A P-value approach for Phase II monitoring of multivariate profiles

In some applications where the quality characteristic of interest is a profile, it is possible to use multiple linear regressions to model process quality. In this paper, we propose using a P-value approach to evaluate performance of multivariate profiles in Phase II. The average run length (ARL) is used to evaluate performance of the proposed method under different shifts in the model parameters. In our proposed approach, P-values for all observed levels within a sample are calculated. If any P-value is less than a specific threshold, the chart signals out of control. The main advantage of this approach is its ease of implementation in practice. Performance of the proposed method is compared to another commonly used method involving the T2 control charts. Simulation results indicate that the proposed P-value approach performs quite well under the various conditions considered. Given that it is a straightforward and easy to implement approach, as well as a monitoring scheme that only requires a single control chart, the P-value method is quite competitive in practice.