A Nonparametric General Linear Profile Monitoring

In some applications, the quality of a process is characterized by the functional relationship between a response variable and one or more explanatory variables. Profile monitoring is a technique for checking the stability of this relationship over time. General linear profile monitoring is particularly useful in practice due to its simplicity and flexibility. The existing monitoring methods suffer from a drawback in that they all assume the error distribution to be normal. When the underlying distribution is misspecified, the consistency and efficiency of the commonly used least-square-estimator (LSE) is likely to be inefficient and as a consequence the detection ability of the procedures based on LSE would be substantially reduced. Moreover, the control charts for monitoring the estimated profile parameters, designed under the normality assumption, would result in a rather large bias from the nominal value in the in-control (IC) average run length (ARL) which reduces the ability of the chart to detect process changes ∗Corresponding author. Email: [email protected].