Change point estimation of high-yield processes with a linear trend disturbance

Abstract

In this paper, the maximum likelihood estimator (MLE) of the change point in a high-yield process when a linear trend disturbance occurs in the proportion nonconformity of the process is first derived. Then, the performances of the proposed change point estimator in terms of both accuracy and precision are compared to the MLE of the change point designed for step changes. The results of the comparison analysis that is performed using Monte Carlo simulation experiments show that not only the average estimates of the change point estimator designed for linear trends are closer to the real change point, but also its mean square error is smaller than the one of the estimator designed for step changes for almost all shifts. In addition, better precisions are obtained by the proposed estimator than the ones obtained by the estimator designed for step changes. In short, in the presence of a linear trend disturbance, the MLE of the change point designed for linear trend disturbances outperforms the MLE of the change point designed for step changes.