Approximate design and performance of the robust control charts for monitoring dispersion in Phase I

This article designs and studies the approximate performance of robust dispersion charts, namely, MAD chart, S_n chart, and Q_n chart, in Phase I analysis (recently developed in the literature). The proposed limits are based on false alarm probability for monitoring the dispersion of a process in Phase I analysis. The charting constants are determined to achieve the required nominal FAP (FAP₀). The performance of these structures is evaluated in (i) the attained false alarm rate and (ii) the probability of signals for out-of-control situations. The analysis shows that the proposed design of Phase I robust dispersion charts correctly controls the FAP and shows a good performance in detecting the shifts in the process variation. An illustrative example is used to explain the practical implementation of these limits.