Phase II monitoring of linear profiles using a P-value approach

We propose a P-value-based method to assess the performance of linear profiles in phase II. Performance of the proposed method is evaluated by the average run length criterion under various shifts in the intercept, slope and error standard deviation of a linear model. In our proposed approach, P-values are computed at each level within a sample. If at least one of the P-values is less than a pre-specified significance level, chart signals out-of-control. The primary advantage of our approach is that only one control chart is required to monitor three parameters simultaneously: the intercept, slope, and standard deviation. A comprehensive comparison of the proposed method and the existing KMW-Shewhart method for monitoring linear profiles is conducted. In addition, the effect that number of observations within a sample has on the performance of the proposed method is investigated. A simulation study shows that the proposed P-value method performs satisfactorily in terms of average run length compared to KMW-Shewhart method.