared error loss was considered to acquire the point and credible estimates. To compare the efficiency of the various offered approaches, a simulation study was carried out with varied sample sizes and censoring designs. The simulation findings show that the Bayesian approach via the likelihood function provides better estimates when compared with other methods. Finally, the utility of the proposed techniques was illustrated by analyzing two real data sets indicating the failure times of a white organic light-emitting diode and a pump motor. [ABSTRACT FROM AUTHOR]

Widely used methods such as Cox proportional hazards, accelerated failure time, and Bennet proportional odds models do not model the quantiles directly, but rather allow to assess the influence of the covariates only on the location of the distribution. Quantile regression allows to assess the effects of covariates, not only on a location parameter (such as a mean or median) but also on specific percentiles of the conditional distribution. In recent years, a large family of flexible two-piece asymmetric distributions where the location parameter coincides with a specific quantile of the distribution has been studied. In a conditional (regression) setting the use of such a family of two-piece asymmetric distributions has only been investigated in the complete data case in the literature. In this paper, we propose a semi-parametric procedure to estimate the conditional quantile curves of two-piece asymmetric distributions based on right censored survival data. We use a local likelihood estimation technique in a multi-parameter functional form, via which the effect of a covariate on the location, scale, and index of the conditional survival distribution can be assessed. The finite sample performance of the estimators is investigated via simulations, and the methodology is illustrated on real data examples. [ABSTRACT FROM AUTHOR]

In this paper, statistical inference of an inverted exponentiated Rayleigh model is studied when the failure times are obtained under a modified progressive hybrid censoring. The maximum likelihood estimators of the model parameters together with associated existence and uniqueness are established, and approximate confidence intervals are constructed based on asymptotic theory. Alternatively, generalized point and interval estimates for unknown parameters are also constructed based on the proposed pivotal quantities for comparison. In addition, predictive intervals of remaining useful life from the inverted exponentiated Rayleigh distribution are also constructed under classical and generalized inferential approaches, respectively. Finally, extensive simulation studies are carried out to compare the performance of the proposed methods, and two real-life examples are analyzed for illustration. The numerical results indicate that both traditional likelihood and generalized inferential methods work satisfactorily, and that our proposed generalized approach appears much more appealing and are superior to classical results. [ABSTRACT FROM AUTHOR]

The two-parameter Rayleigh distribution, as an extended distribution of the Rayleigh distribution, has been widely applied in reliability analysis. With the introduction of the location parameter, two-parameter Rayleigh distribution becomes more flexible in fitting real-data. In this paper, based on generalized progressively hybrid censored(GPHC) sample from the two-parameter Rayleigh distribution, Classical and Bayesian inferences are discussed. The Newton-Raphson(NR) and Expectation-Maximization(EM) algorithms are used to compute the maximum likelihood estimates(MLEs). As well as the asymptotic confidence interval(ACI) estimation is obtained through the asymptotic distribution theory of maximum likelihood estimation(MLE) and computation of the observed Fisher information matrix. In Bayesian frame, the estimation of unknown parameters and prediction of future observable are taken into consideration. Due to Bayesian estimation is challenging to compute precisely and for the purpose of comparison, the Lindley's approximation, the Tierney-Kadane(TK) approximation and Markov chain Monte Carlo(MCMC) method are employed to obtain Bayesian estimates. Then, combining the MCMC algorithm mentioned in the article, the one- and two- samples Bayesian prediction are obtained. Finally, the simulation results are provided and a real-life data set is used for illustration purpose. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the statistical inference of interval-censored recurrence event data under an informative observation process. We establish an additive semiparametric mean model for the recurrence event process. Since the observation process may contain relevant information about potential underlying recurrence event processes, which leads to confounding bias, therefore, we introduced a propensity score into the additive semiparametric mean model to adjust for confounding bias, which possibly exists. Furthermore, the estimation equations were used to estimate the parameters of the covariate effects, and the asymptotic normality of the estimator under large samples is proven. Through simulation studies, we illustrated that the proposed method works well, and it was applied to the analysis of bladder cancer data. [ABSTRACT FROM AUTHOR]

The increasing prominence of the problem of censored data in various fields has made studying how to perform parameter estimation and variable selection in censored mixed-effects models one of the hotspots of current research. In this paper, considering the situation that the response variable is restricted by the bilateral limit, a double-penalty Bayesian Tobit quantile regression model was constructed to carry out parameter estimation and variable selection in the interval-censored mixed-effects model, and at the same time, the fixed-effects and random effects coefficients are compressed in Tobit's mixed-effects model, so as to reduce the estimation error of the model at the same time as the variable selection of the model is carried out. The posterior distribution of each unknown parameter was derived using the conditional Laplace prior and the mixed truncated normal distribution of interval-censored data, and then the Gibbs sampling algorithm for unknown parameter estimation was constructed. Through Monte Carlo simulation, it was found that the new method is more advantageous than the classical method in terms of variable selection and parameter estimation accuracy in various situations, such as different model sparsity, different data censoring ratios and different random error distributions, and the model is able to realize automatic variable selection. Finally, the new method is used to analyze the correlation between the crime rate and various economic indicators in China. [ABSTRACT FROM AUTHOR]

Competing risks models, also known as weakest-link models, are utilized to analyze diverse strength distributions exhibiting multi-modality, often attributed to various types of defects within the material. The weakest-link theory posits that a material's fracture is dictated by its most severe defect. However, multimodal problems can become intricate due to potential censoring, a common constraint stemming from time and cost limitations during experiments. Additionally, determining the mode of failure can be challenging due to factors like the absence of suitable diagnostic tools, costly autopsy procedures, and other obstacles, collectively referred to as the masking problem. In this paper, we investigate the distribution of strength for multimodal failures with censored data. We consider both full and partial maskings and present an EM-type parameter estimate for the Birnbaum-Saunders distribution under competing risks. We compare the results with those obtained from other distributions, such as lognormal, Weibull, and Wald (inverse-Gaussian) distributions. The effectiveness of the proposed method is demonstrated through two illustrative examples, as well as an analysis of the sensitivity of parameter estimates to variations in starting values. [ABSTRACT FROM AUTHOR]

To reduce total test time and increase the efficiency of statistical analysis of a life-testing experiment adaptive progressive Type-II censoring scheme has been proposed. This paper addresses the statistical inference of the unknown parameters, reliability, and hazard rate functions of logistic exponential distribution under adaptive progressive Type-II censored samples. Maximum likelihood estimates (MLEs) and maximum product spacing estimates (MPSEs) for the model parameters, reliability, and hazard rate functions can not be obtained explicitly, hence these are derived numerically using the Newton–Raphson method. Bayes estimates for the unknown parameters and reliability and hazard rate functions are computed under squared error loss function (SELF) and linear exponential loss function (LLF). It has been observed that the Bayes estimates are not in explicit forms, hence an approximation method such as Markov Chain Monte Carlo (MCMC) method is employed. Further, asymptotic confidence intervals (ACIs) and highest posterior density (HPD) credible intervals for the unknown parameters, reliability, and hazard rate functions are constructed. Besides, point and interval Bayesian predictions have been derived for future samples. A Monte Carlo simulation study has been carried out to compare the performance of the proposed estimates. Furthermore, three different optimality criteria have been considered to obtain the optimal censoring plan. Two real-life data sets, one from electronic industry and other one from COVID-19 data set containing the daily death rate from France are re-analyzed to demonstrate the proposed methodology. [ABSTRACT FROM AUTHOR]

In this paper, we propose a parametric accelerated failure time (AFT) hazard-based regression model with the extended alpha-power exponential (EAPE) baseline distribution. The proposed model is called the extended alpha-power exponential-AFT (EAPE-AFT) regression model. We show that the EAPE distribution is closed under the AFT model. The parameters of the proposed EAPE-AFT model have been estimated by using the method of maximum likelihood estimation. An extensive simulation study was also conducted to examine the performance of the estimates under several scenarios based on the shapes of the baseline hazard function. Finally, real-life censored survival data has been used to illustrate the applicability of the proposed model. [ABSTRACT FROM AUTHOR]

The proportional odds (PO) model is one of the most commonly used models for regression analysis of failure time data in survival analysis. It assumes that the odds of the failure is proportional to the baseline odds at any point in time given the covariate. The model focus on the situation that the ratio of the hazards converges to unity as time goes to infinity, while the proportional hazards (PH) model has a constant ratio of hazards over time. In the paper, we consider a general type of failure time data, case K interval-censored data, that include case I or case II interval-censored data as special cases. We propose a PO model-based unified penalized variable selection procedure that involves minimizing a negative sieve log-likelihood function plus a broken adaptive ridge penalty, with the initial values obtained from the ridge regression estimator. The proposed approach allows dependent censoring, which occurs quite often and could lead to biased or misleading estimates without considering it. We show that the proposed selection method has oracle properties and the estimator is semiparametrically efficient. The numerical studies suggest that the proposed approach works well for practical situations. In addition, the method is applied to an ADNI study that motivates this investigation. [ABSTRACT FROM AUTHOR]

Estimation of reliability and stress–strength parameters is important in the manufacturing industry. In this paper, we develop shrinkage-type estimators for the reliability and stress–strength parameters based on progressively censored data from a rich class of distributions. These new estimators improve the performance of the commonly used Maximum Likelihood Estimators (MLEs) by reducing their mean squared errors. We provide analytical asymptotic and bootstrap confidence intervals for the targeted parameters. Through a detailed simulation study, we demonstrate that the new estimators have better performance than the MLEs. Finally, we illustrate the application of the new methods to two industrial data sets, showcasing their practical relevance and effectiveness. [ABSTRACT FROM AUTHOR]

In this paper, estimation and prediction inference of power Muth distribution, with the progressive censoring data, are described. The maximum likelihood and Bayesian approaches of the unknown parameters are considered. Several Bayesian estimators are obtained against different symmetric and asymmetric loss functions, such as squared error, linex and general entropy. Also, the asymptotic confidence intervals and highest posterior density credible intervals of them are derived. Most focus of this paper is Bayesian prediction of the removed units in multiple stages of the progressively censored sample, so that, the Gibbs and Metropolis samplers are used, to reach this end. To compare the performance of different methods, Mont Carlo simulation is employed. Moreover, one practical data set is analyzed for illustrative purposes. [ABSTRACT FROM AUTHOR]

In this paper, the empirical likelihood and estimations problems in varying coefficient models with right censored data are investigated by using a bias correction method. Naive and residual-adjusted empirical likelihood ratios and estimators of the coefficient functions are constructed, their asymptotic distributions are obtained, and a consistent estimator of the asymptotic variance is given. The obtained results can be directly used to construct the confidence regions of the coefficient functions. Furthermore, a new method for constructing pointwise confidence intervals and simultaneous confidence bands for each coefficient function is also proposed. The proposed method is to directly calibrate the empirical log-likelihood ratio so that the obtained ratio is asymptotically chi-squared. Undersmoothing of each coefficient function is avoided, and existing data-driven methods can also effectively select the optimal bandwidth. Simulation study is performed to compare the empirical likelihood with the normal approximation-based method. An example of real data is used to illustrate our approach. [ABSTRACT FROM AUTHOR]

This paper investigates an adapted loss function for the estimation of a linear regression with right censored responses. The adapted loss function could be used in composite quantile regression, which is a good method to handle the responses with high censored rate. Under some regular conditions, we establish the consistency and asymptotic normality of the resulting estimator. For estimation of regression parameters, we propose the MMCD algorithm, which generates satisfactory results for the proposed estimator. In addition, the algorithm can also be extended to the fused adaptive lasso penalized method to identify the interquantile commonality. The finite sample performances of the methods are further illustrated by numerical results and the analysis of two real datasets. [ABSTRACT FROM AUTHOR]

The log-normal and the log-logistic distributions are two of the most commonly used distributions for studying positively skewed lifetime data. Both the distributions share number of interesting properties, and for a certain range of parameters their cumulative and hazard functions can also be similar in nature. However, selecting a more appropriate distribution and discriminating among them for a given data to best fit is an important issue. Further, when the data are observed in the presence of some censoring scheme the problem becomes more challenging. In this paper, we address the problem of selecting a more appropriate distribution by discriminating based on the random samples drawn in the presence of type-II censoring. We consider the difference of the maximized log-likelihood functions, and compute the asymptotic distribution of the discrimination statistic. We further propose a modified discriminating approach, and compute the probabilities of correct selection to check the performance of the discrimination procedure. Finally, simulation study is conducted, and two real data sets are analysed for the illustration purpose. [ABSTRACT FROM AUTHOR]

Recently, an improved adaptive Type-II progressive censoring scheme is proposed to ensure that the experimental time will not pass a pre-fixed time and ends the test after recording a pre-fixed number of failures. This paper studies the inference of the competing risks model from Weibull distribution under the improved adaptive progressive Type-II censoring. For this goal, we used the latent failure time model with Weibull lifetime distributions with common shape parameters. The point and interval estimation problems of parameters, reliability and hazard rate functions using the maximum likelihood and Bayesian estimation methods are considered. Moreover, making use of the asymptotic normality of classical estimators and delta method, approximate intervals are constructed via the observed Fisher information matrix. Following the assumption of independent gamma priors, the Bayes estimates of the scale parameters have closed expressions, but when the common shape parameter is unknown, the Bayes estimates cannot be formed explicitly. To solve this difficulty, we recommend using Markov chain Monte Carlo routine to compute the Bayes estimates and to construct credible intervals. A comprehensive Monte Carlo simulation is conducted to judge the behavior of the offered methods. Ultimately, analysis of electrodes data from the life-test of high-stress voltage endurance is provided to illustrate all proposed inferential procedures. [ABSTRACT FROM AUTHOR]

Competing risks data frequently appear in real-world operations like quality inspections, survival analysis, reliability tests, and clinical trials. From the quality point of view, relative risk rate can be considered an interesting quality indicator in analyzing the competing risks data for statistical process monitoring purposes. The relative risk rate measures the proportion of failures caused by the primary risk among a set of competing risks. This paper introduces two Shewhart-type control charts for monitoring the relative risk rate when the lifetimes of competing risks are independent Weibull random variables. The former chart is constructed based on the maximum likelihood estimation method, while the latter is developed based on the Bayesian approach. The proposed control charts can be applied in Phase II. The calculation of the Bayesian control charts and the evaluation of both process monitoring techniques have been done based on Monte Carlo simulations. The performance of the proposed control charts has been examined based on the average run length metric. The illustrative example is also discussed in detail to demonstrate the applicability of the proposed methods. [ABSTRACT FROM AUTHOR]

This paper considers a partially linear regression model relating a right-censored response variable to predictors and an extra covariate with measured error. The main problem here is that censorship and measurement error problems need to be solved to estimate the model correctly. In this sense, we propose three modified semiparametric estimators obtained from local polynomial regression, kernel smoothing, and B-spline smoothing methods based on kernel deconvolution approach and synthetic data transformation. Here, kernel deconvolution technique is used to solve the measurement error problem in the model and synthetic data transformation is considered to add the effect of censorship to the estimation procedure, which is a very common method in the literature. The performances of the introduced estimators are compared in the detailed Monte-Carlo simulation study. In addition, Carotid endarterectomy data is used as real-world data example and results are presented. According to the results, it is seen that the deconvoluted local polynomial method gives more qualified estimates than other two methods. [ABSTRACT FROM AUTHOR]

In this paper, we have considered the classical and Bayesian inference of the unknown parameters of the lifetime distribution based on the observations obtained from a simple step‐stress life‐testing (SSLT) experiment and when more than one cause of failures are observed. We have used the Tampered Random Variable (TRV) approach. The main advantage of the TRV approach is that it can be easily extended to a multiple step‐stress model as well as for different lifetime distributions. In this paper, it is assumed that the lifetime of the experimental units at each stress level follows Weibull distribution with the same shape parameter and different scale parameters. Further, we have introduced different tempering co‐efficient for different causes of failures. The maximum likelihood estimators and the associated asymptotic confidence intervals are obtained based on Type‐II censored observations. Further, we have considered the Bayesian inference of the unknown model parameters based on a fairly general class prior distributions. An extensive simulation study is performed to examine the performances of the proposed method, and the analysis of a real data set has been provided to show how the method can be used in practice. We have compared the TRV model with some of the other existing models, and the TRV model provides a better fit in terms of information theoretic criteria. We have also provided some optimality criteria, to determine the optimal stress change time and some sensitivity analyses have been performed. Most of the methods can be extended for other lifetime distributions also. [ABSTRACT FROM AUTHOR]

This paper discusses the challenging issues that reliability practitioners face in conducting destructive tests that lead to completely censored lifetimes, especially in estimating the defect rate of products. Manufacturers need to measure the defect rate for quality control purposes, but obtaining enough defective devices for accurate estimation is not easy when the defect rate is relatively low. To address the issues, a Bayesian approach for estimating the defect rate is proposed in this paper. The proposed method is devised to make up for the heavy computational burdens of the Metropolis-Hastings algorithm. To quantify the uncertainty in the Bayesian estimation, a nonparametric bootstrap technique is employed to construct a credible interval for the defect rate. The performance of the proposed method is evaluated through a variety of Monte Carlo simulation studies. The efficiency of the proposed Bayesian estimation procedure is validated using a real-world dataset of return-springs in DC motor systems under an accelerated destructive degradation test. • Estimate the defect rate of products in conducting destructive tests with completely censored lifetime data. • Propose a computationally efficient Bayesian estimator of an analytical form for the defect rate with masking. • Propose a nonparametric bootstrap technique to construct a credible interval for the defect rate. • The proposed method is validated using accelerated destructive degradation testing data of return-springs. [ABSTRACT FROM AUTHOR]

Survival analysis is widely used in fields such as medical research and reliability engineering to analyze data where not all subjects experience the event of interest by the end of the study. It requires dedicated methods capable of handling censored cases. This paper extends the collection of techniques applicable to censored data by introducing a novel algorithm for interpretable recommendations based on a set of survival action rules. Each action rule contains recommendations for changing the values of attributes describing examples. As a result of applying the action rules, an example is moved from a group characterized by a survival curve to another group with a significantly different survival rate. In practice, an example can be covered by several induced rules. To decide which attribute values should be changed, we propose a recommendation algorithm that analyzes all actions suggested by the rules covering the example. The efficiency of the algorithm has been evaluated on several benchmark datasets. We also present a qualitative analysis of the generated recommendations through a case study. The results indicate that the proposed method produces high-quality recommendations and leads to a significant change in the estimated survival time. [ABSTRACT FROM AUTHOR]

In this paper, we obtain the stress-strength reliability estimation under balanced joint Type-II progressive censoring scheme for independent samples from two different populations. We simultaneously place two independent samples where the experimental units follow Weibull distributions with common shape parameter β and different scale parameters α, λ, respectively. The maximum likelihood estimators of the unknown parameters are derived. Further, the Bayesian inference is considered using Lindley's approximation and Gibbs sampling method. Extensive simulations are performed to see the effectiveness of the proposed estimation methods. Further, we derive the optimal censoring scheme in the Bayesian framework by using the variable neighbourhood search method proposed by [Bhattacharya et al. On optimum life-testing plans under type-ii progressive censoring scheme using variable neighbourhood search algorithm. Test. 2016;25(2):309–330]. Further, some simulation schemes are provided to compare the performances of the estimations under the jointly censored samples versus two separate censored samples. [ABSTRACT FROM AUTHOR]

In this paper we extend the family of test proposed by Majumder and Mitra [Detecting trend change in failure functions-an L-statistic approach. Stat Pap. 2019;62:31–52. doi: ] for testing exponentiality against bathtub (BT) failure rate (upside down bathtub (UBT)) to randomly right censored case. We derive the asymptotic distribution of the test statistic and using Monte Carlo simulation we obtain the empirical powers for certain alternative distributions. As a special case the asymptotic distribution of the test statistic proposed by Park [Testing whether failure rate changes its trend. IEEE Trans Reliab. 1988;37(4):375–378. doi: ] is obtained. Finally some examples of real life data are given for illustrative purpose. [ABSTRACT FROM AUTHOR]

This paper considers inference on the partial area under the receiver operating characteristic curve based on two independent progressively Type-II censored samples from the populations that are belonging to the lower truncated proportional hazard rate models with the same baseline distributions. The maximum likelihood estimator, a generalized pivotal estimator and some Bayes estimators are obtained for three structures of prior distributions. The percentile bootstrap confidence interval, a generalized pivotal confidence interval and some Bayesian credible intervals are also presented. A Monte-Carlo simulation study is used to evaluate the performances of the obtained point estimators and confidence and credible intervals. Finally, a real data set is applied for illustrative purposes. [ABSTRACT FROM AUTHOR]

This paper investigates statistical inferences for product lifetimes following the inverted modified Lindley distribution, utilizing progressive Type-II censored data. The estimation of model parameters employs the maximum likelihood method, complemented by the construction of approximate confidence intervals. Bayesian estimates are also explored, incorporating squared error and linear exponential loss functions with noninformative priors. To approximate Bayes estimates, the proposal presents Gibbs sampling based on the MCMC algorithm. This results in the generation of the greatest posterior density credible intervals for the parameters. A real data analysis is conducted to validate the accuracy of all the models and methods discussed. Finally, computational studies using Monte Carlo simulations are presented to compare the suggested estimators. [ABSTRACT FROM AUTHOR]

In this paper, a unit inverse Weibull distribution as well as its basic structural properties is proposed. Furthermore, classical inferences for multicomponent reliability are discussed under type-II censoring when stress and strength components have a common parameter. The maximum likelihood estimator of the reliability is obtained and in sequel an asymptotic interval is constructed. Pivotal quantities are constructed and then generalized point and interval estimators are obtained for the reliability. Likelihood and pivotal quantities-based estimations are presented when all parameters are unequal as well. The performance of different estimators is investigated using simulation studies and real-life examples are studied from an application viewpoint. Finally, some concluding remarks are given. [ABSTRACT FROM AUTHOR]

Two-parameter exponential distributions have a widespread application in insurance, medical and industrial production. However, incomplete samples are often obtained due to experimental conditions. In this paper, a new adaptive exponentially weighted moving average control chart, called AEWMA-LR control chart, is proposed for monitoring the quality characteristics of two-parameter exponential distributions based on type-II censored data. The proposed monitoring scheme aims to achieve an adaptive effect by combining exponentially weighted moving averages and adjusting the weight factors according to the relative magnitude of the estimated location and scale parameter shifts. We explored the effects of smooth parameters, sample size, and censored parameters on the performance of AEWMA-LR control charts through a Monte Carlo simulation study. Then, a comparative analysis was conducted with existing EWMA-LR and EWMA-Max-MLE control charts based on the two-parameter exponential model. The simulation results of zero-state average run length (ARL) and conditional expected delay (CED) show that the proposed monitoring scheme outperforms the existing control charts. Finally, to demonstrate the usefulness of the AEWMA-LR control chart in real-world applications, we give three instances of two-parameter exponential distributions based on type-II right censored data. [ABSTRACT FROM AUTHOR]

Progressive type-II (Prog-II) censoring schemes are gaining traction in estimating the parameters, and reliability characteristics of lifetime distributions. The focus of this paper is to enhance the accuracy and reliability of such estimations for the inverse power exponentiated Pareto (IPEP) distribution, a flexible extension of the exponentiated Pareto distribution suitable for modeling engineering and medical data. We aim to develop novel statistical inference methods applicable under Prog-II censoring, leading to a deeper understanding of failure time behavior, improved decision-making, and enhanced overall model reliability. Our investigation employs both classical and Bayesian approaches. The classical technique involves constructing maximum likelihood estimators of the model parameters and their bootstrap covariance intervals. Using the Gibbs process constructed by the Metropolis–Hasting sampler technique, the Markov chain Monte Carlo method provides Bayesian estimates of the unknown parameters. In addition, an actual data analysis is carried out to examine the estimation process's performance under this ideal scheme. [ABSTRACT FROM AUTHOR]

Concrete pavement performance models are evaluated, calibrated, and validated using field data from databases like the Long-Term Pavement Program. Conceptually, performance model predictions should match field data considering a reliability of 50%; that is, there is a 50% probability that the predictions of a certain distress indicator are higher or lower than the field data. However, modern pavements are designed for higher levels of reliability (usually 90% to 95%). Local performance model evaluation for higher levels of reliability requires a high amount of field data that traditional databases lack. Pavement management system (PMS) databases can be a useful resource for high reliability model analysis because of the large amount of data collected locally and regularly. However, when selecting and filtering field databases (of any source), the effect of censored performance data due to rehabilitation, removal from service, or modification of pavement sections is usually ignored. This paper proposes an approach for the use of PMS databases accounting for censored performance data to evaluate the accuracy of performance models' high reliability predictions. The approach is exemplified using a PMS transverse joint faulting database. Results show that by addressing the "survival issue," i.e., accounting for the censored performance data, the resulting PMS-based reliability model improves the faulting model accuracy in matching the field data for high reliability levels. [ABSTRACT FROM AUTHOR]

When a researcher wants to perform a life-test comparison study of items made by two separate lines inside the same institution, joint censoring strategies are particularly important. In this paper, we present a new joint Type-I hybrid censoring that enables an experimenter to stop the investigation as soon as a pre-specified number of failures or time is first achieved. In the context of newly censored data, the estimates of the unknown mean lifetimes of two different Rayleigh populations are acquired using maximum likelihood and Bayesian inferential techniques. The normality characteristic of classical estimators is used to offer asymptotic confidence interval bounds for each unknown parameter. Against gamma conjugate priors, the Bayes estimators and related credible intervals are gathered about symmetric and asymmetric loss functions. Since classical and Bayes estimators are acquired in closed form, simulation tests can be easily made to evaluate the effectiveness of the proposed methodologies. The efficiency of the suggested approaches is examined in terms of four metrics, namely: Root mean squared error, average relative absolute bias, average confidence length, and coverage probability. To demonstrate the applicability of the offered approaches to real events, two real applications employing data sets from the engineering area are analyzed. As a result, when the experimenter's primary goal is to complete the test as soon as the total number of failures or the threshold period is recorded, the numerical results reveal that the recommended strategy is adaptable and very helpful in completing the study. [ABSTRACT FROM AUTHOR]

This paper centers on the examination of the Lomax distribution in the context of randomly censored data. Our primary objectives include deriving maximum likelihood estimators and constructing confidence intervals based on the Fisher information matrix for the unknown parameters in the context of randomly censored data. Furthermore, we develop Bayes estimators utilizing gamma priors, considering both squared error and general entropy loss functions. We also calculate Bayesian credible intervals for the parameters. To offer practical insights, we apply these methods to a real-world dataset subject to random censorship. Finally, for comparative purposes, we conduct a Monte Carlo simulation to assess the various estimation techniques introduced in this study. [ABSTRACT FROM AUTHOR]

The problem of examining how well the data fit a supposed distribution is very important, and it must be confirmed prior to any data analysis, because many data analysis methods assume a specific distribution of data. For this purpose, histograms or Q-Q plots are employed for the assessment of data distribution. Additionally, a GoF TstS utilizes distance measurements between the empirical distribution function and the theoretical cumulative distribution function (cdf) to evaluate data distribution. In life-testing or reliability studies, the observed failure time of test units may not be recorded in some situations. The GoF TstSs for completely observed data can no longer be used in progressive type II censored data (PrCsD). In this paper, we suggest a GoF TstSs and new plot method for the GoF test of symmetric and asymmetric location-scale distribution (LoScD) based on PrCsD. The power of the suggested TstSs is estimated through Monte Carlo (MC) simulations, and it is compared with that of the TstSs using the order statistics (OrSt). Furthermore, we analyzed real data examples (symmetric and asymmetric data). [ABSTRACT FROM AUTHOR]

In this paper, statistical inferences for the parameters, reliability, and failure rate functions (as parameters) of the exponentiated Kies distribution are accomplished using maximum likelihood and both Lindley and Markov chain Monte Carlo techniques, under adaptive Type-II progressive censoring. Depending on the Fisher information matrix and the delta method, we find the approximate confidence intervals for the parameters and the reliability and failure rate functions, respectively. Furthermore, the samples generated from Markov chains Monte Carlo are used to generate credible intervals for the parameters, reliability, and failure rates functions. Symmetric and asymmetric loss functions are also used to find Bayes estimators using Markov chain Monte Carlo and Lindley techniques. Comparisons between the two techniques of evaluation for different estimators under different sizes of data sets are conducted. Finally, a real-life example is applied to clarify the results of the used techniques. [ABSTRACT FROM AUTHOR]

In our paper, we introduce a novel extension of the Lomax distribution, aiming to enhance its applicability in various contexts. We emphasize a pragmatic approach in deriving mathematical properties of the new distribution, prioritizing its practical implications. Three distinct methods for characterizing the distribution are thoroughly discussed to provide a comprehensive understanding. The parameters of this newly proposed distribution are estimated through a diverse set of classical methodologies as well as Bayes’ method. Additionally, we develop the censored case maximum likelihood method to address scenarios where data may be incomplete. We meticulously compare the efficacy of likelihood estimation and Bayesian estimation using Pitman’s proximity criterion, thereby offering insights into their relative performance. For Bayesian estimation, we employ three distinct loss functions: the generalized quadratic, the Linex, and the entropy functions, each offering unique perspectives on the estimation process. Through extensive simulation experiments, we meticulously evaluate the performance of all estimation methods under various conditions, providing valuable insights into their practical utility. Furthermore, we conduct a comparative analysis between the Bayesian technique and the censored maximum likelihood method using the BB algorithm, facilitating a nuanced understanding of their respective strengths and weaknesses. In addition to estimation methodologies, we delve into the construction of the Nikulin-Rao-Robson statistic for the new model under both uncensored and censored cases. Detailed simulation studies and the presentation of two real-world applications elucidate the practical significance of our proposed statistics in diverse scenarios. Overall, our paper not only introduces a novel extension of the Lomax distribution but also provides a comprehensive exploration of various estimation techniques and statistical measures, underpinning its practical relevance across different domains. [ABSTRACT FROM AUTHOR]

Control charts with conditional expected value (CEV) can be used with novel statistical techniques to monitor the means of moderately and lowly censored data. In recent years, machine learning and deep learning have been successfully combined with quality technology to solve many process control problems. This paper proposes a residual control chart combining a convolutional neural network (CNN) and support vector regression (SVR) for type-I censored data with the Weibull model. The CEV and exponentially weighted moving average (EWMA) statistics are used to generate training data for the CNN and SVR. The average run length shows that the proposed chart approach outperforms the traditional EWMA CEV chart approach in various shift sizes and censored rates. The proposed chart approach is suitable to be used in detecting small shift size for highly censored data. An illustrative example presents the application of the proposed method in an electronics industry. [ABSTRACT FROM AUTHOR]

AbstractModel checking evaluates the appropriateness of a statistical model based on the observed data, and it is essential to make valid statistical analyses. In this paper, a new procedure for model checking type II censored data is proposed. This procedure combines the Kullback-Leibler divergence, the Dirichlet process, and the relative belief ratio. The method is implemented via a computational algorithm and is explained through several examples. [ABSTRACT FROM AUTHOR]

Analysis of jointly censoring schemes has received considerable attention in the last few years. In this paper, maximum likelihood and Bayes methods of estimation are used to estimate the unknown parameters of two Gompertz populations under a joint progressive Type-II censoring scheme. Bayesian estimations of the unknown parameters are obtained based on squared error loss functions under the assumption of independent gamma priors. We propose to apply the Markov Chain Monte Carlo technique to carry out a Bayes estimation procedure. The approximate, bootstrap, and credible confidence intervals for the unknown parameters are also obtained. Also, reliability and hazard rate function of the two Gompertz populations under joint progressive Type-II censoring scheme is obtained and the corresponding approximate confidence intervals. Finally, all the theoretical results obtained are assessed and compared using two real-world data sets and Monte Carlo simulation studies. [ABSTRACT FROM AUTHOR]

The proportional hazard regression models are widely used statistical tools for analyzing survival data and estimating the effects of covariates on survival times. It is assumed that the effects of the covariates are constant across the time. In this paper, we propose a novel extension of the proportional hazard model by incorporating an exponentiated-Weibull distribution to model the baseline line hazard function. The proposed model offers more flexibility in capturing various shapes of failure rates and accommodates both monotonic and non-monotonic hazard shapes. The performance evaluation of the proposed model and comparison with other commonly used survival models including the generalized log–logistic, Weibull, Gompertz, and exponentiated exponential PH regression models are explored using simulation results. The results demonstrate the ability of the introduced model to capture the baseline hazard shapes and to estimate the effect of covariates on the hazard function accurately. Furthermore, two real survival medical data sets are analyzed to illustrate the practical importance of the proposed model to provide accurate predictions of survival outcomes for individual patients. Finally, the survival data analysis reveal that the model is a powerful tool for analyzing complex survival data. [ABSTRACT FROM AUTHOR]

In studies with time-to-event outcomes, multiple, inter-correlated, and time-varying covariates are commonly observed. It is of great interest to model their joint effects by allowing a flexible functional form and to delineate their relative contributions to survival risk. A class of semiparametric transformation (ST) models offers flexible specifications of the intensity function and can be a general framework to accommodate nonlinear covariate effects. In this paper, we propose a partial-linear single-index (PLSI) transformation model that reduces the dimensionality of multiple covariates into a single index and provides interpretable estimates of the covariate effects. We develop an iterative algorithm using the regression spline technique to model the nonparametric single-index function for possibly nonlinear joint effects, followed by nonparametric maximum likelihood estimation. We also propose a nonparametric testing procedure to formally examine the linearity of covariate effects. We conduct Monte Carlo simulation studies to compare the PLSI transformation model with the standard ST model and apply it to NYU Langone Health de-identified electronic health record data on COVID-19 hospitalized patients' mortality and a Veteran's Administration lung cancer trial. [ABSTRACT FROM AUTHOR]