A generalization of the exponential distribution is presented. The generalization always has its mode at zero and yet allows for increasing, decreasing and constant hazard rates. It can be used as an alternative to the gamma, Weibull and exponentiated exponential distributions.A comprehensive account of the mathematical properties of the generalization is presented. A real data example is discussed to illustrate its applicability.

In this article, we propose control charts for the quantiles of the Weibull distribution, for type II censored data, based on the distribution of a pivotal quantity conditioned on ancillary statistics. These control charts must be considered as alternatives to bootstrap type control charts. We derive an analytical form of the conditional distribution function of the monitored statistic and we use this function to propose ARL‐unbiased control limits. We further demonstrate that the proposed conditional chart have a general analytical form for the ARL that can be evaluated numerically without use of simulations and we also show that these charts perform at least as well as the bootstrap type ones. We finally apply the conditional charts to a dataset on the strength of carbon fibers to detect shifts in a specified Weibull quantile. Copyright © 2014 John Wiley & Sons, Ltd.

The accelerated degradation test (ADT) has become critical for product reliability assessment. In performing the ADT for newly developed products, a constant-stress ADT may be impractical or sometimes impossible where the available size of testing units and the testing duration are heavily bounded to meet the short development period of the products. As an alternative, a step-stress accelerated degradation test (SSADT) can be a useful tool for satisfying the test limitation, and for making up for uncertainty in selecting appropriate levels of stress. Occasionally, the elevated stress under SSADT not only accelerates the performance degradation of products, but it may also expedite traumatic failures. This paper proposes a modeling approach to simultaneously analyze linear degradation data and traumatic failures with competing risks in an SSADT experiment. Under the modeling approach, a cumulative exposure model is considered. The failure rate corresponding to each failure mode is described as a function of the degradation level at the moment of failure. No parametric assumptions are made regarding the failure-time distribution to extend the proposed method to more general cases. We derive maximum likelihood estimates of the model parameters, then estimate failure rates and product reliability based on the degradation level to failure. Asymptotic properties of the maximum likelihood estimates are also discussed. The proposed model is applied to accelerated degradation data from plastic substrate active matrix light-emitting diodes (AMOLEDs), along with sensitivity analysis.

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In this paper, we develop a Bayesian approach for monitoring Weibull quantiles under Type II censoring when prior information is negligible relative to the data. The posterior median of quantiles is considered as the monitored statistic. A method based on the relationship between Bayesian and conditional limits under an appropriate prior distribution is proposed to obtain the posterior median of quantiles in closed form. A pivotal quantity based on the monitored statistic is proposed, and its distribution is conditionally derived. Then, the Bayes‐conditional control limits are proposed. For the proposed charts, the probability of out‐of‐control can be derived without use of simulation. The performance of the Bayes‐conditional charts is compared with the bootstrap charts through the simulation methods. The results show that to monitor the first quantiles, the lower‐sided Bayes‐conditional charts perform better than bootstrap charts in detecting a downward shift caused by decreasing in the shape parameter. Finally, an illustrative example is provided. Copyright © 2016 John Wiley & Sons, Ltd.