Bayesian Prediction Intervals Based on Type‐I Hybrid Censored Data from the Lomax Distribution under Step‐Stress Model

Abstract

The Bayesian prediction of future failures from Lomax distribution is the subject of this research. The observed data is censored using a Type-I hybrid censoring scheme under a step-stress partially accelerated life test. There are two types of sampling schemes considered: one-sample and two-sample. We create predictive intervals for failure observations in the future. Bayesian prediction intervals are constructed using MCMC algorithms. After all, two numerical examples, simulation study and a real-life example are provided for both one-sample and two-sample methods for the purpose of illustration.

Reliability analysis of the triple modular redundancy system under step-partially accelerated life tests using Lomax distribution

“…It is evident from the results shown in Table 2 that every p-value exceeds 0.05 indicating that the model with CDF (18) matches the two real sets of data presented well. Drawing the empirical CDF alongside CDF (18) for each real set of data further illustrates this point, see Figure 3.…”

“…31 , is an alternative to the ML method for estimating the unknown parameters in continuous distributions. For CDF (18), define where n+1 i=1 D i (α, β, γ ) = 1 , F * (t 0 ) = 0 , and F * (t (n+1) ) = 1. Maximization of the geometric mean of the uniform spacings, given in the next equation, will yield the MPSEs ( ᾱ, β, γ ) of (α, β, γ ; t), or equivalently, by maximization of the following function, M(α, β, γ ; t) = ln[G(α, β, γ ; t)],…”

“…A step-stress PALT operates with two distinct stress levels, with the initial stress being at the standard level, and a predetermined moment when the stress is altered (as discussed in references [13][14][15][16][17][18][19][20][21] ).…”