Morvarid Derakhshan Andisheh Journal of Quality Engineering and Management 3134-0849 14 2 2024 08 22 Statistical-economic design of control charts RNLMVSIT2 Statistical-economic design of control charts RNLMVSIT2 162 176 214759 10.48313/jqem.2024.214759 FA Asghar Seif Department of Statistics, Faculty of Basic Sciences, Bu-Ali Sina University, Hamedan, Iran. 0000-0002-7044-3240 Mitra Abdolmohammadi Department of Statistics, Science and Research Branch, Islamic Azad University, Tehran, Iran. Journal Article 2023 10 10 Purpose: In many industrial processes, there are situations where simultaneous monitoring and control of two or more dependent variables are necessary. In such cases, univariate control of quality characteristics can be misleading when considered independently. In the classical approach, when a quality characteristic falls outside the specified technical limits, the quality loss is regarded as a cost. All products within the technical limits of the quality characteristic are assumed to have similar quality, regardless of the deviation of the quality characteristic from its target value. However, it is essential to distinguish between products that fall within the technical limits of the quality characteristic, as any deviation from the target value incurs a proportional loss. Methodology: This paper introduces, for the first time in the literature, a reflected normal loss function to determine the average cost of producing non-conforming products when two quality characteristics are evaluated. In summary, this study focuses on the statistical-economic design of a multivariate T²-Hotelling control chart with multivariate variable sampling intervals in the presence of a reflected normal multivariate loss function (RNLMVSIT²). Additionally, a sensitivity analysis is conducted to examine the effects of time and cost parameters on the design parameters and the average cost. Findings: The results demonstrate the satisfactory performance of the proposed models. Originality/Value: This paper introduces, for the first time in the literature, a reflected normal loss function to determine the average cost of producing non-conforming products when two quality characteristics are evaluated. Purpose: In many industrial processes, there are situations where simultaneous monitoring and control of two or more dependent variables are necessary. In such cases, univariate control of quality characteristics can be misleading when considered independently. In the classical approach, when a quality characteristic falls outside the specified technical limits, the quality loss is regarded as a cost. All products within the technical limits of the quality characteristic are assumed to have similar quality, regardless of the deviation of the quality characteristic from its target value. However, it is essential to distinguish between products that fall within the technical limits of the quality characteristic, as any deviation from the target value incurs a proportional loss. Methodology: This paper introduces, for the first time in the literature, a reflected normal loss function to determine the average cost of producing non-conforming products when two quality characteristics are evaluated. In summary, this study focuses on the statistical-economic design of a multivariate T²-Hotelling control chart with multivariate variable sampling intervals in the presence of a reflected normal multivariate loss function (RNLMVSIT²). Additionally, a sensitivity analysis is conducted to examine the effects of time and cost parameters on the design parameters and the average cost. Findings: The results demonstrate the satisfactory performance of the proposed models. Originality/Value: This paper introduces, for the first time in the literature, a reflected normal loss function to determine the average cost of producing non-conforming products when two quality characteristics are evaluated.

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