Poisson–logarithmic half-logistic distribution with inference under a progressive-stress model based on adaptive type-II progressive hybrid censoring

Abstract

The researchers, engineers, and physical experimenters may face difficulty to get a distribution that fits the failure data arising from certain systems. So, in this paper, a new distribution is introduced, named Poisson–logarithmic half-logistic distribution, based on a parallel–series system’s failure times. Specific statistical properties are investigated for the introduced distribution. Also, two real data sets are considered to compare the introduced distribution with some other distributions. The progressive-stress accelerated life test is applied using an increasing exponential function of time to units whose lifetimes are expected to follow the new distribution at normal stress conditions. Different estimation methods, such as maximum likelihood, percentile, least squares, and weighted least square methods, are considered on the basis of adaptive type-II progressive hybrid censoring. To assess the efficiency of the estimation methods, a simulation study is conducted, as well as numerical calculations.

Statistical Prediction Based on Ordered Ranked Set Sampling Using Type-II Censored Data from the Rayleigh Distribution under Progressive-Stress Accelerated Life Tests

“…PDF (11) and HRF (12) are plotted in Figure 2 for θ � 1.5, λ � 2.0, and diferent values of c and d. It can be noticed that PDF (11) is always unimodal, while HRF ( 12) is always increasing since β > 2.…”

“…Previous studies of the PRSALT have indicated that the imposed stress is expressed as an increasing linear function of time, see [5,6,9]. While in some papers such as [7,11,34], the authors suggested PRSALTs taking into account that the imposed stress is represented as a nonlinear increasing function of time. Te PRSALT is performed under the following fundamental assumptions.…”

“…We presume that X RSS is a one-cycle RSS from a given population under PRSALT with CDF (9) and PDF (11). Te CDF and PDF of X p,rr , p � 1, .…”

“…Several techniques, including progressive stress, step stress, and constant stress, can be used to apply stress to ALTs. For further explanation on ALTs and PALTs, one can refer to [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15].…”

Utilizing Bayesian inference in accelerated testing models under constant stress via ordered ranked set sampling and hybrid censoring with practical validation

“…It can also be useful in survival analysis and reliability engineering when dealing with skewed data and non-negative lifetimes. Moreover, it has been applied as a life-testing model by several authors, see, for example 19 , 20 .…”