Predicting Failure times for some Unobserved Events with Application to Real-Life Data

This study aims to predict failure times for some units in some lifetime experiments. In some practical situations, the experimenter may not be able to register the failure times of all units during the experiment. Recently, this situation can be described by a new type of censored data called multiply-hybrid censored data. In this paper, the linear failure rate distribution is well-fitted to some real-life data and hence some statistical inference approaches are applied to estimate the distribution parameters. A two-sample prediction approach applied to extrapolate a new sample simulates the observed data for predicting the failure times for the unobserved units

Component Reliability Estimation From Partially Masked and Censored System Life Data Under Competing Risks.

This research presents new approaches to the estimation of component reliability distribution parameters from partially masked and/or censored system life data. Such data are common in continuous production environments. The methods were tested on Monte Carlo simulated data and compared to the only alternative suggested in literature. This alternative did not converge on many masked datasets. The new methods produce accurate parameter estimates, particularly at low masking levels. They show little bias. One method ignores masked data and treats them as censored observations. It works well if at least 2 known-cause failures of each component type have been observed and is particularly useful for analysis of any size datasets with a small fraction of masked observations. It provides quick and accurate estimates. A second method performs well when the number of masked observations is small but forms a significant portion of the dataset and/or when the assumption of independent masking does not hold. The third method provides accurate estimates when the dataset is small but contains a large fraction of masked observations and when independent masking is assumed. The latter two methods provide an indication which component most likely caused each masked system failure, albeit at the price of much computation time. The methods were implemented in user-friendly software that can be used to apply the method on simulated or real-life data. An application of the methods to real-life industrial data is presented. This research shows that masked system life data can be used effectively to estimate component life distribution parameters in a situation where such data form a large portion of the dataset and few known failures exist. It also demonstrates that a small fraction of masked data in a dataset can safely be treated as censored observations without much effect on the accuracy of the resulting estimates. These results are important as masked system life data are becoming more prevalent in industrial production environments. The research results are gauged to be useful in continuous manufacturing environments, e.g. in the petrochemical industry. They will also likely interest the electronics and automotive industry where masked observations are common

Bayesian and Frequentist Two-Sample Predictions of the Inverse Weibull Model Based on Generalized Order Statistics

2000 Mathematics Subject Classification: 62E16,62F15, 62H12, 62M20.This paper is concerned with the problem of deriving Bayesian prediction bounds for the future observations (two-sample prediction) from the inverse Weibull distribution based on generalized order statistics (GOS). Study the two side interval Bayesian prediction, point prediction under symmetric and asymmetric loss functions and the maximum likelihood (ML) prediction using "plug-in" procedure for future observations from the inverse Weibull distribution based on GOS. Study the problem of predicting future records based on observed progressive type II censored data and observed order statistics from the inverse Weibull distribution. Finally, a numerical example using real data are used to illustrate the procedure

Variable Selection for Nonparametric Gaussian Process Priors: Models and Computational Strategies

This paper presents a unified treatment of Gaussian process models that extends to data from the exponential dispersion family and to survival data. Our specific interest is in the analysis of data sets with predictors that have an a priori unknown form of possibly nonlinear associations to the response. The modeling approach we describe incorporates Gaussian processes in a generalized linear model framework to obtain a class of nonparametric regression models where the covariance matrix depends on the predictors. We consider, in particular, continuous, categorical and count responses. We also look into models that account for survival outcomes. We explore alternative covariance formulations for the Gaussian process prior and demonstrate the flexibility of the construction. Next, we focus on the important problem of selecting variables from the set of possible predictors and describe a general framework that employs mixture priors. We compare alternative MCMC strategies for posterior inference and achieve a computationally efficient and practical approach. We demonstrate performances on simulated and benchmark data sets.Comment: Published in at http://dx.doi.org/10.1214/11-STS354 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

On the Type-I Half-logistic Distribution and Related Contributions: A Review

The half-logistic (HL) distribution is a widely considered statistical model for studying lifetime phenomena arising in science, engineering, finance, and biomedical sciences. One of its weaknesses is that it has a decreasing probability density function and an increasing hazard rate function only. Due to that, researchers have been modifying the HL distribution to have more functional ability. This article provides an extensive overview of the HL distribution and its generalization (or extensions). The recent advancements regarding the HL distribution have led to numerous results in modern theory and statistical computing techniques across science and engineering. This work extended the body of literature in a summarized way to clarify some of the states of knowledge, potentials, and important roles played by the HL distribution and related models in probability theory and statistical studies in various areas and applications. In particular, at least sixty-seven flexible extensions of the HL distribution have been proposed in the past few years. We give a brief introduction to these distributions, emphasizing model parameters, properties derived, and the estimation method. Conclusively, there is no doubt that this summary could create a consensus between various related results in both theory and applications of the HL-related models to develop an interest in future studies

Inference About The Generalized Exponential Quantiles Based On Progressively Type-Ii Censored Data

In this study, we are interested in investigating the performance of likelihood inference procedures for the ℎ quantile of the Generalized Exponential distribution based on progressively censored data. The maximum likelihood estimator and three types of classical confidence intervals have been considered, namely asymptotic, percentile, and bootstrap-t confidence intervals. We considered Bayesian inference too. The Bayes estimator based on the squared error loss function and two types of Bayesian intervals were considered, namely the equal tailed interval and the highest posterior density interval. We conducted simulation studies to investigate and compare the point estimators in terms of their biases and mean squared errors. We compared the various types of intervals using their coverage probability and expected lengths. The simulations and comparisons were made under various types of censoring schemes and sample sizes. We presented two examples for data analysis, one of them is based on simulated data set and the other one based on a real lifetime data. Finally, we compared the classical inference and the Bayesian inference procedures. We concluded that Bias and MSE for classical statistics estimators show bitter results than the Bayesian estimators. Also, Bayesian intervals which attain the nominal error rate have the best average widths. We presented our conclusions and discussed ideas for possible future research