A generalized modified Weibull distribution for lifetime modeling

FUDMA JOURNAL OF SCIENCES, 2020

A lifetime model called Transmuted Exponential-Weibull Distribution was proposed in this research. Several statistical properties were derived and presented in an explicit form. Maximum likelihood technique is employed for the estimation of model parameters, and a simulation study was performed to examine the behavior of various estimates under different sample sizes and initial parameter values. Through using real-life datasets, it was empirically shown that the new model provides sufficient fits relative to other existing models.

2003

The exponential, Rayleigh, linear failure rate and Weibull distributions are the most commonly used distributions for analyzing lifetime data. These distributions have several desirable properties and nice physical interpretations. This paper introduces a new distribution named modified Weibull distribution. This distribution generalizes the following distributions: (1) exponential, (2) Rayleigh, (3) linear failure rate, and (4) Weibull. The properties of the modified Weibull distribution are discussed. The maximum likelihood estimates of its unknown parameters are obtained. A real data set is analyzed and it observed that the present distribution can provide a better fit than some other known distributions.

Journal of Statistical Research of Iran, 2014

In this paper we introduce a four-parameter generalized Weibull distribution. This new distribution has a more general form of failure rate function. It is more general for modeling than six ageing classes of life distributions with appropriate choices of parameter values, so it can display decreasing, increasing, bathtub shaped, unimodal, increasing-decreasing increasing and decreasing-increasing-decreasing failure rates. The new distribution has also a bimodal density function. The moments are obtained and the method of maximum likelihood is used to estimate the model parameters. Also, the observed information matrix is obtained. Two applications are presented to illustrate the advantage of the proposed distribution.

IEEE Transactions on Reliability, 2000

A three-parameter lifetime distribution with increasing, decreasing, bathtub, and upside down bathtub shaped failure rates is introduced. The new model includes the Weibull distribution as a special case. A motivation is given using a competing risks interpretation when restricting its parametric space. Various statistical properties, and reliability aspects are explored; and the estimation of parameters is studied using the standard maximum likelihood procedures. Applications of the model to real data are also included.

2014

The Weibull distribution is a popular and widely used distribution in reliability and in lifetime data analysis. Since 1958, the Weibull distribution has been modified by many researchers to allow for non-monotonic hazard functions. Many modifications of the Weibull distribution have achieved the above purpose. On the other hand, the number of parameters has increased, the forms of the survival and hazard functions have become more complicated and the estimation problems have risen.This thesis provides an extensive review of some discrete and continuous versions of the modifications of the Weibull distribution, which could serve as an important reference and encourage further modifications of the Weibull distribution. Four different modifications of the Weibull distribution are proposed to address some of the above problems using different techniques. First model, with five parameters, is constructed by considering a two-component serial system with one component following a Weibull...

Quality and Reliability Engineering International, 1995

The complementary Weibull distribution may serve as a lietime model for various applications. A modification of this distribution is introduced. Its purpose is to enable the calculation of the MTBF integral, which does not exist for the regular complementary Weibull function. An efficient quadrature technique is provided. Its utility is validated through some examples.

IJMAO, 2020

The paper introduces a new distribution called the Lomax-Weibull distribution using the competing risk approach of constructing lifetime distributions. Some structural and mathematical properties of the proposed lifetime distribution are considered. Parameter estimation of the Lomax Weibull distribution is obtained using maximum likelihood estimation. The applicability and exibility of the new distribution in lifetime analysis is illustrated with the aid of two real life examples.

International Journal of Data Science and Analysis, 2017

The present article considers a new function to propose a new lifetime distribution. The new distribution is introduced by mixing up a linear system of the two logarithms of cumulative hazard functions. The proposed model is called new extended flexible Weibull distribution and is able to model lifetime with bathtub shaped failure rates and offers greater flexibility. Therefore, it can be quite valuable to use an alternative model to other existing lifetime distributions, where, modeling of real data sets with bathtub shaped failure rates are of interest. A brief description of the statistical properties along with estimation of the parameters through maximum likelihood procedure are discussed. The potentiality of the proposed model is showed by discussing two real data sets. For these data sets, the proposed model outclasses the Flexible Weibull Extension, Inverse Flexible Weibull Extension and Modified Weibull distributions.

2009

The exponential, Rayleigh, linear failure rate and Weibull distributions are the most commonly used distributions for analyzing lifetime data. These distributions have several desirable properties and nice physical interpretations. This paper introduces a new distribution named modified Weibull distribution. This distribution generalizes the following distributions: (1) exponential, (2) Rayleigh, (3) linear failure rate, and (4) Weibull. The properties of the modified Weibull distribution are discussed. The maximum likelihood estimates of its unknown parameters are obtained. A real data set is analyzed and it observed that the present distribution can provide a better fit than some other known distributions. M.S.C. 2000: 46N30, 47N30, 65C60.

Anais da Academia Brasileira de Ciências

We introduce a new three-parameter lifetime model called the Lindley Weibull distribution, which accommodates unimodal and bathtub, and a broad variety of monotone failure rates. We provide a comprehensive account of some of its mathematical properties including ordinary and incomplete moments, quantile and generating functions and order statistics. The new density function can be expressed as a linear combination of exponentiated Weibull densities. The maximum likelihood method is used to estimate the model parameters. We present simulation results to assess the performance of the maximum likelihood estimation. We prove empirically the importance and flexibility of the new distribution in modeling two data sets.