A new generalized odd log-logistic flexible Weibull regression model with applications in repairable systems

Abstract We define and study a four-parameter model called the generalized odd log-logistic flexible Weibull distribution. The new distribution can be used effectively in the context of reliability since it accommodates different hazard rate forms such as monotone, unimodal, bathtub-shaped, increasing-decreasing-increasing, among possible others. We provide an extensive study of the quantile function. Further, we present a parametric regression model based on the new distribution as an alternative to the location-scale regression model. An important property of this new regression model is that it does not need the assumption of proportional risks. We use the method of maximum likelihood for estimating the model parameters and perform various simulations for different parameter settings, sample sizes and censoring percentages. Applications in real engineering data sets illustrate the flexibility of the proposed models.

[1]  I. Olkin,et al.  A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families , 1997 .

[2]  Emrah Altun,et al.  The generalized odd log-logistic family of distributions: properties, regression models and applications , 2017 .

[3]  Chin-Diew Lai,et al.  A flexible Weibull extension , 2007, Reliab. Eng. Syst. Saf..

[4]  Abdelfattah Mustafa,et al.  The Exponential Flexible Weibull Extension Distribution , 2016, 1605.08152.

[5]  Anthony C. Atkinson,et al.  Plots, transformations, and regression : an introduction to graphical methods of diagnostic regression analysis , 1987 .

[6]  Morad Alizadeh,et al.  A new log-location regression model: estimation, influence diagnostics and residual analysis , 2017 .

[7]  Min Xie,et al.  Integrated beta model for bathtub-shaped hazard rate data , 2016 .

[8]  Gauss M. Cordeiro,et al.  The Transmuted Generalized Modified Weibull Distribution , 2017 .

[9]  Zohdy M. Nofal,et al.  The Weibull Fréchet distribution and its applications , 2016 .

[10]  B. Dhillon.  Life Distributions , 1981, IEEE Transactions on Reliability.

[11]  Rodrigo Rossetto Pescim,et al.  The new class of Kummer beta generalized distributions: theory and applications , 2013 .

[12]  Ayman Alzaatreh,et al.  A new method for generating families of continuous distributions , 2013 .

[13]  Gauss M. Cordeiro,et al.  The log-odd log-logistic Weibull regression model: modelling, estimation, influence diagnostics and residual analysis , 2016 .

[14]  Gauss M. Cordeiro,et al.  The exponentiated generalized gamma distribution with application to lifetime data , 2011 .

[15]  Gilberto A. Paula,et al.  Residuals for log-Burr XII regression models in survival analysis , 2011 .

[16]  Thiago G. Ramires,et al.  A new generalized Weibull family of distributions: mathematical properties and applications , 2015, Journal of Statistical Distributions and Applications.

[17]  Gauss M. Cordeiro,et al.  Generalized Beta-Generated Distributions , 2010, Comput. Stat. Data Anal..

[18]  D. N. Prabhakar Murthy,et al.  A modified Weibull distribution , 2003, IEEE Trans. Reliab..

[19]  Chin-Diew Lai,et al.  Useful periods for lifetime distributions with bathtub shaped hazard rate functions , 2006, IEEE Transactions on Reliability.

[20]  Michael W Kattan,et al.  A power series beta Weibull regression model for predicting breast carcinoma , 2015, Statistics in medicine.

[21]  Francis K.N. Leung,et al.  A repair‐replacement study for gearboxes using geometric processes , 2000 .

[22]  Saralees Nadarajah,et al.  The Kumaraswamy Weibull distribution with application to failure data , 2010, J. Frankl. Inst..

[23]  F. Famoye,et al.  BETA-NORMAL DISTRIBUTION AND ITS APPLICATIONS , 2002 .

[24]  J. Moors,et al.  A quantile alternative for kurtosis , 1988 .

[25]  Vasiliy V. Krivtsov.  Practical extensions to NHPP application in repairable system reliability analysis , 2007, Reliab. Eng. Syst. Saf..

[26]  Bo Henry Lindqvist,et al.  Statistical Modeling and Analysis of Repairable Systems , 2006, 0708.0362.

[27]  Gauss M. Cordeiro,et al.  An extended-G geometric family , 2016 .

[28]  Heleno Bolfarine,et al.  Deviance residuals in generalised log-gamma regression models with censored observations , 2008 .

[29]  Jamal N. Al Abbasi,et al.  Kumaraswamy Inverse Flexible Weibull Distribution: Theory and Application , 2016 .

[30]  Sangun Park,et al.  A general class of flexible Weibull distributions , 2018 .

[31]  Gauss M. Cordeiro,et al.  The Lomax generator of distributions: Properties, minification process and regression model , 2014, Appl. Math. Comput..

[32]  Bo Henry Lindqvist,et al.  The Trend-Renewal Process for Statistical Analysis of Repairable Systems , 2003, Technometrics.

[33]  Gauss M. Cordeiro,et al.  The McDonald Weibull model , 2014 .

[34]  Gianpaolo Pulcini,et al.  Modeling the failure data of a repairable equipment with bathtub type failure intensity , 2001, Reliab. Eng. Syst. Saf..

[35]  Gauss M. Cordeiro,et al.  The beta modified Weibull distribution , 2010, Lifetime data analysis.

[36]  Gauss M. Cordeiro,et al.  The Weibull-G Family of Probability Distributions , 2014, Journal of Data Science.

[37]  M. H. Tahir,et al.  The Poisson-X family of distributions , 2016 .

[38]  G. G. Hamedani,et al.  The Topp-Leone Generated Weibull Distribution: Regression Model, Characterizations and Applications , 2016 .

[39]  Ramesh C. Gupta,et al.  Proportional reversed hazard rate model and its applications , 2007 .

[40]  Gauss M. Cordeiro,et al.  The log-exponentiated Weibull regression model for interval-censored data , 2010, Comput. Stat. Data Anal..

[41]  Magne Vollan Aarset,et al.  How to Identify a Bathtub Hazard Rate , 1987, IEEE Transactions on Reliability.