Optimal performance of the variable sample sizes Hotelling’s T² control chart in the presence of measurement errors

Abstract

The effect of measurement errors on the performance of adaptive control charts has rarely been investigated in the univariate case and, as far as we know, it has not been investigated at all in the multivariate case. In this paper, we evaluate the effect of measurement errors on the VSS (Variable Sample Sizes) Hotelling’s T² control chart. To do so, we suggest using six different performance measures: (i) the average and (ii) the standard deviation of the run length, (iii) the average and (iv) the standard deviation of the number of observations to signal, (v) the average and (vi) the standard deviation of the number of switches to signal. These performance measures should be as small as possible when the process is out-of-control to ensure an optimal chart efficiency. We use two models for defining the objective function which includes at least one of these performance measures. We find the optimal values of the sample sizes and the overall performance measures for each model and for different values of the measurement errors variance, the numbers of measurements and the values of the error model’s constants. Finally, we present an illustrative example to show the application of the proposed method.

Keywords:

• Variable Sample Sizes (VSS) control charts
• Hotelling’s T² control charts
• linearly covariate error model
• overall performance measures
• Markov Chain
• optimization