The economic and economic-statistical designs of the Hotelling's T~2 chart based on the expected average run length

摘要

Existing economic and economic-statistical designs require practitioners to specify the Mahalanobis Distance Shift Size (MDSS) as an exact value. However, practitioners may find it difficult to specify this distance. This article proposes the economic and economic-statistical designs of the Hotelling's T~2 chart, where practitioners do not have to specify the MDSS. Adopting optimal design parameters based on the wrong MDSS results in a significant increase in cost. In comparison, adopting the optimal design parameters based on the proposed methodology results in a slight increase in cost. This article also studies the effects of different input parameters and statistical constraints.