Cumulative exposure lognormal model with hybrid

Abstract

This research aims to analyze data coming from step stress life testing experiments that are commonly used to make inferences on the reliability of products and machines. Customers expect a reliable product that can still perform its functions for a long period of time. For this reason, factories are pressured to design and make products that can operate for a long enough period of time while performing its functions. Step stress experiments are accelerated experiments for which the stress level increases at a preset time to obtain failure data faster and make the necessary analysis. To analyze step stress data, a model that extrapolates the information obtained from the accelerated tests to normal use conditions needs to be fit to the life test data. In this study, we will use the Cumulative Exposure Model (CEM) to analyze simple step stress lognormal life test data and estimate the model parameter and survival function in the case where hybrid censoring is present in the data. This study uses the maximum likelihood estimation method and the Maximum Likelihood Estimators (MLEs) properties to find the point and interval estimates of the parameters, in addition to finding the point and interval estimates for the survival function. The MLEs are obtained numerically since the ML equations cannot be found explicitly. The approximate confidence interval for estimating the model parameters was constructed based on the asymptotic property of the MLEs. To obtain the approximate confidence interval for estimating the survival function, the delta method is used. The bootstrap-t intervals and percentile intervals were also constructed to estimate the model parameters and survival function. Furthermore, a simulation study has been performed to examine the proposed methods of estimation under different hybrid censoring schemes. The Bias, MSE, coverage probability and average lengths have been calculated to study and compare the performance of the point and interval estimators of the model parameters and survival function. Finally, an illustrative example has been made to view and illustrate how the proposed methods work