Characterizations of Distributions Through Aging Intensity

In this paper, we characterize univariate positive absolutely continuous random variable through the aging intensity function. Using this function, we propose the characterizations of Weibull- and inverse-Weibull-related distributions. They are alternatives to the basic two-parameter Weibull distribution to be used in reliability analysis of elements and systems. We find that for presented distributions, it is easier to characterize them through their aging intensity function than through their failure rate function. Further on, some other than Weibull family life distributions are presented. However, in their case, characterization through the failure rate seems to be easier. Moreover, aging intensity orders are studied for the considered Weibull distributions. They allow us to decide that one random variable has the better aging property than another one. To show the practical usefulness of the aging intensity, the analysis of this function through some data is performed.

[1]  Hoang Pham,et al.  On Recent Generalizations of the Weibull Distribution , 2007, IEEE Transactions on Reliability.

[2]  Adriana Hornikova,et al.  Stochastic Ageing and Dependence for Reliability , 2007, Technometrics.

[3]  John P. Klein,et al.  Characterization Problems Associated With the Exponential Distribution. , 1987 .

[4]  S. Alam,et al.  Properties of aging intensity function , 2007 .

[5]  Necip Doganaksoy,et al.  Weibull Models , 2004, Technometrics.

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

[7]  J. Shanthikumar,et al.  Multivariate Stochastic Orders , 2007 .

[8]  D. N. Prabhakar Murthy,et al.  A study of Weibull shape parameter: Properties and significance , 2011, Reliab. Eng. Syst. Saf..

[9]  Samuel Kotz,et al.  On some recent modifications of Weibull distribution , 2005, IEEE Transactions on Reliability.

[10]  Majid Rezaei,et al.  On the Reversed Average Intensity Order , 2014 .

[11]  Jayant V. Deshpande,et al.  SOME RESULTS ON THE RELATIVE AGEING OF TWO LIFE DISTRIBUTIONS , 1994 .

[12]  Saralees Nadarajah,et al.  Modifications of the Weibull distribution: A review , 2014, Reliab. Eng. Syst. Saf..

[13]  Subarna Bhattacharjee,et al.  Inequalities involving expectations to characterize distributions , 2013 .

[14]  D. G. Holloway.  The strength of glass , 1960 .

[15]  R. Jiang,et al.  Aging property of unimodal failure rate models , 2003, Reliab. Eng. Syst. Saf..

[16]  W. Weibull.  A Statistical Distribution Function of Wide Applicability , 1951 .

[17]  Richard E. Barlow,et al.  Statistical Analysis of Reliability and Life Testing Models , 1975 .

[18]  K. Phani,et al.  A New Modified Weibull Distribution Function , 1987 .

[19]  Magdalena Szymkowiak,et al.  Characterizations of distributions through selected functions of reliability theory , 2017 .

[20]  Subarna Bhattacharjee,et al.  Reliability analysis using ageing intensity function , 2013 .

[21]  Magdalena Szymkowiak,et al.  Characterizations of Discrete Weibull related distributions , 2016 .