Resumen de Adaptive Generalized Likelihood Ratio Control Charts for Detecting Unknown Patterned Mean Shifts
Giovanna Capizzi, Guido Masarotto
Traditional statistical control schemes have been mainly focused on detecting constant mean shifts. In many practical applications, however, the mean of the observed sequence can exhibit a time-varying behavior after the fault occurrence. Shewhart control charts supplemented with sensitizing run rules have been suggested for detecting nonrandom dynamic mean patterns. However, the choice of a particular set of run rules requires some prior knowledge of the possible expected patterns. In addition, the resulting schemes can have poor performance against small shifts. When the mean shift pattern is known in advance, generalized likelihood ratio (GLR), cumulative score (CUSCORE), and optimal general linear filter (OGLF) control charts have also been proposed for change-point detection. Further, some adaptive CUSCORE schemes have been recently developed for detecting an unknown patterned mean shift. However, these adaptive CUSCOREs assume the occurrence of one-sided mean shifts. Hence, their performance may be poor in the case of an oscillatory behavior of the process mean. To overcome these limitations, we propose estimating a possible pattern in the mean using an exponentially weighted moving average (EWMA), which is especially e↵ective with one-sided shifts in the mean, combined with a wavelet smoother, which is e↵ective in estimating oscillatory mean patterns. The two estimates then drive two separate conventional GLR tests for significance. A control chart is proposed for observations from normal distributions and then extended to a completely distribution-free setting. Extensive simulation results demonstrate the efficiency of the proposed charts with a wide variety of patterned mean shifts in both the independent and autocorrelated scenarios and with a wide variety of distributions. In addition, the proposed scheme provides post-signal diagnostic information that estimates the change-point location and the shift pattern of the mean. An R package is available online as supplementary material.
