A new model for a lifetime distribution with bathtub shaped failure rate

Weibull-Related Distributions for the Modelling of Bathtub Shaped Failure Rate Functions

“…The change point of the bathtub curve in this case is t* = a (l//3 -1) 1//3 (12) This new model is asymptotically related to the traditional twoparameter Weibull distribution. As the scale parameter a approaches infinity, we have that 13 + o{{t/aY)]} « 1 -expj-Aa 1 -^} which is a standard two-parameter Weibull distribution with a shape parameter of (3 (when A tends to oo with a in such a manner that ofi~x/A is held constant).…”

Transformation of the bathtub failure rate data in reliability for using Weibull-model analysis

“…In order to deal with problems indicating bathtub-shaped failure rates, many specialized distributions have been proposed, these include Stacy's [35] generalized gamma, Prentice's generalized F distribution [30], the four-parameter family introduced by Graver and Acar [13], a threeparameter (IDB) family proposed by Hjorth [15], a three parameter family studied by Glaser [12] and a two-parameter family introduced by Haupt and Schabe [14]. A reasonable comprehensive account of the models for bathtub-shaped failure rates was given by Rajarshi and Rajarshi [31].…”

The Log-logistic Weibull Distribution with Applications to Lifetime Data

“…The distribution proposed by (Hjorth 1980) is such an example. Later on, (Rajarshi and Rajarshi 1988) presented a revision of these distributions, and (Haupt and Schäbe 1992) put forward a new lifetime model with bathtub-shaped failure rates. Unfortunately, these models are not sufficient to address various practical situations, so new classes of distributions were presented based on the modifications of the Weibull distribution to satisfy non-monotonic failure rate.…”