Journal of Quality Engineering and Management

Abstract The purpose of this paper is to investigate the reliability parameter R = P (X <Y) based on samples with type 2 incremental censorship in which X and Y are independent random variables with generalized inverse exponential distribution with different shape parameters and the same scale parameter. The maximum likelihood estimator (MLE) and the nonlinear estimator with uniform uniform variance (UMVUE) of the parameter R are obtained and different confidence intervals are provided. Also, Bayesian R estimator and HPD confidence interval using Gibbs sampling method are proposed. Monte Carlo simulations have been performed to compare the performance of different methods.

Abstract Control charts are among the most important tools in statistical process control, used to monitor the extent of variation in a process. When a assignable cause deviation is observed in a control chart, identifying the root causes of the change and determining the time at which the deviation began—referred to as the change point—is crucial and impactful. In some statistical process control problems, the quality of a product or the performance of a process is described by the relationship between a response variable and one or more independent variables, known as a profile. In many applications, such as calibration, this relationship is described by a linear profile, while in other situations more complex models, such as Poisson regression profiles, are required. In this paper, the maximum likelihood estimation method is employed to detect change points in Phase II monitoring of Poisson regression profiles, and its performance is evaluated through simulation.