Weighted Linear Failure Rate Distribution: Properties, Regression Model, and Applications

This paper introduces a new comprehensive four-parameter distribution called the modified generalized linear failure rate (MGLFR) distribution. The method generalizes some well-known and most commonly used distributions in reliability such as exponential, Rayleigh, linear failure rate, generalized linear failure rate and modified Weibull distribution. The study also investigates some essential properties of this new distribution and considers the problem of the evaluation of system reliability by describing the lifetimes of components based on a fuzzy MGLFR distribution and by developing fuzzy reliability characteristics. The results can be applied to determine the reliability of real objects where parameters of lifetime variable are subject to uncertainty.

We introduce in this paper a new six-parameters generalized version of the generalized linear failure rate (GLFR) distribution which is called McDonald Generalized Linear failure rate (McGLFR) 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, and upside down bathtub-and bathtub shaped failure rate function depending on its parameters. It includes some well-known lifetime distributions as special sub-models. Some structural properties of the new distribution are studied. Moreover we discuss maximum likelihood estimation of the unknown parameters of the new model.

ABSTRACTIn a load-sharing system, the failure of a component affects the residual lifetime of the surviving components. We propose a model for the load-sharing phenomenon in k-out-of-m systems. The model is based on exponentiated conditional distributions of the order statistics formed by the failure times of the components. For an illustration, we consider two component parallel systems with the initial lifetimes of the components having Weibull and linear failure rate distributions. We analyze one data set to show that the proposed model may be a better fit than the model based on sequential order statistics.

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.

For the first time, a five-parameter distribution, called the kumaraswamy quadratic hazard rate distribution is defined and studied. The new distribution contains as special models some well-known distributions discussed in lifetime literature, such as the Linear failure rate, Exponential and Rayleigh distributions, among several others. We obtain the moments, moment generating and quantile functions. We discuss the method of maximum likelihood to estimate the model parameters and determine the observed information matrix. A real data sets illustrate the importance and flexibility of the proposed models. Normal 0 false false false EN-US X-NONE AR-SA

Exponentiated generalized linear exponential distribution

Analyzing the reliability of the aging class of life distribution provides important information about how long a product lasts and sustainability measures that are essential for determining the environmental impact and formulating resource-saving plans. The study emphasizes the goodness-of-fit technique of the nonparametric test for the NBRUmgf class because age data are crucial for applications. Evaluations were conducted using the test’s asymptotic properties and Pitman efficiency methodology for some selected asymmetric probability models, and the outcomes were compared with those of alternative methods. We assessed the test’s power against widely used reliability distributions for some well-known alternative asymmetric distributions, including the Weibull, Gamma, and linear failure rate (LFR) distributions, and provided percentiles for both censored and uncensored data. This study shows the efficacy of the test in various sectors using real-world datasets and comprehensive tables of test statistics.

A new family of Marshall–Olkin extended generalized linear exponential distribution

A new exponentiated generalized linear exponential distribution (NEGLED) is introduced, which poses increasing, decreasing, bathtub-shaped, and constant hazard rate. Its various mathematical properties such as moments, quantiles, order statistics, hazard rate function (HRF), stress–strength parameter, etc. are derived. Five distributions, exponential distribution (ED), generalized linear exponential distribution (GLED), Rayleigh distribution (RD), Weibull distribution (WD), and generalized linear failure rate distribution (GLFRD) were used for comparison with NEGLED model using a dataset of blood cancer patients. Estimation of the parameters using the maximum likelihood estimation (MLE) method was obtained and to evaluate their performance a simulation study has been carried out. Finally, a dataset of 40 Leukemia patients was analysed for illustrative purpose proving that the NEGLED outperforms compared distributions.

The quality performance of many vital systems depends on how long the units are performing; hence, research works started focusing on increasing the reliability of systems while taking into consideration that many factors may cause the failures of operating systems. In this study, the combination of a parametric generalized linear failure rate distribution model and an adaptive progressive Type-II censoring scheme for practical purposes is explored. A comprehensive investigation is performed on the risk factors that cause failure and determines which of the factors has a more harmful effect on the units. A lifetime experiment is performed under the condition of an adaptive progressive Type-II censoring scheme to obtain observations as a result of the competing factors of failures. The obtained observations are assumed to follow a three-parameter generalized linear failure rate distribution and are assumed to be competing to cause failure. Two statistical inference methods are employed for estimating this model’s parameters: the frequentist maximum likelihood method and the Bayesian approach. Our model’s validity is demonstrated through extensive simulations and real data applications in the medical and electrical engineering fields.

This paper introduces a new lifetime distribution, the so-called odd log-logistic exponentiated Weibull distribution. The new distribution has the advantage of being capable of modeling various shapes of aging and failure criteria. We derive various of its structural properties including ordinary and incomplete moments, quantile and generating functions, and order statistics. The new density function can be expressed as a linear mixture of exponentiated Weibull densities. We propose a log-linear regression model using a new distribution, the log-odd log-logistic exponentiated Weibull distribution. The maximum-likelihood method is used to estimate the model parameters. Simulation results to assess the performance of the maximum-likelihood estimation are discussed. We prove empirically the importance and flexibility of the new model by modeling four real data sets.

Degradation models are widely used to assess the lifetime information of highly reliable products possessing quality characteristics that both degrade over time and can be related to reliability. The performance of a degradation model largely depends on an appropriate model description of the product's degradation path. Conventionally, the random or mixed-effect model is one of the most well-known approaches presented in the literature in which the normal distribution is commonly adopted to represent unit-to-unit variability in the degradation model. However, this assumption may not appropriately signify accurate projections for practical applications. This paper is motivated by laser data wherein the normal distribution is relaxed with a skew-normal distribution that consequently provides greater flexibility as it can capture a broad range, non-normal, asymmetric behavior in unit-to-unit variability. Based on the proposed degradation model, we first derive analytical expressions for a product's lifetime distribution along with its corresponding mean-time-to-failure ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MTTF</i> ). We then utilize the laser data to illustrate advantages gained by the proposed model. Finally, we address effects from the skewness parameter with regard to the accuracy of both a product's <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MTTF</i> and its <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</i> th failure quantile; especially when the underlying skew-normal distribution is mis-specified as a normal distribution. The result demonstrates that effects from the skewness parameter on the tail probabilities of a product's lifetime distribution are not negligible when the random effect of the true degradation model follows a skew-normal distribution.

In this paper we propose a new lifetime model, called the odd generalized exponential linear failure rate distribution.Some statistical properties of the proposed distribution such as the moments, the quantiles, the median, and the mode are investigated.The method of maximum likelihood is used for estimating the model parameters.An applications to real data is carried out to illustrate that the new distribution is more flexible and effective than other popular distributions in modeling lifetime data.

The existence of nonmonotonic hazard rates was recognized from the study of human mortality three centuries ago. Among such hazard rates, ones with bathtub or upside-down bathtub shape have received considerable attention during the last five decades. Several models have been suggested to represent lifetimes possessing bathtub-shaped hazard rates. In this chapter, we review the existing results and also discuss some new models based on quantile functions. We discuss separately bathtub-shaped distributions with two parameters, three parameters, and then more flexible families. Among the two-parameter models, the Topp-Leone distribution, exponential power, lognormal, inverse Gaussian, Birnbaum and Saunders distributions, Dhillon’s model, beta, Haupt-Schabe models, loglogistic, Avinadev and Raz model, inverse Weibull, Chen’s model and a flexible Weibull extension are presented along with their quantile functions. The quadratic failure rate distribution, truncated normal, cubic exponential family, Hjorth model, generalized Weibull model of Mudholkar and Kollia, exponentiated Weibull, Marshall-Olkin family, generalized exponential, modified Weibull extension, modified Weibull, generalized power Weibull, logistic exponential, generalized linear failure rate distribution, generalized exponential power, upper truncated Weibull, geometric-exponential, Weibull-Poisson and transformed model are some of the distributions considered under three-parameter versions. Distributions with more than three parameters introduced by Murthy et al., Jiang et al., Xie and Lai, Phani, Agarwal and Kalla, Kalla, Gupta and Lvin, and Carrasco et al. are presented as more flexible families. We also introduce general methods that enable the construction of distributions with nonmonotone hazard functions. In the case of many of the models so far specified, the hazard quantile functions and their analysis are also presented to facilitate a quantile-based study. Finally, the properties of total time on test transforms and Parzen’s score function are utilized to develop some new methods of deriving quantile functions that have bathtub hazard quantile functions.

The aim of this expository paper is to present the properties of the linear skew-t distribution, which is a specific example of a symmetry modulated-distribution. The skewing function remains the distribution function of Student’s t, but its argument is simpler than that used for the standard skew-t. The linear skew-t offers different insights, for example, different moments and tail behavior, and can be simpler to use for empirical work. It is shown that the distribution may be expressed as a hidden truncation model. The paper describes an extended version of the distribution that is analogous to the extended skew-t. For certain parameter values, the distribution is bimodal. The paper presents expressions for the moments of the distribution and shows that numerical integration methods are required. A multivariate version of the distribution is described. The bivariate version of the distribution may also be bimodal. The distribution is not closed under marginalization, and stochastic ordering is not satisfied. The properties of the distribution are illustrated with numerous examples of the density functions, table of moments and critical values. The results in this paper suggest that the linear skew-t may be useful for some applications, but that it should be used with care for methodological work.