The Poisson-exponential lifetime distribution

In this paper we proposed a new two-parameters lifetime distribution with increasing failure rate. The new distribution arises on a latent complementary risk problem base. The properties of the proposed distribution are discussed, including a formal proof of its probability density function and explicit algebraic formulae for its reliability and failure rate functions, quantiles and moments, including the mean and variance. A simple EM-type algorithm for iteratively computing maximum likelihood estimates is presented. The Fisher information matrix is derived analytically in order to obtaining the asymptotic covariance matrix. The methodology is illustrated on a real data set.     

The complementary exponential power lifetime model

In this paper we propose a new lifetime distribution which can handle bathtub-shaped, unimodal, increasing and decreasing hazard rate functions. The model has three parameters and generalizes the exponential power distribution proposed by Smith and Bain (1975) with the inclusion of an additional shape parameter. The maximum likelihood estimation procedure is discussed. A small-scale simulation study examines the performance of the likelihood ratio statistics under small and moderate sized samples. Three real datasets illustrate the methodology.     

Exponentiated Weibull–Poisson distribution: Model,properties and applications

In this paper we propose a new four-parameters distribution with increasing, decreasing, bathtub-shaped and unimodal failure rate, called as the exponentiated Weibull–Poisson (EWP) distribution. The new distribution arises on a latent complementary risk problem base and is obtained by compounding exponentiated Weibull (EW) and Poisson distributions. This distribution contains several lifetime sub-models such as: generalized exponential-Poisson (GEP), complementary Weibull–Poisson (CWP), complementary exponential-Poisson (CEP), exponentiated Rayleigh–Poisson (ERP) and Rayleigh–Poisson (RP) distributions.We obtain several properties of the new distribution such as its probability density function, its reliability and failure rate functions, quantiles and moments. The maximum likelihood estimation procedure via an EM-algorithm is presented in this paper. Sub-models of the EWP distribution are studied in details. In the end, applications to two real data sets are given to show the flexibility and potentiality of the new distribution.     

The Lindley distribution applied to competing risks lifetime data

Competing risks data usually arises in studies in which the death or failure of an individual or an item may be classified into one of k ≥ 2 mutually exclusive causes. In this paper a simple competing risks distribution is proposed as a possible alternative to the Exponential or Weibull distributions usually considered in lifetime data analysis. We consider the case when the competing risks have a Lindley distribution. Also, we assume that the competing events are uncorrelated and that each subject can experience only one type of event at any particular time.     

The bivariate generalized linear failure rate distribution and its multivariate extension

The two-parameter linear failure rate distribution has been used quite successfully to analyze lifetime data. Recently, a new three-parameter distribution, known as the generalized linear failure rate distribution, has been introduced by exponentiating the linear failure rate distribution. The generalized linear failure rate distribution is a very flexible lifetime distribution, and the probability density function of the generalized linear failure rate distribution can take different shapes. Its hazard function also can be increasing, decreasing and bathtub shaped. The main aim of this paper is to introduce a bivariate generalized linear failure rate distribution, whose marginals are generalized linear failure rate distributions. It is obtained using the same approach as was adopted to obtain the Marshall-Olkin bivariate exponential distribution. Different properties of this new distribution are established. The bivariate generalized linear failure rate distribution has five parameters and the maximum likelihood estimators are obtained using the EM algorithm. A data set is analyzed for illustrative purposes. Finally, some generalizations to the multivariate case are proposed.     

A new distribution with decreasing, increasing and upside-down bathtub failure rate

The modeling and analysis of lifetimes is an important aspect of statistical work in a wide variety of scientific and technological fields. For the first time, the so-called generalized exponential geometric distribution is introduced. The new distribution can have a decreasing, increasing and upside-down bathtub failure rate function depending on its parameters. It includes the exponential geometric (Adamidis and Loukas, 1998), the generalized exponential (Gupta and Kundu, 1999) and the extended exponential geometric (Adamidis et al., 2005) distributions as special sub-models. We provide a comprehensive mathematical treatment of the distribution and derive expressions for the moment generating function, characteristic function and rth moment. An expression for Rényi entropy is obtained, and estimation of the stress-strength parameter is discussed. We estimate the parameters by maximum likelihood and obtain the Fisher information matrix. The flexibility of the new model is illustrated in an application to a real data set.     

A new lifetime distribution

A new two-parameter distribution with decreasing failure rate is introduced. Various properties of the introduced distribution are discussed. The EM algorithm is used to determine the maximum likelihood estimates and the asymptotic variances and covariance of these estimates are obtained. Simulation studies are performed in order to assess the accuracy of the approximation of the variances and covariance of the maximum likelihood estimates and investigate the convergence of the proposed EM scheme. Illustrative examples based on real data are also given.     

A generalized modified Weibull distribution for lifetime modeling

A four parameter generalization of the Weibull distribution capable of modeling a bathtub-shaped hazard rate function is defined and studied. The beauty and importance of this distribution lies in its ability to model monotone as well as non-monotone failure rates, which are quite common in lifetime problems and reliability. The new distribution has a number of well-known lifetime special sub-models, such as the Weibull, extreme value, exponentiated Weibull, generalized Rayleigh and modified Weibull distributions, among others. We derive two infinite sum representations for its moments. The density of the order statistics is obtained. The method of maximum likelihood is used for estimating the model parameters. Also, the observed information matrix is obtained. Two applications are presented to illustrate the proposed distribution.     

A generalized modified Weibull distribution for lifetime modeling

A four parameter generalization of the Weibull distribution capable of modeling a bathtub-shaped hazard rate function is defined and studied. The beauty and importance of this distribution lies in its ability to model monotone as well as non-monotone failure rates, which are quite common in lifetime problems and reliability. The new distribution has a number of well-known lifetime special sub-models, such as the Weibull, extreme value, exponentiated Weibull, generalized Rayleigh and modified Weibull distributions, among others. We derive two infinite sum representations for its moments. The density of the order statistics is obtained. The method of maximum likelihood is used for estimating the model parameters. Also, the observed information matrix is obtained. Two applications are presented to illustrate the proposed distribution.     

A compound class of Weibull and power series distributions

In this paper we introduce the Weibull power series (WPS) class of distributions which is obtained by compounding Weibull and power series distributions, where the compounding procedure follows same way that was previously carried out by Adamidis and Loukas (1998). This new class of distributions has as a particular case the two-parameter exponential power series (EPS) class of distributions (Chahkandi and Ganjali, 2009), which contains several lifetime models such as: exponential geometric (Adamidis and Loukas, 1998), exponential Poisson (Kus, 2007) and exponential logarithmic (Tahmasbi and Rezaei, 2008) distributions. The hazard function of our class can be increasing, decreasing and upside down bathtub shaped, among others, while the hazard function of an EPS distribution is only decreasing. We obtain several properties of the WPS distributions such as moments, order statistics, estimation by maximum likelihood and inference for a large sample. Furthermore, the EM algorithm is also used to determine the maximum likelihood estimates of the parameters and we discuss maximum entropy characterizations under suitable constraints. Special distributions are studied in some detail. Applications to two real data sets are given to show the flexibility and potentiality of the new class of distributions.     

EM algorithm for one-shot device testing under the exponential distribution

The EM algorithm is a powerful technique for determining the maximum likelihood estimates (MLEs) in the presence of binary data since the maximum likelihood estimators of the parameters cannot be expressed in a closed-form. In this paper, we consider one-shot devices that can be used only once and are destroyed after use, and so the actual observation is on the conditions rather than on the real lifetimes of the devices under test. Here, we develop the EM algorithm for such data under the exponential distribution for the lifetimes. Due to the advances in manufacturing design and technology, products have become highly reliable with long lifetimes. For this reason, accelerated life tests are performed to collect useful information on the parameters of the lifetime distribution. For such a test, the Bayesian approach with normal prior was proposed recently by Fan et al. (2009). Here, through a simulation study, we show that the EM algorithm and the mentioned Bayesian approach are both useful techniques for analyzing such binary data arising from one-shot device testing and then make a comparative study of their performance and show that, while the Bayesian approach is good for highly reliable products, the EM algorithm method is good for moderate and low reliability situations.     

增长因子动态模型法Bayes可靠性评定

对于寿命分布为指数分布的可靠性增长试验,将历史数据进行折合,从而运用Bayes方法对失效率进行评估具有重要的意义.研究了增长因子折合法,针对可靠性增长多阶段试验的特点,对采用延缓纠正的可靠性增长模式进行分析,结合AMSAA模型,建立增长因子的动态模型,通过历史数据获得增长因子.运用数据折合和共轭分布,获得当前阶段的验后分布,然后,对多阶段可靠性增长的失效率作Bayes估计,给出了失效率的无偏估计和置信下限.最后通过实例给出了运用该方法进行分析的基本步骤,结果表明该方法具有一定的适用性.     

Lindley distribution and its application

A treatment of the mathematical properties is provided for the Lindley distribution. The properties studied include: moments, cumulants, characteristic function, failure rate function, mean residual life function, mean deviations, Lorenz curve, stochastic ordering, entropies, asymptotic distribution of the extreme order statistics, distributions of sums, products and ratios, maximum likelihood estimation and simulation schemes. An application to waiting time data at a bank is described.     

Exponential splines and minimal-support bases for curve representation

Our interest is to characterize the spline-like integer-shift-invariant bases capable of reproducing exponential polynomial curves. We prove that any compact-support function that reproduces a subspace of the exponential polynomials can be expressed as the convolution of an exponential B-spline with a compact-support distribution. As a direct consequence of this factorization theorem, we show that the minimal-support basis functions of that subspace are linear combinations of derivatives of exponential B-splines. These minimal-support basis functions form a natural multiscale hierarchy, which we utilize to design fast multiresolution algorithms and subdivision schemes for the representation of closed geometric curves. This makes them attractive from a computational point of view. Finally, we illustrate our scheme by constructing minimal-support bases that reproduce ellipses and higher-order harmonic curves.     

A two-parameter lifetime distribution with decreasing failure rate

In this paper, a new two-parameter lifetime distribution with decreasing failure rate is introduced. Various properties of the proposed distribution are discussed. The estimation of the parameters attained by the EM algorithm and their asymptotic variances and covariances are obtained. In order to assess the accuracy of the approximation of variances and covariances of the maximum likelihood estimators, simulation studies are performed and experimental results are illustrated based on real data sets.     

Estimation for mixed exponential distributions under type-II progressively hybrid censored samples

The type-II progressively hybrid censoring scheme can be deemed as a mixture of type-II progressive and hybrid censoring schemes, which has been utilized to analyze lifetime data in the literature for exponential distribution and Weibull distribution and so on, where the experiment terminates at a pre-specified time. However, little attention has been paid to parametric estimation under this censoring scheme for the mixed exponential distribution (MED) model, which is an important model in life data analysis. Based on type-II progressively hybrid censored samples, the estimation problem of the MED is addressed. The closed form of maximum likelihood estimators (MLEs) of unknown parameters using the EM algorithm are obtained. Some Monte Carlo simulations are implemented and a real data set is analyzed to illustrate the performance of the proposed method.     

On testing alternative classes of life distribution with guaranteed survival times

Nonparametric procedures are proposed for testing exponentiality against several new aging classes of life distributions. The main idea is to test if the lifetime of a system, whose failure time has occurred in between visits, belongs to some alternative new aging classes of life distribution. This knowledge enables us to better estimate premium amounts for clients by more accurately estimating value when encountering left or interval-censored data. One possible approach to perform these tests is based on the empirical distribution function. The limiting distributions of the presented test statistics are given for a well known alternative when the null distribution is exponential. For small sample sizes, the power of the tests are calculated. The results derived by a Monte Carlo method show an excellent power of these procedures for some common alternative distributions.     

Analysis of dependent competing risks in the presence of progressive hybrid censoring using Marshall–Olkin bivariate Weibull distribution

The lifetime of subjects in reliability and survival analysis in the presence of several causes of failure (i.e., competing risks) has attracted attention in the literature. Most studies have simplified the computations by assuming that the causes are independent, though this does not hold. Dependent competing risks under progressively hybrid censoring condition using a Marshall–Olkin bivariate Weibull distribution is investigated. Maximum likelihood and approximated maximum likelihood estimators are developed for estimating the unknown parameters. Asymptotic distributions of the maximum likelihood estimators are used to construct approximate confidence intervals using the observed Fisher information matrix. Based on a simulation and real applications, it is illustrated that when a parametric distributional assumption is nearly true, a close approximation could be achieved by deliberately censoring the number of subjects and the study duration using Type-II progressively hybrid censoring, which might help to save time and money in research studies.     

On some lifetime distributions with decreasing failure rate

A new two-parameter distribution family with decreasing failure rate arising by mixing power-series distribution and exponential distribution is introduced. This family includes some well-used mixing distributions. Various properties of this family are discussed and the estimation of parameters are obtained by method of maximum likelihood. An EM algorithm is proposed for computing the estimates and expression for their asymptotic variances and covariances are derived. Simulation studies are performed and experimental results are illustrated based on real data sets.     

基于性能退化分析的电连接器可靠性评估

某型电连接器具有寿命长、可靠性高的特点,传统的基于失效寿命数据的可靠性评估方法行不通。提出了基于性能退化分析的可靠性评估方法,给出了进行评估的一般步骤,并以温度为加速应力设计了该型电连接器的加速退化试验。分析了电连接器的接触失效机理,进而推导出退化模型,估计出了样品的伪寿命值。利用Anderson-Darling统计量确定寿命分布类型为对数正态分布,对寿命分布函数和Arrhenius加速方程的参数值进行了极大似然估计,推导出了该型电连接器在工作温度下的可靠度函数,得出t0.9为244 240h。