An additive power‐transformed half‐logistic model and its applications in reliability

Abstract

An additive power‐transformed half‐logistic distribution is proposed to model lifetime data having bathtub‐shaped hazard rate function. The model is derived as the sum of hazard rates of two independently distributed power transformed half‐logistic distributions. Some properties of the model like shapes of hazard function, quantile function, mean time between failure (MTBF), probability of failure due to early birth defect and due to ageing are discussed. The graphical estimation technique based on probability plotting procedure is demonstrated to be useful in estimating the parameters of this model. The method of maximum likelihood estimation is discussed for estimating the model parameters and simulation study is considered to show the performance of the estimates. Finally the usefulness of the developed distribution is illustrated by applying it to two real life datasets from engineering reliability.

Exponentiated half‐logistic Weibull distribution with reliability inference

“…Various attempts have been made to extend the applicability of the half‐logistic distribution. For instance, generalized half‐logistic distribution (or exponentiated half‐logistic distribution) was introduced by Kantam et al., 14 power half‐logistic distribution, 15 Generalized half‐logistic Poisson distributions by Muhammad, 16 the additive power‐transformed half‐logistic by Xavier et al., 17 and the Poisson‐generalized half logistic by Muhammad and Liu 18 . Furthermore, a novel approach was presented by Cordeiro et al., 19 wherein a new generator of continuous distributions emerged based on the exponentiated half‐logistic distribution.…”

The Chen–Perks Distribution: Properties and Reliability Applications

“…For this, Thach established the triple additive WD, which is an excellent fit to the bathtub curve; however, makes it complex as it has too many parameters to estimate. Other distributions based on the additive methodology can be seen in [17][18][19][20][21][22].…”