In this paper we introduce a new lifetime distribution by compounding exponential and Poisson-Lindley distributions, named exponential Poisson-Lindley distribution. Several properties are derived, such as density, failure rate, mean lifetime, moments, order statistics and Rényi entropy. Furthermore, estimation by maximum likelihood and inference for large sample are discussed. The paper is motivated by two applications to real data sets and we hope that this model be able to attract wider applicability in survival and reliability.
Competing risks data with discrete lifetime comes up in practice. However, only limited literature exists for such data. In this paper, we propose a non-parametric test based on U-statistics for testing independence of time to failure and cause of failure of competing risks data when the lifetime is a discrete random variable. Asymptotic distribution of the proposed test statistic is derived. An extensive Monte Carlo simulation study is conducted to assess the finite sample performance of the proposed test. The flexibility of the testing procedure is illustrated using real data sets on oral ca…
The linear exponential distribution is a generalization of the exponential and Rayleigh distributions. This distribution is one of the best models to fit data with increasing failure rate (IFR). But it does not provide a reasonable fit for modeling data with decreasing failure rate (DFR) and bathtub shaped failure rate (BTFR). To overcome this drawback, we propose a new record-based transmuted generalized linear exponential (RTGLE) distribution by using the technique of Balakrishnan and He (2021). The family of RTGLE distributions is more flexible to fit the data sets with IFR, DFR, and BTFR, …
We introduce in this paper a new class of distributions which generalizes the linear failure rate (LFR) distribution and is obtained by compounding the LFR distribution and power series (PS) class of distributions. This new class of distributions is called the linear failure rate-power series (LFRPS) distributions and contains some new distributions such as linear failure rate geometric (LFRG) distribution, linear failure rate Poisson (LFRP) distribution, linear failure rate logarithmic (LFRL) distribution, linear failure rate binomial (LFRB) distribution and Raylight-power series (RPS) class …
The two-parameter distribution known as exponential-Poisson (EP) distribution, which has decreasing failure rate, was introduced by Kus (2007). In this paper we generalize the EP distribution and show that the failure rate of the new distribution can be decreasing or increasing. The failure rate can also be upside-down bathtub shaped. A comprehensive mathematical treatment of the new distribution is provided. We provide closed-form expressions for the density, cumulative distribution, survival and failure rate functions; we also obtain the density of the $i$th order statistic. We derive the $r…
We introduce in this paper a new four-parameter generalized version of the linear failure rate (LFR) distribution which is called Beta-linear failure rate (BLFR) distribution. The new distribution is quite flexible and can be used effectively in modeling survival data and reliability problems. It can have a constant, decreasing, increasing, upside-down bathtub (unimodal) and bathtub-shaped failure rate function depending on its parameters. It includes some well-known lifetime distributions as special submodels. We provide a comprehensive account of the mathematical properties of the new distri…
In this paper, we introduce a new extension of the generalized linear failure rate distributions. It includes some well-known lifetime distributions such as extension of generalized exponential and generalized linear failure rate distributions as special sub-models. In addition, it can have a constant, decreasing, increasing, upside-down bathtub (unimodal), and bathtub-shaped hazard rate function depending on its parameters. We provide some of its statistical properties such as moments, quantiles, skewness, kurtosis, hazard rate function, and reversible hazard rate function. The maximum likeli…
In this paper, we proposed a new lifetime distribution namely generalized weighted Lindley (GLW) distribution. The GLW distribution is a useful generalization of the weighted Lindley distribution, which accommodates increasing, decreasing, decreasing-increasing-decreasing, bathtub, or unimodal hazard functions, making the GWL distribution a flexible model for reliability data. A significant account of mathematical properties of the new distribution are presented. Different estimation procedures are also given such as, maximum likelihood estimators, method of moments, ordinary and weighted leas…
In this paper, a competing risks model is analyzed based on improved adaptive type-II progressive censored sample (IAT-II PCS). Two independent competing causes of failures are considered. It is assumed that lifetimes of the competing causes of failure follow exponential distributions with different means. Maximum likelihood estimators (MLEs) for the unknown model parameters are obtained. Using asymptotic normality property of MLE, the asymptotic confidence intervals are constructed. Existence and uniqueness properties of the MLEs are studied. Further, bootstrap confidence intervals are comput…
In this paper we introduce the exponentiated Weibull power series (EWPS) class of distributions which is obtained by compounding exponentiated Weibull and power series distributions, where the compounding procedure follows same way that was previously carried out by Roman et al. (2010) and Cancho et al. (2011) in introducing the complementary exponential-geometric (CEG) and the two-parameter Poisson-exponential (PE) lifetime distributions, respectively. This distribution contains several lifetime models such as: exponentiated weibull-geometric (EWG), exponentiated weibull-binomial (EWB), expon…
In this paper a new lifetime distribution which is obtained by compounding Lindley and geometric distributions, named Lindley-geometric (LG) distribution, is introduced. Several properties of the new distribution such as density, failure rate, mean lifetime, moments, and order statistics are derived. Furthermore, estimation by maximum likelihood and inference for large sample are discussed. The paper is motivated by two applications to real data sets and we hope that this model be able to attract wider applicability in survival and reliability.
The Cauchy-Rayleigh (CR) distribution has been successfully used to describe asymmetric and heavy-tail events from radar imagery. Employing such model to describe lifetime data may then seem attractive, but some drawbacks arise: its probability density function does not cover non-modal behavior as well as the CR hazard rate function (hrf) assumes only one form. To outperform this difficulty, we introduce an extended CR model, called exponentiated Cauchy-Rayleigh (ECR) distribution. This model has two parameters and hrf with decreasing, decreasing-increasing-decreasing and upside-down bathtub f…
The second-largest order statistic is of special importance in reliability theory since it represents the time to failure of a $2$-out-of-$n$ system. Consider two $2$-out-of-$n$ systems with heterogeneous random lifetimes. The lifetimes are assumed to follow heterogeneous general exponentiated location-scale models. In this communication, the usual stochastic and reversed hazard rate orders between the systems' lifetimes are established under two cases. For the case of independent random lifetimes, the usual stochastic order and the reversed hazard rate order between the second-largest order s…
In engineering systems, it is usually assumed that lifetimes of components are independent and identically distributed (iid). But, the failure of a component results in a higher load on the remaining components and hence causes the distribution of the surviving components change. For modeling this kind of systems, the theory of sequential order statistics (SOS) can be used. Assuming Weibull distribution for lifetimes of components and conditionally proportional hazard rates model as a special case of the SOS theory, the maximum likelihood estimates of the unknown parameters are obtained in dif…
One-shot devices analysis involves an extreme case of interval censoring, wherein one can only know whether the failure time is either before or after the test time. Some kind of one-shot devices do not get destroyed when tested, and so can continue within the experiment, providing extra information for inference, if they did not fail before an inspection time. In addition, their reliability can be rapidly estimated via accelerated life tests (ALTs) by running the tests at varying and higher stress levels than working conditions. In particular, step-stress tests allow the experimenter to incre…
In this paper, we consider the situation under a life test, in which the failure time of the test units are not related deterministically to an observable stochastic time varying covariate. In such a case, the joint distribution of failure time and a marker value would be useful for modeling the step stress life test. The problem of accelerating such an experiment is considered as the main aim of this paper. We present a step stress accelerated model based on a bivariate Wiener process with one component as the latent (unobservable) degradation process, which determines the failure times and t…
We focus on the problem of establishing the optimal upper bounds on generalized order statistics which are based on the underlying cdf belonging to the family of distributions with decreasing failure rate and decreasing failure rate on the average. This issue has been previously considered by Bieniek [Projection bounds on expectations of generalized order statistics from DFR and DFRA families, Statistics, 2006; 40: 339--351], who established upper nonnegative mean-variance bounds with use of the projections of the compositions of density functions of the uniform generalized order statistic and…
This paper introduces a new four-parameter lifetime model called the Weibull Birnbaum-Saunders distribution. This new distribution represents a more flexible model for the lifetime data. Its failure rate function can be increasing, decreasing, upside-down bathtub shaped, bathtub-shaped or modified bathtub shaped depending on its parameters. Some structural properties of the proposed model are investigated including expansions for the cumulative and density functions, moments, generating function, mean deviations, order statistics and reliability. The maximum likelihood estimation method is use…
Accelerated life-testing (ALT) is a very useful technique for examining the reliability of highly reliable products. It allows testing the products at higher than usual stress conditions to induce failures more quickly and economically than under typical conditions. A special case of ALT are step-stress tests that allow experimenter to increase the stress levels at fixed times. This paper deals with the multiple step step-stress model under the cumulative exposure model with lognormally distributed lifetimes in the presence of Type-II and Progressive Type-II censoring. For this model, the maxi…
Here, we introduce a new class of Lindley generated distributions which results in more flexible model with increasing failure rate (IFR), decreasing failure rate(DFR) and up-side down hazard functions for different choices of parametric values. We explore, various distributional properties including limiting distribution of extreme order statistics explored. Maximum likelihood estimators and the confidence intervals of the parameters are obtained. The applicability of the proposed distribution is shown through modelling two sets of real data on bladder cancer patients and waiting time in a qu…
In this article, we proposed a new probability distribution named as power Maxwell distribution (PMaD). It is another extension of Maxwell distribution (MaD) which would lead more flexibility to analyze the data with non-monotone failure rate. Different statistical properties such as reliability characteristics, moments, quantiles, mean deviation, generating function, conditional moments, stochastic ordering, residual lifetime function and various entropy measures have been derived. The estimation of the parameters for the proposed probability distribution has been addressed by maximum likelih…
Institute of Informatics（信息学研究所）；University of Munich (LMU)（慕尼黑大学（LMU））
The main objective of Prognostics and Health Management is to estimate the Remaining Useful Lifetime (RUL), namely, the time that a system or a piece of equipment is still in working order before starting to function incorrectly. In recent years, numerous machine learning algorithms have been proposed for RUL estimation, mainly focusing on providing more accurate RUL predictions. However, there are many sources of uncertainty in the problem, such as inherent randomness of systems failure, lack of knowledge regarding their future states, and inaccuracy of the underlying predictive models, makin…
This paper introduces a simple index that helps to assess the degree of aging or rejuvenation of a (non)repairable system. The index ranges from -1 to 1 and is negative for the class of decreasing failure rate distributions (or deteriorating point processes) and is positive for the increasing failure rate distributions (or improving point processes). The introduced index is distribution free.
In this paper, we introduce a new four-parameter generalization of the exponentiated Weibull (EW) distribution, called the exponentiated Weibull-logarithmic (EWL) distribution, which obtained by compounding EW and logarithmic distributions. The new distribution arises on a latent complementary risks scenario, in which the lifetime associated with a particular risk is not observable; rather, we observe only the maximum lifetime value among all risks. The distribution exhibits decreasing, increasing, unimodal and bathtub-shaped hazard rate functions, depending on its parameters and contains seve…
The Kumaraswamy Inverse Weibull distribution has the ability to model failure rates that have unimodal shapes and are quite common in reliability and biological studies. The three-parameter Kumaraswamy Inverse Weibull distribution with decreasing and unimodal failure rate is introduced. We provide a comprehensive treatment of the mathematical properties of the Kumaraswany Inverse Weibull distribution and derive expressions for its moment generating function and the $r$-th generalized moment. Some properties of the model with some graphs of density and hazard function are discussed. We also dis…
Handling missing values plays an important role in the analysis of survival data, especially, the ones marked by cure fraction. In this paper, we discuss the properties and implementation of stochastic approximations to the expectation-maximization (EM) algorithm to obtain maximum likelihood (ML) type estimates in situations where missing data arise naturally due to right censoring and a proportion of individuals are immune to the event of interest. A flexible family of three parameter exponentiated-Weibull (EW) distributions is assumed to characterize lifetimes of the non-immune individuals a…
