Evaluating the performance of variable sampling interval Hotelling T2 charting scheme for compositional data in the presence of measurement error

Abstract

AbstractThe variable sampling interval (VSI) scheme is a well‐known technique for improving the detection ability of control charts (CCs). In the proposed study, measurement error (ME) has been applied to investigate the effectiveness of the Hotelling T2 charting scheme for compositional data (CoDa) using VSI. The current study considered the case of the monitoring phase, assuming that process parameters are known using the continuous times Markov chain model. The evaluation of the proposed scheme has been done using the average time to signal. The authors studied the impact of MEs on the performance of the Hotelling T2 CC for CoDa using VSI, and additionally, the authors also examined the impact of linearly covariate error model parameters on the performance of Hotelling T2 VSI CoDa CC. Six cases for the variance–covariance matrix were used to study the impact of different involved parameters. The effect of ME, sampling interval (SI), powering operator (b), error variance (, and subgroup size (m) has been studied on the performance of proposed CCs by increasing the value of one parameter while keeping the other parameters fixed. The ME and σ have a negative impact on the performance of the proposed CC, while SI, b and m have a positive impact on the performance of the proposed CC. Among all the six cases, the correlated cases (negatively and positively) with equal variance performed better than all the other four cases. In the end, an illustrative example of muesli production with part CoDa (where p is the number of variables in CoDa vector) is provided for the practical implementation of the Hotelling T2 VSI CoDa CC in the presence of ME.