A New Synthetic Triple Sampling X̅ Control Chart

In this study, the synthetic triple sampling (STS) <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mover accent="true"> <m:mi>X</m:mi> <m:mo>¯</m:mo> </m:mover> </m:math> {X̄} chart is introduced to monitor the process mean more effectively. The developed STS <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mover accent="true"> <m:mi>X</m:mi> <m:mo>¯</m:mo> </m:mover> </m:math> {X̄} chart combines the triple sampling (TS) <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mover accent="true"> <m:mi>X</m:mi> <m:mo>¯</m:mo> </m:mover> </m:math> {X̄} chart and the conforming run length (CRL) chart to enhance shift detection capabilities. The performance of the STS <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mover accent="true"> <m:mi>X</m:mi> <m:mo>¯</m:mo> </m:mover> </m:math> {X̄} chart is compared with that of the TS <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mover accent="true"> <m:mi>X</m:mi> <m:mo>¯</m:mo> </m:mover> </m:math> {X̄} and synthetic double sampling (SDS) <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mover accent="true"> <m:mi>X</m:mi> <m:mo>¯</m:mo> </m:mover> </m:math> {X̄} charts on the basis of the average number of observations to signal (ANOS) and expected ANOS (EANOS) as key performance metrics. Results show that the process shift detection effectiveness of the STS <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mover accent="true"> <m:mi>X</m:mi> <m:mo>¯</m:mo> </m:mover> </m:math> {X̄} chart is generally superior to that of the TS <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mover accent="true"> <m:mi>X</m:mi> <m:mo>¯</m:mo> </m:mover> </m:math> {X̄} and SDS <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mover accent="true"> <m:mi>X</m:mi> <m:mo>¯</m:mo> </m:mover> </m:math> {X̄} charts. Real industrial data are adopted to demonstrate the implementation of the STS <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mover accent="true"> <m:mi>X</m:mi> <m:mo>¯</m:mo> </m:mover> </m:math> {X̄} chart.