Analysis Of Lifetime Data Research Articles

Beyond precision: accelerated life testing for fuzzy life time data

Reliability analysis comprises statistical analysis techniques that make inferences based on life time data. Swift progress has been observed in life time data analyses during the last few decades. Accelerated life testing models are regarded as the most popular techniques for engineering life time data analysis. Their main aim is to model life times under different stress levels that are more severe than the usual stress level. The existing techniques consider life times as precise measurements and do not contemplate the imprecision of observations. In fact, life time measurements are not precise quantities but more or less fuzzy. Therefore, in addition to standard statistical tools, fuzzy model approaches are also essential. The current study generalizes some parametric and nonparametric classical estimation procedures for accelerated life testing in order to accommodate both fuzziness and random variation. The proposed estimators cover both uncertainties, which make them more applicable and practicable for life time analysis. The results of fuzzy life times are considered under various stress conditions, and comparisons with precise life time analysis are further presented in examples.

Marsall Olkin extended Topp–Leone distribution

new families of distributions by adding a parameter to a distribution. In this paper,Marshall-Olkin extended Topp-Leone (MOETL) distribution is introduced. Somestatistical properties of the MOETL are studied. The performance of the maximumlikelihood estimates is investigated by means of a Marckov chain Monte Carlo(MCMC) simulation study. Model parameters are obtained using maximumlikelihood method of estimation. Life time data analysis is performed todemonstrate the models applicability and flexibility. Akaike and Bayesianinformation criteria (AIC, BIC) illustrate the extended distribution provides betterfit compared to the original distribution.

The inverse power Lindley distribution in the presence of left-censored data

ABSTRACTIn this study, classical and Bayesian inference methods are introduced to analyze lifetime data sets in the presence of left censoring considering two generalizations of the Lindley distribution: a first generalization proposed by Ghitany et al. [Power Lindley distribution and associated inference, Comput. Statist. Data Anal. 64 (2013), pp. 20–33], denoted as a power Lindley distribution and a second generalization proposed by Sharma et al. [The inverse Lindley distribution: A stress–strength reliability model with application to head and neck cancer data, J. Ind. Prod. Eng. 32 (2015), pp. 162–173], denoted as an inverse Lindley distribution. In our approach, we have used a distribution obtained from these two generalizations denoted as an inverse power Lindley distribution. A numerical illustration is presented considering a dataset of thyroglobulin levels present in a group of individuals with differentiated cancer of thyroid.

The performance assessment on the lifetime performance index of products following Chen lifetime distribution based on the progressive type I interval censored sample

In the competitive manufacturing markets, quality engineers frequently are dedicated to evaluate whether the quality performance of products met the desire level. The lifetime performance index (LPI) C L is used to monitor the larger-the-better performance of lifetimes of products. Chen lifetime distribution with bathtub shape or increasing failure rate function has many applications in the lifetime data analysis. The maximum likelihood estimator for C L is derived and used to propose a hypothesis testing procedure under a lower specification limit based on the progressive type I interval censored sample. Finally, two practical examples are given to demonstrate the application of our proposed testing procedure to assess whether the lifetime performance reached the desire level.

A new family of distributions to analyze lifetime data

In this paper, a new family of distributions is proposed by using quantile functions of known distributions. Some general properties of this family are studied. A special case of the proposed family is studied in detail, namely the Lomax-Weibull distribution. Some structural properties of the special model are established. This distribution has been applied to several censored and uncensored data sets with various shapes.

Proportional Reversed Hazards Rates Model with Quantile Regression

In this paper, we introduce a parametric quantile regression model using Govindarajulu distribution for the analysis of life time data. The properties of the model are studied. We estimate the parameters of the model using maximum likelihood method. Asymptotic properties of the estimators are discussed. Finally, we apply the proposed model to a real life data.

On Bivariate Generalized Linear Failure Rate-Power Series Class of Distributions

Recently, it has been observed that the bivariate generalized linear failure rate distribution can be used quite effectively to analyze lifetime data in two dimensions. This paper introduces a more general class of bivariate distributions. We refer to this new class of distributions as bivariate generalized linear failure rate-power series model. This new class of bivariate distributions contains several lifetime models such as: generalized linear failure rate-power series, bivariate generalized linear failure rate, and bivariate generalized linear failure rate geometric distributions as special cases among others. The construction and characteristics of the proposed bivariate distribution are presented along with estimation procedures for the model parameters based on maximum likelihood. The marginal and conditional laws are also studied. We present an application to the real data set, where our model provides a better fit than other models.

Estimating the Parameter of a Exponential Distribution under Multiply Type II Censored Competing Risks Data

In lifetime data analysis, it is generally note that more than 1 risk factor (RF) may be appear at the same moment. Namely, a failure of unit is often arisen by one of the RFs. Moreover, it is known that the lifetimes of items may not be checked exactly. Therefore, we derive the estimators of parameters of exponential distribution (ED) with multiply type II censored competing risks (MCCR) data. We consider the maximum likelihood estimator (MLE) for parameters of ED with MCCR data. We also obtain the Bayes estimators (BEs) for parameter of the ED with MCCR data under the squared error loss function (SELF), DeGroot loss function (DLF) and precautionary loss function (PLF). Lindley’s approximate (LA) method is used to compute these BEs. The BEs of parameters are better than the respective MLE in terms of mean squared errors (MSEs) and biases. The choice of SELF seems to be a reasonable choice for Bayes estimation of parameters. A real data analysis has been provided.

Bayesian estimation of auc of a constant shape bi- weibull failure time distribution

A Receiver Operating Characteristic (ROC) curve provides quick access to the quality of classification in many medical diagnoses. The Weibull distribution has been observed as one of the most useful distributions, for modeling and analyzing lifetime data in Engineering, Biology, Survival and other fields. Studies have been done vigorously in the literature to determine the best method in estimating its parameters. In this paper, we examine the performance of Bayesian Estimator using Jeffreys‘ Prior Information and Extension of Jeffreys‘ Prior Information with three Loss functions, namely, the Linear Exponential Loss,General Entropy Loss, and Square Error Loss for estimating the AUC values for Constant Shape Bi-Weibull failure time distribution. Theoretical results are validated by simulation studies. Simulations indicated that estimate of AUC values were good even for relatively small sample sizes (n=25). When AUC≤0.6, which indicated a marked overlap between the outcomes in diseased and non-diseased populations. An illustrative example is also provided to explain the concepts.

On bivariate inverse Weibull distribution

Inverse Weibull distribution has been used quite successfully to analyze lifetime data which has non-monotone hazard function. The main aim of this paper is to introduce bivariate inverse Weibull distribution along the same line as the Marshall–Olkin bivariate exponential distribution, so that the marginals have inverse Weibull distributions. The proposed bivariate inverse Weibull distribution has four parameters and it has a singular component. Therefore, it can be used quite successfully if there are ties in the data. The joint probability density function, the joint cumulative distribution function and the joint survival function are all in closed forms. Several properties of this distribution have been discussed. It is observed that the proposed distribution can be obtained from the Marshall–Olkin copula. The maximum likelihood estimators of the unknown parameters cannot be obtained in closed form, and we propose to use EM algorithm to compute the maximum likelihood estimators. We propose to use parametric bootstrap method for construction of confidence intervals of the different parameters. We present some simulation experiments results to show the performances of the EM algorithm and they are quite satisfactory. We provide the Bayesian analysis of the unknown parameters based on very flexible priors. We analyze one bivariate American Football League data set for illustrative purposes, and it is observed that this model provides a slightly better fit than some of the existing models. Finally, we present some generalization to the multivariate case.

Scale mixtures log-Birnbaum–Saunders regression models with censored data: a Bayesian approach

ABSTRACTThe main objective of this paper is to develop a full Bayesian analysis for the Birnbaum–Saunders (BS) regression model based on scale mixtures of the normal (SMN) distribution with right-censored survival data. The BS distributions based on SMN models are a very general approach for analysing lifetime data, which has as special cases the Student-t-BS, slash-BS and the contaminated normal-BS distributions, being a flexible alternative to the use of the corresponding BS distribution or any other well-known compatible model, such as the log-normal distribution. A Gibbs sample algorithm with Metropolis–Hastings algorithm is used to obtain the Bayesian estimates of the parameters. Moreover, some discussions on the model selection to compare the fitted models are given and case-deletion influence diagnostics are developed for the joint posterior distribution based on the Kullback–Leibler divergence. The newly developed procedures are illustrated on a real data set previously analysed under BS regression models.

On Discriminating between Gamma and Log-logistic Distributions in Case of Progressive Type II Censoring

Gamma and log-logistic distributions are two popular distributions for analyzing lifetime data. In this paper, the problem of discriminating between these two distribution functions is considered in case of progressive type II censoring. The ratio of the maximized likelihood test (RML) is used to discriminate between them. Some simulation experiments were performed to see how the probability of correct selection (PCS) under each model work for small sample sizes. Real data life is analyzed to see how the proposed method works in practice. As a special case of progressive type II censoring, the problem of discriminating between gamma and log-logistic in case of complete samples is considered. The RML and the ratio of Minimized Kullback-Leibler Divergence (RMKLD) tests are used to discriminate between them. The asymptotic results are used to estimate the PCS which is used to calculate the minimum sample size required for discriminating between two distributions. Two real life data are analyzed.

Transmuted generalized exponential distribution: A generalization of the exponential distribution with applications to survival data

ABSTRACTIn this article, we investigate the potential usefulness of the three-parameter transmuted generalized exponential distribution for analyzing lifetime data. We compare it with various generalizations of the two-parameter exponential distribution using maximum likelihood estimation. Some mathematical properties of the new extended model including expressions for the quantile and moments are investigated. We propose a location-scale regression model, based on the log-transmuted generalized exponential distribution. Two applications with real data are given to illustrate the proposed family of lifetime distributions.

The new Burr distribution and its application

This paper derives a new family of Burr-type distributions as new Burr distribution. This particular skewed distribution that can be used quite effectively in analyzing lifetime data. It is observed that the new distribution has modified unimodal hazard function. Various properties of the new Burr distribution, such that moments, quantile functions, hazard function, and Shannon’s entropy are obtained. The exact form of the probability density function and moments of i{mathrm{th}}-order statistics in a sample of size n from new Burr distribution are derived. Estimation of parameters and change-point of hazard function by the maximum likelihood method are discussed. Change-point of hazard function is usually of great interest in medical or industrial applications. The flexibility of the new model is illustrated with an application to a real data set. In addition, a goodness-of-fit test statistic based on the Rényi Kullback–Leibler information is used.

A 3-state defect model for light-induced degradation in boron-doped float-zone silicon

We report on a light-induced bulk defect activation and subsequent deactivation in boron doped float-zone silicon that can be described by a 3-state model. During treatment at elevated temperature and illumination, a sample first converts from an initial high lifetime state into a degraded low lifetime state and then shows a recovery reaction leading to a third high lifetime state that is then stable under degradation conditions. Furthermore, it is shown that reverse reactions into the initial state appear to be possible both from the degraded as well as the regenerated state. An injection dependent analysis of lifetime data yields a defect capture cross section ratio of ∼20 suggesting a positively charged defect. (© 2016 WILEY-VCH Verlag GmbH &Co. KGaA, Weinheim)

The odd Lindley Nadarajah-Haghighi distribution

In this paper, a new three-parameter model which can be used in lifetime data analysis is introduced. Its failure rate function can be decreasing, increasing, constant and bathtub-shaped depending on its parameters. We derive explicit expressions for some of its statistical and mathematical quantities including the ordinary moments, generating function, incomplete moments, order statistics, moment of residual life and reversed residual life. Some useful characterizations are presented. Maximum likelihood method is used to estimate the model parameters. Simulation results to assess the performance of the maximum likelihood estimators are discussed in case of uncensored data. The censored maximum likelihood estimation is presented in the general case of the multi-censored data. We demonstrate empirically the importance and flexibility of the new model in modeling real data set. https://doi.org/10.28919/jmcs/3417

The length-biased weighted exponentiated inverted Weibull distribution

AbstractLength-Biased distributions are a special case of the more general form known as weighted distributions. We can exploit the conceptuality of Length-Biased distribution in the development of appropriate models for lifetime data. Its method is adjusting the original probability density function from real data and the expectation of those data. This modification can lead to correct conclusions of the models. Therefore, we introduced the Length-Biased version of the weighted Exponentiated inverted Weibull distribution in this paper. Various properties and the expressions for moments, coefficient of skewness, coefficient of kurtosis, moment generating function, hazard rate function, etc. are derived. The maximum likelihood estimates of the parameters of the proposed distribution are determined. The study results suggest that this distribution is an efficacious model in life time data analysis and other related fields.

New extended burr type X distribution

This study introduces a new extended distribution of the Burr Type X distribution, using Marshall-Olkin method called the Marshall-Olkin Extended Burr Type X distribution. The new distribution is formulated by inducing a tilt parameter in the Burr Type X distribution of Marshall-Olkin, to account for the significance of the size of an event. Model parameters are obtained using maximum likelihood and Bayesian methods of estimation. The scale and shape parameters are specifically defined to identify the dimensions and density of an event. Mathematical and statistical properties and limitations of the distribution are also presented. Lifetime data analysis is performed to demonstrate the model’s applicability and flexibility. Akaike and Bayesian Information Criteria illustrate that the new distribution provides better fit compared to other distributions. This work is licensed under a Creative Commons Attribution 4.0 International License .

Parameter estimation of the flexible Weibull distribution for type I censored samples

ABSTRACTOften in practice one is interested in the situation where the lifetime data are censored. Censorship is a common phenomenon frequently encountered when analyzing lifetime data due to time constraints. In this paper, the flexible Weibull distribution proposed in Bebbington et al. [A flexible Weibull extension, Reliab. Eng. Syst. Safety 92 (2007), pp. 719–726] is studied using maximum likelihood technics based on three different algorithms: Newton Raphson, Levenberg Marquardt and Trust Region reflective. The proposed parameter estimation method is introduced and proved to work from theoretical and practical point of view. On one hand, we apply a maximum likelihood estimation method using complete simulated and real data. On the other hand, we study for the first time the model using simulated and real data for type I censored samples. The estimation results are approved by a statistical test.

On pseudo-Mittag-Leffler functions and applications

The Mittag-Leffer function and related distribution are valuable in statistics, applied mathematics and lifetime data analysis. In this paper, we introduce the concept of pseudo-Mittag-Leffler functions. Then, we discuss the pseudo-fractional boundary value problems in two classes of pseudo-Caputo fractional derivative and pseudo-Riemann–Liouville fractional derivative to get the pseudo-integral inequalities of Lyapunov-type. Also, as an application, we obtain the nonexistence of real zeros of pseudo-Mittag-Leffler functions. Our results generalize the corresponding ones in the literature. Finally, two open problems for further investigations are given.