The log-normal modified Weibull distribution and its reliability implications

Abstract This paper introduces a new lifetime distribution to describe and analyze monotone, upside-down bathtub, bathtub-shaped and modified bathtub-shaped failure rates. An important property of the new distribution is that it can have a bathtub-shaped failure rate function with a long flat region, which may be very useful in reliability contexts. Some structural properties of the new model are obtained, and a detailed study of its mean residual life function is provided. In particular, we focus on the fundamental associations between the failure rate and mean residual life regarding their change points. The maximum likelihood method is used to estimate the model parameters. The usefulness of the new distribution is illustrated by means of empirical applications to three real datasets from engineering reliability in order to prove its versatility in practice.

[1]  G. M. Borzadaran,et al.  On the change points of mean residual life and failure rate functions for some generalized gamma type distributions , 2014 .

[2]  Narayanaswamy Balakrishnan,et al.  A General Purpose Approximate Goodness-of-Fit Test , 1995 .

[3]  F.K Wang,et al.  A new model with bathtub-shaped failure rate using an additive Burr XII distribution , 2000, Reliab. Eng. Syst. Saf..

[4]  Saad J. Almalki,et al.  A new modified Weibull distribution , 2013, Reliab. Eng. Syst. Saf..

[5]  R. Jiang,et al.  A new bathtub curve model with a finite support , 2013, Reliab. Eng. Syst. Saf..

[6]  Hendrik Schäbe,et al.  A new model for a lifetime distribution with bathtub shaped failure rate , 1992 .

[7]  Richard E. Barlow,et al.  Stochastic Ageing and Dependence for Reliability , 2006 .

[8]  Xiaofeng Du,et al.  An additive modified Weibull distribution , 2016, Reliab. Eng. Syst. Saf..

[9]  Rose D. Baker,et al.  New survival distributions that quantify the gain from eliminating flawed components , 2019, Reliab. Eng. Syst. Saf..

[10]  Loon Ching Tang,et al.  Mean residual life of lifetime distributions , 1999 .

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

[12]  Luis Alberto Rodríguez-Picón,et al.  Reliability analysis for electronic devices using beta-Weibull distribution , 2017, Qual. Reliab. Eng. Int..

[13]  Gauss M. Cordeiro,et al.  The exponential–Weibull lifetime distribution , 2014 .

[14]  Filippo Domma,et al.  A new class of distribution functions for lifetime data , 2014, Reliab. Eng. Syst. Saf..

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

[16]  G. S. Mudholkar,et al.  A Generalization of the Weibull Distribution with Application to the Analysis of Survival Data , 1996 .

[17]  R Core Team,et al.  R: A language and environment for statistical computing. , 2014 .

[18]  Enrique López Droguett,et al.  On the q-Weibull distribution for reliability applications: An adaptive hybrid artificial bee colony algorithm for parameter estimation , 2017, Reliab. Eng. Syst. Saf..

[19]  James R. King,et al.  Probability Charts for Decision Making , 1981 .

[20]  Gauss M. Cordeiro,et al.  Computational Statistics and Data Analysis a Generalized Modified Weibull Distribution for Lifetime Modeling , 2022 .

[21]  A. T. Ertürk,et al.  Failure analysis of wire-breaks in aluminum conductor production and investigation of early failure reasons for transmission lines , 2018 .

[22]  Deo Kumar Srivastava,et al.  The exponentiated Weibull family: a reanalysis of the bus-motor-failure data , 1995 .

[23]  W. Meeker.  Accelerated Testing: Statistical Models, Test Plans, and Data Analyses , 1991 .

[24]  M. Zuo,et al.  Optimal Reliability Modeling: Principles and Applications , 2002 .

[25]  Jie Mi.  Bathtub failure rate and upside-down bathtub mean residual life , 1995 .

[26]  Min Xie,et al.  On the upper truncated Weibull distribution and its reliability implications , 2011, Reliab. Eng. Syst. Saf..

[27]  H. Bakouch,et al.  Beta Sarhan–Zaindin modified Weibull distribution , 2016 .

[28]  Min Xie,et al.  Reliability analysis using an additive Weibull model with bathtub-shaped failure rate function , 1996 .

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

[30]  Thong Ngee Goh,et al.  A modified Weibull extension with bathtub-shaped failure rate function , 2002, Reliab. Eng. Syst. Saf..

[31]  U. Hjorth.  A Reliability Distribution With Increasing, Decreasing, Constant and Bathtub-Shaped Failure Rates , 1980 .

[32]  Gauss M. Cordeiro,et al.  A new generalized odd log-logistic flexible Weibull regression model with applications in repairable systems , 2018, Reliab. Eng. Syst. Saf..

[33]  Qiming Chen,et al.  Five and four-parameter lifetime distributions for bathtub-shaped failure rate using Perks mortality equation , 2016, Reliab. Eng. Syst. Saf..

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

[35]  Chin-Diew Lai,et al.  MEAN RESIDUAL LIFE AND OTHER PROPERTIES OF WEIBULL RELATED BATHTUB SHAPE FAILURE RATE DISTRIBUTIONS , 2004 .

[36]  Thong Ngee Goh,et al.  On changing points of mean residual life and failure rate function for some generalized Weibull distributions , 2004, Reliab. Eng. Syst. Saf..

[37]  Edilson Machado de Assis,et al.  Generalized q‐Weibull model and the bathtub curve , 2013 .

[38]  W. Nelson.  Statistical Methods for Reliability Data , 1998 .