Abstract
In reliability analysis and life-testing experiments, the researcher is often interested in the effects of changing stress factors such as “temperature”, “voltage” and “load” on the lifetimes of the units. Step-stress (SS) test, which is a special class from the well-known accelerated life-tests, allows the experimenter to increase the stress levels at some constant times to obtain information on the unknown parameters of the life models more speedily than under usual operating conditions. In this paper, a simple SS model from the exponentiated Lomax (ExpLx) distribution when there is time limitation on the duration of the experiment is considered. Bayesian estimates of the parameters assuming a cumulative exposure model with lifetimes being ExpLx distribution are resultant using Markov chain Monte Carlo (M.C.M.C) procedures. Also, the credible intervals and predicted values of the scale parameter, reliability and hazard are derived. Finally, the numerical study and real data are presented to illustrate the proposed study
Highlights
Introduction and motivationGenerally, there are two well-known types of SS loadings which are concerned in accelerating life tests ALTs: The 1st is the linearly increasing stress and the 2nd is the stable stress
We reflect the Bayesian estimation of the scale parameter, reliability, hazard rate of the distribution of failure time (FT) under regular operating conditions and the SS ALT model based on cumulative break that helps a log linear model
We find the probability density and cumulative distribution functions (P-D-F & C-D-F) for lifetimes from the exponentiated Lomax (ExpLx) model
Summary
There are two well-known types of SS loadings which are concerned in accelerating life tests ALTs: The 1st is the linearly increasing stress and the 2nd is the stable stress. Li (2002) studied a Bayesian method for estimating the failure rate (FR) for exponential (Exp) distribution. We reflect the Bayesian estimation of the scale parameter, reliability, hazard rate of the distribution of FTs under regular operating conditions and the SS ALT model based on cumulative break that helps a log linear model. Where ∆0= τ1 − τ0, u0 = 0 and ∆j−2= τj−1 − τj−2, j=2,3,...,k, by taking the root θ and taking the root – β to two sides, the cumulative exposure model for j steps is written as follows. Where uj−1 = − exp (b(xj−1 − xj)) (∆j−2 + uj−2) It seen that F(t), for a SS pattern F(t), can be printed in the form: 0, t ≤ τ0.
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