Gamma lifetimes and one-shot device testing analysis

A Bayesian Approach for One-Shot Device Testing With Exponential Lifetimes Under Competing Risks

“…The resultant posterior distribution in (30) in the masked cause case is similar to the original one presented in (7). So, it is easy to derive the posterior distributions for different prior distributions, namely, the exponential, normal, and Dirichlet distributions; and the results will be quite similar to those in (17), (21), and (25), respectively.…”

“…Balakrishnan and Ling [4] developed the Expectation-Maximization (EM) algorithm for estimating the parameters of a one-shot device testing model under exponential lifetimes, and further extended it to the case of multiple stress levels [5]. Subsequently, they generalized their results to the cases of Weibull [6] and gamma lifetime distributions [7].…”

Probability density function of the equivalent stress amplitude using statistical transformation

“…A point-topoint transformation is performed by using Eqs. (11) and (19), and is given as a histogram, whilst the probability densities using the proposed procedure are given as curves. There is a good agreement between the calculated and empirically obtained probability densities in both cases and for both mean stress correction methods.…”

“…Lin et al [10] used the EM algorithm to estimate the unknown parameters of the normal mixture distribution, which was then used to evaluate the operational safety of multi-mode engineering systems. Balakrishnan [11] used the EM algorithm to estimate the unknown parameters of a Gamma distribution. The Gamma distribution was used for the analysis of a one-shot device, testing data under accelerated life-tests.…”

Structural Reliability Analysis Using Orthogonalizable Power Polynomial Basis Vector

“…However, even if the performance function is explicit, the nonlinearity of the function and the non-Gaussian distribution of random variables always make it impossible to obtain the exact solution of this multi-fold integral [1], [2]. Various methods have been used to analyze the failure probability of structures subjected to random material parameters, such as the first-and second-order reliability methods (FORM/SORM) [3], [4], the simulation methods [5]- [7], the traditional perturbation stochastic finite element methods (PSFEM) [8], [9], the response surface method [10], [11], and so on. However, more or less problems exist in the above mentioned methods.…”