The variable parameters T <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$^{2}$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msup> <mrow/> <mn>2</mn> </msup> </math> </EquationSource> </InlineEquation> chart with run rules
The Hotelling’s <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$$\textit{T}^{2 }$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msup> <mi mathvariant="italic">T</mi> <mn>2</mn> </msup> </math> </EquationSource> </InlineEquation>control chart with variable parameters (VP <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$$T^{2})$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <msup> <mi>T</mi> <mn>2</mn> </msup> <mrow> <mo>)</mo> </mrow> </mrow> </math> </EquationSource> </InlineEquation> has been shown to have better statistical performance than other adaptive control schemes in detecting small to moderate process mean shifts. In this paper, we investigate the statistical performance of the VP <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$$T^{2}$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msup> <mi>T</mi> <mn>2</mn> </msup> </math> </EquationSource> </InlineEquation> control chart coupled with run rules. We consider two well-known run rules schemes. Statistical performance is evaluated by using a Markov chain modeling the random shock mechanism of the monitored process. The in-control time interval of the process is assumed to follow an exponential distribution. A genetic algorithm has been designed to select the optimal chart design parameters. We provide an extensive numerical analysis indicating that the VP <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$$T^{2}$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msup> <mi>T</mi> <mn>2</mn> </msup> </math> </EquationSource> </InlineEquation> control chart with run rules outperforms other charts for small sizes of the mean shift expressed through the Mahalanobis distance. Copyright Springer-Verlag Berlin Heidelberg 2014
