Modified Weibull Research Articles

A Generalized Class of Exponentiated Modified Weibull Distribution With Applications

Abstract: In this paper, a new class of five parameter gamma-exponentiated or generalized modified Weibull (GEMW) distribution which includes exponential, Rayleigh, Weibull, modified Weibull, exponentiated Weibull, exponentiated exponential, exponentiated modified Weibull, exponentiated modified exponential, gamma-exponentiated exponential, gamma exponentiated Rayleigh, gamma-modified Weibull, gamma-modified exponential, gamma-Weibull, gamma-Rayleigh and gamma-exponential distributions as special cases is proposed and studied. Mathematical properties of this new class of distributions including moments, mean deviations, Bonferroni and Lorenz curves, distribution of order statistics and Renyi entropy are presented. Maximum likelihood estimation technique is used to estimate the model parameters and applications to real data sets presented in order to illustrate the usefulness of this new class of distributions and its sub-models.

Estimation of the Parameters of the Modified Weibull Distribution with Bathtub-shaped Failure Rate Function

Estimation of the Parameters of the Modified Weibull Distribution with Bathtub-shaped Failure Rate Function

Transmuted Modified Weibull Distribution for Modeling Skewed Lifetime Dataset; Properties and Application

A new five parameter model called Generalized Modified Weibull distribution is proposed and studied. The new distribution generalizes the Modified Weibull Distribution introduced by Lai et al. (2003) using transformed – Transformer framework of Alzaatreh et al. (2014) which resulted to a distribution capable of modeling skewed data (positively or negatively skewed data), as well as, symmetric data. Property of a proper probability density function was used to ascertain that the resulting function is a proper probability density function. Statistical properties of the newly generated distribution were studied. Graph of probability density function of the distribution was used to show that it is capable of modeling skewed data. Graph of cumulative density functions of the distribution was plotted using varying parameter values. Monte Carlo simulation approach was used for the test of homogeneity of the distribution and it was observed that the parameters in the distribution approach the true values as sample size increases. Maximum likelihood Estimation method was used for estimation of the model parameters. Real life dataset was used for model comparison as well as demonstration of its application.

A New Bivariate Distribution With Applications on Dependent Competing Risks Data

A new bivariate distribution is proposed in this paper using the univariate modified Weibull extension distribution. The proposed distribution is referred to as the bivariate Modified Weibull Extension (BMWE) distribution. The BMWE distribution is of Marshall-Olkin type. We discuss some of the statistical properties of the BMWE  distribution.  Applications of this distribution to dependent competing risks data are discussed.  The maximum likelihood estimators (MLE) of the model parameters using both bivariate data and dependent competing risks data are discussed. These MLE's cannot be obtained in closed form. Therefore, numerical optimization methods are  applied. A simulation study is carried out to investigate the performance of the estimation technique. Two real data sets;  one bivariate data set and another dependent competing risks data set, are analyzed using the proposed distribution for illustrative and comparison purposes.

Statistical Inference for the Modified Weibull Model Based on the Generalized Order Statistics

Statistical Inference for the Modified Weibull Model Based on the Generalized Order Statistics

THE EXPONENTIAL MODIFIED WEIBULL LOGISTIC DISTRIBUTION (EMWL)

This paper introduces a new distribution named Exponential Modified Weibull logistic distribution. This distribution generalizes the following distributions: (1) Linear Failure Rate Logistic Distribution, (2) Weibull Logistic Distribution, (3) Rayleigh Logistic Distribution, (4) Exponential Logistic Distribution, where the failure rate, Weibull, Rayleigh and exponential distributions are the distributions most used for analyzing lifetime data. The properties of the new distribution are derived that include expressions for the rthmoment, characteristic function and quantile function. The estimation of model parameters are performed by the method of maximum likelihood and hence evaluation of the performance of maximum likelihood estimation using simulation.

Estimation of the Modified Weibull Additive Hazards Regression Model under Competing Risks

The additive hazard regression model plays an important role when the excess risk is the quantity of interest compared to the relative risks, where the proportional hazard model is better. This paper discusses parametric regression analysis of survival data using the additive hazards model with competing risks in the presence of independent right censoring. In this paper, the baseline hazard function is parameterized using a modified Weibull distribution as a lifetime model. The model parameters are estimated using maximum likelihood and Bayesian estimation methods. We also derive the asymptotic confidence interval and the Bayes credible interval of the unknown parameters. The finite sample behaviour of the proposed estimators is investigated through a Monte Carlo simulation study. The proposed model is applied to liver transplant data.

Multi-component Reliability Inference in Modified Weibull Extension Distribution and Progressive Censoring Scheme.

The statistical inference of multi-component reliability stress-strength system with nonidentical-component strengths is considered for the modified Weibull extension distribution in the presence of progressive censoring samples. For this aim, we study the estimation of multi-component reliability parameter in classical and Bayesian inference. So we derive some point and interval estimates such as maximum likelihood estimation, asymptotic confidence intervals, uniformly minimum variance unbiased estimation, approximate and exact Bayes estimation and highest posterior density intervals. Comparing of different estimates is provided by employing the Monte Carlo simulation, the mean squared error and coverage probabilities. Finally, one real data is utilized to illustrate the applicability of this new model.

The New Bivariate Odd Generalized Exponential Modified Weibull Distribution with Application

The New Bivariate Odd Generalized Exponential Modified Weibull Distribution with Application

Topp–Leone Modified Weibull Model: Theory and Applications to Medical and Engineering Data

In this article, a four parameter lifetime model called the Topp–Leone modified Weibull distribution is proposed. The suggested distribution can be considered as an alternative to Kumaraswamy Weibull, generalized modified Weibull, extend odd Weibull Lomax, Weibull-Lomax, Marshall-Olkin alpha power extended Weibull and exponentiated generalized alpha power exponential distributions, etc. The suggested model includes the Topp-Leone Weibull, Topp-Leone Linear failure rate, Topp-Leone exponential and Topp-Leone Rayleigh distributions as a special case. Several characteristics of the new suggested model including quantile function, moments, moment generating function, central moments, mean, variance, coefficient of skewness, coefficient of kurtosis, incomplete moments, the mean residual life and the mean inactive time are derived. The probability density function of the Topp–Leone modified Weibull distribution can be right skewed and uni-modal shaped but, the hazard rate function may be decreasing, increasing, J-shaped, U-shaped and bathtub on its parameters. Three different methods of estimation as; maximum likelihood, maximum product spacing and Bayesian methods are used to estimate the model parameters. For illustrative reasons, applications of the Topp–Leone modified Weibull model to four real data sets related to medical and engineering sciences are provided and contrasted with the fit reached by several other well-known distributions.

Construction of an Alternative Bivariate Distribution with Discrete Modified Weibull as Marginals

Construction of an Alternative Bivariate Distribution with Discrete Modified Weibull as Marginals

The Estimation of Survival Function for Modified Weibull Extension Distribution Using Two-Symmetric Pentagonal Fuzzy Numbers with Simulation

In this paper, the parameters of the Modified Weibull Extension Distribution are estimated using the maximum likelihood estimator method and the Monte Carlo method in the simulation procedure to generate many different sample sizes, with many different replicates of the sample sizes. Following that finding, the Survival function’s estimate. Then fuzzify the estimation of the parameters for the same different sample sizes with the same difference in replicated sample sizes that was obtained from the Monte Carlo method in the simulation procedure by the new proposed method of expanding the Confidence Interval of estimated parameters to nine fuzzy numbers. Then, transform all the fuzzy parameters to crisp parameters using the proposed ranking functions with (proposed Linear Two- Symmetric Pentagonal Fuzzy Numbers, and proposed Non Linear Two-Symmetric Pentagonal Fuzzy Numbers). Accordingly, finding the Survival function. The outcome of Survival functions before and after fuzzy work will be compared using mean square error.

Statistical Inference for Multi State Systems under the Generalized Modified Weibull Class

Multi state systems can be seen as semi-Markov processes by considering an arbitrary distribution function for sojourn times. Especially, in this work, the Modified Weibull distribution is employed to be the distribution of sojourn times with a shape parameter λ such that is member of a distributions family that is closed under minima. Parameters estimators are provided and the proposed methodology is evaluated using a detailed simulation procedure.

Reliability Analysis of the Inverse Modified Weibull Model with Applications

This paper presents a novel flexible inverse modified Weibull model with a concave Weibull probability diagram that describes various reliability phenomena. We investigate some essential attributes and reliability properties of this model. The new model exhibits an increasing or unimodal form of the hazard rate function, making it more suitable for simulating certain aging classes of life distributions with appropriate choices of parameter values. We used the Weibull probability paper approach and the maximum likelihood method to estimate the model's parameters. In addition, we conduct a simulation study to investigate the behavior and efficiency of these estimators. Finally, we analyze a maintenance dataset to demonstrate the usefulness of the proposed model.

Poisson modified weibull distribution with inferences on stress‐strength reliability model

AbstractThis paper is devoted to study a new four‐parameter model called a Poisson Modified Weibull Distribution (PMW). The motivation for the new distribution is to obtain the hazard rate function with multiple shapes, the most important of which is the bathtub shape which is very useful in the reliability analysis. Some of its statistical properties are discussed. Maximum likelihood, method of moments and Bayesian techniques are used for estimating the parameters and the Fisher's information matrix is presented. In specific, we focus on the study of Stress‐ Strength reliability parameter, , when and have a PMW distribution. The maximum likelihood and Bayesian estimators for are derived. A simulation study is performed to compare the performance of each method of estimation. Moreover, the goodness of fit for PMW distribution comparison with other models are carried out by means of two applications to real data sets to illustrate the flexibility of the proposed model. Finally, the Stress‐Strength model for PMW distribution was applied to a real data representing the failure times for two types of electrical insulators.

Bivariate Discrete Modified Weibull (BDMW) Distribution

Bivariate Discrete Modified Weibull (BDMW) Distribution

The Beta Reduced Modified Weibull Distribution with Applications to Reliability Data

In this paper, we introduce a new probability distribution with application in reliability called the beta reduced modified Weibull distribution. The proposed distribution presents a more flexible model and has the capability to capture decreasing, increasing, bathtub, unimodal (upside-down bathtub) and modified unimodal shaped hazard rates. Also, this distribution has a bathtub-shaped hazard rate function with a long useful life period, which is desirable property in reliability analysis. We obtain the expansions for the moments, quantile function, stress-strength reliability, density function of the order statistics and their moments. We use the method of maximum likelihood to estimate the model parameters for complete and right-censored data. We evaluate the performance of the maximum likelihood estimators in a simulation study. We analyze three reliability data sets, complete and censored, to examine the flexibility of the proposed model.

Analysis of Type-II Censored Competing Risks’ Data under Reduced New Modified Weibull Distribution

Models with the bathtub-shaped hazard rate function are widely used in lifetime analysis and reliability engineering. In this paper, we adopted the reduced new modified Weibull (RNMW) distribution with a bathtub-shaped hazard rate function. Under consideration that the population units are failing with two independent causes of failure and the failure time is distributed with RNMW distribution, we formulate the model which is known as competing risks model. The model parameters under the type-II censoring scheme are estimated with the maximum likelihood method with the corresponding asymptotic confidence intervals. Also, the Bayes point and credible intervals with the help of MCMC methods are constructed. The real and simulated datasets are analyzed for illustrative purposes. Finally, the estimators are compared with the Monte Carlo simulation study.

A New Generalized of Exponentiated Modified Weibull Distribution

A New Generalized of Exponentiated Modified Weibull Distribution

Development and Evaluation of a Fluctuating Plume Model for Odor Impact Assessment

For environmental odor nuisance, it is extremely important to identify the instantaneous concentration statistics. In this work, a Fluctuating Plume Model for different statistical moments is proposed. It provides data in terms of mean concentrations, variance, and intensity of concentration. The 90th percentile peak-to-mean factor, R90, was tested here by comparing it with the experimental results (Uttenweiler field experiment), considering different Probability Distribution Functions (PDFs): Gamma and the Modified Weibull. Seventy-two percent of the simulated mean concentration values fell within a factor 2 compared to the experimental ones: the model was judged acceptable. Both the modelled results for standard deviation, σC, and concentration intensity, Ic, overestimate the experimental data. This evidence can be due to the non-ideality of the measurement system. The propagation of those errors to the estimation of R90 is complex, but the ranges covered are quite repeatable: the obtained values are 1–3 for the Gamma, 1.5–4 for Modified Weibull PDF, and experimental ones from 1.4 to 3.6.