Modified T ² Control Chart of Principal Components When KDR and TSR Methods of Score Estimation are Used in Phase II

ABSTRACT When Phase II multivariate process control is performed using the chart of principal components and missing data occurs, KDR and TSR imputation methods allow for the calculation of the statistic. However, Hotelling's chart's performance has been shown to be affected by this procedure in situations with a known population covariance matrix. We propose a modification to the Phase II statistic in scenarios with an unknown population covariance matrix when missing data is estimated using KDR and TSR methods. The aim of this paper is to assess the performance of the proposed control chart. To do so, we perform a simulation study where we estimate average run length (ARL) curves for a series of covariance structures under different scenarios. Estimated ARLs are compared to those of Hotelling's chart with complete data. Results show the new chart's ARL curve is equivalent to that of the chart with complete data and, for a given covariance structure, constant for percentages of missing information of 5%–20 . Additionally, we show that a large Phase I sample size is necessary to achieve the specified false alarm rate when the conventional control limit is used. For these situations, we suggest how to adjust the chart's limit for a target significance level and a given Phase I sample size.