In this paper, we proposed a new three-parameters lifetime distribution with unimodal, increasing and decreasing hazard rate. The new distribution, the complementary Weibull geometric (CWG), is complementary to the Weibull-geometric (WG) model proposed by Barreto-Souza et al. (The Weibull-Geometric distribution, J. Statist. Comput. Simul. 1 (2010), pp. 1-13). The CWG distribution arises on a latent complementary risks scenarios, where the lifetime associated with a particular risk is not observable, rather we observe only the maximum lifetime value among all risks. The properties of the proposed distribution are discussed, including a formal proof of its probability density function and explicit algebraic formulas for its reliability and hazard rate functions, moments, density of order statistics and their moments. We provide expressions for the Rényi and Shannon entropies. The parameter estimation is based on the usual maximum likelihood approach. We obtain the observed information matrix and discuss inferences issues. We report a hazard function comparison study between the WG distribution and our complementary one. The flexibility and potentiality of the new distribution is illustrated by means of three real dataset, where we also made a comparison between Weibull, WG and CWG modelling approach.

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In this paper, we present a Bayesian methodology for modelling accelerated lifetime tests under a stress response relationship with a threshold stress. Both Laplace and MCMC methods are considered. The methodology is described in detail for the case when an exponential distribution is assumed to express the behaviour of lifetimes, and a power law model with a threshold stress is assumed as the stress response relationship. We assume vague but proper priors for the parameters of interest. The methodology is illustrated by a accelerated failure test on an electrical insulation film.Accelerated Life Tests, Threshold Stress, Bayesian Approach, Mcmc, Laplace Approxiation,

Abstract. In this paper we propose an accelerated lifetime test model with threshold stress under a Log-logistic distribution to express the behavior of lifetimes and a general stress-response relationship. We present a sampling-based inference procedure of the model based on Markov Chain Monte Carlo techniques. We assume proper but vague priors for the parameters of interest. The methodology is illustrated on an artificial and real lifetime data set.