Competing Risks Step-Stress Model with Lagged Effect under Gompertz Distribution

In many survival analysis studies, the failure of a product may be attributed to one of several competing risks. In addition, if survival time is long, researchers can adopt accelerated life tests, causing devices to fail more quickly. One popular type of accelerated life tests is the step-stress test, and in this test, the stress level changes at a predetermined point time. The manner that stress levels change abruptly and increase discontinuously has been studied extensively. This paper considers a more realistic situation where the effect of stress increases cannot be achieved all at once, but with a lag time, and we propose a step-stress model consisting of two independent competing risks with a lag period in which the failure time caused by different risks at different stress levels obey Gompertz distribution, and the range of lag period is predetermined. The unknown parameters are estimated by maximum likelihood estimation and least squares estimation. For comparison, asymptotic confidence intervals and percentile bootstrap confidence intervals are constructed. By using Monte-Carlo simulations, we obtain the means and mean square errors of the maximum likelihood estimates and the least squares estimates, as well as the mean lengths and coverage rates of the two confidence intervals, which show the performance of various methods. Finally, in order to illustrate the model and proposed methods, we analyze a dataset from a solar energy experiment.

Reliability of one-shot device with generalized gamma lifetime under cyclic accelerated life-test

One-shot devices are products or equipments that can be used only once. A nature characteristic of one-shot devices is that they get destroyed immediately after their use, and therefore their actual lifetimes are never observable. The only information observed is the condition whether they worked or not at the time they are used. These days the quality of products are significantly improved, so that the information obtained under a normal test during a short time is quite limited. A typical test to induce more failures is the accelerated life-test, which is developed by increasing the stress levels under test. In this paper, we will investigate the reliability of one-shot devices with generalized gamma fatigue life under accelerated life-tests with various cyclic temperature fluctuations by assuming a Norris-Landzberg model. Generalized gamma involves many common lifetime distributions, such as gamma, Weibull, lognormal, and positive stable distributions, as special cases. Norris-Landzberg model takes not only temperature change, highest testing temperature, but also the cycling frequency into account when modeling the number of cycles-to-failure, resulting a generalized model with the well-known Coffin-Manson model and Coffin-Manson-Arrhenius model as special cases. Associated inferences are developed. The performance of the proposed model and inferential methods will be evaluated with simulation study and model discrimination. Finally, the chip-scale package solder joints data is analyzed to illustrate the considered model and inferential methods developed in this paper.

The Exponentiated Burr–Hatke Distribution and Its Discrete Version: Reliability Properties with CSALT Model, Inference and Applications

Continuous and discrete distributions are essential to model both continuous and discrete lifetime data in several applied sciences. This article introduces two extended versions of the Burr–Hatke model to improve its applicability. The first continuous version is called the exponentiated Burr–Hatke (EBuH) distribution. We also propose a new discrete analog, namely the discrete exponentiated Burr–Hatke (DEBuH) distribution. The probability density and the hazard rate functions exhibit decreasing or upside-down shapes, whereas the reversed hazard rate function. Some statistical and reliability properties of the EBuH distribution are calculated. The EBuH parameters are estimated using some classical estimation techniques. The simulation results are conducted to explore the behavior of the proposed estimators for small and large samples. The applicability of the EBuH and DEBuH models is studied using two real-life data sets. Moreover, the maximum likelihood approach is adopted to estimate the parameters of the EBuH distribution under constant-stress accelerated life-tests (CSALTs). Furthermore, a real data set is analyzed to validate our results under the CSALT model.