Identifying the time of step change and drift in Phase II monitoring of autocorrelated logistic regression profiles

In some profile monitoring applications, the independency assumption of consecutive binary response values within each profile is violated. To the best of our knowledge, estimating the time of a change in the parameters of an autocorrelated binary profile is neglected in the literature. In this paper, two maximum likelihood estimators are proposed to estimate the real time of step changes and drift in Phase II monitoring of binary profiles in the case of within-profile autocorrelation, respectively. Our proposed estimators, not only identify the change point in the autocorrelated logistic regression parameters, but also in autocorrelation coefficient. The performance of the proposed estimators to identify the time of change points either in regression parameters or autocorrelation coefficient is evaluated through simulation studies. The results in terms of the accuracy and precision criteria show the satisfactory performance of the proposed estimators under both step changes and drift. Moreover, a numerical example is given to illustrate the application of the proposed estimators.