Phase II monitoring of logistic regression profiles with estimated parameters

In most profile monitoring applications, the regression parameters are unknown and must be estimated via Phase I reference samples. This study evaluates how parameter estimation affects the average run length (ARL) properties of two well-known charts in Phase II monitoring of logistic regression profiles. In this regard, the performance of T-2 and MEWMA charts established by estimated regression parameters is evaluated for both in-control and out-of-control situations. The results of simulation experiments confirm that estimation error affects the ARL properties of both T-2 and MEWMA charts. Two remedial procedures of increasing the Phase I samples and control limit modification are employed to compensate for the estimation error impact. Then, an illustrative example based on simulated data is given to indicate the impact of estimation error on detection ability of T-2 chart. Finally, a real-life example is provided to represent how estimation error increases the false alarm rate of T-2 chart.