Table S6.1 - Factors for Computing Control Chat Limits (3 sigma)

Auto Pistons at Wenming Chung's plant in Shanghai are produced in a forging process, and the diameter is a critical factor that must be controlled. From sample sizes of 10 pistons produced each day, the mean and the range of this diameter have been as follows:

Auto pistons at Wenming Chung's plant in Shanghai are produced in a forging process, and the diameter is a critical factor that must be controlled. From sample sizes of 10 pistons produced each day, the mean and the range of this diameter have been as follows: \begin{tabular}{cccc} \hline SampleSize,n & MeanFactor,A2 & UpperRange,D4 & LowerRange,D3 \\ \hline 2 & 1.880 & 3.268 & 0 \\ 3 & 1.023 & 2.574 & 0 \\ 4 & 0.729 & 2.282 & 0 \\ 5 & 0.577 & 2.115 & 0 \\ 6 & 0.483 & 2.004 & 0 \\ 7 & 0.419 & 1.924 & 0.076 \\ 8 & 0.373 & 1.864 & 0.136 \\ 9 & 0.337 & 1.816 & 0.184 \\ 10 & 0.308 & 1.777 & 0.223 \\ 12 & 0.266 & 1.716 & 0.284 \\ \hline \end{tabular} c) What are the UCLi and LCLx using 3-sigma? Upper Control Limit (UCLx)=mm (round your response to two decimal places). Lower Control Limit (LCl)=mm (round your response to two decimal places). d) What are the UCL RR and LCLR using 3 sigma? Upper Control Limit (UCL LA)=mm (round your response to ho decimal places). Lower Control Limit (LCLR)=1mm (round your response to fwo decimal places). e) If the true diameter mean should be 155mm and you want this as your center (nominal) line, what are the new UCL- and LCLUpper Control Limit (UCL xX)= mm (round your response to two decimal places). Lower Control Limit (LCLx)= mm (round your response to two decimal places). \begin{tabular}{cccc} \hline SampleSize,n & MeanFactor,A2 & UpperRange,D4 & LowerRange,D3 \\ \hline 2 & 1.880 & 3.268 & 0 \\ 3 & 1.023 & 2.574 & 0 \\ 4 & 0.729 & 2.282 & 0 \\ 5 & 0.577 & 2.115 & 0 \\ 6 & 0.483 & 2.004 & 0 \\ 7 & 0.419 & 1.924 & 0.076 \\ 8 & 0.373 & 1.864 & 0.136 \\ 9 & 0.337 & 1.816 & 0.184 \\ 10 & 0.308 & 1.777 & 0.223 \\ 12 & 0.266 & 1.716 & 0.284 \\ \hline \end{tabular} \begin{tabular}{ccc} \hline Day & Meanx(mm) & RangeR(mm) \\ \hline 1 & 156.9 & 4.2 \\ 2 & 153.2 & 4.4 \\ 3 & 151.6 & 4.3 \\ 4 & 155.5 & 4.8 \\ 5 & 158.6 & 4.7 \\ \hline \end{tabular} x=mm(roundyourresponsetotwodecimalplaces). What is the value of R ? R=mm(roundyourresponsetotwodecimalplaces). c) What are the UCL Lx and LCLusing 3-sigma? Upper Control Limit (UCLx)= mm (round your response to two decimal places). Lower Control Limit (LCL)= mm (round your response to two decimal places). d) What are the UCL RR and LCLR using 3-sigma? Upper Control Limit (UCLR)= mm (round your response to two decimal places). Lower Control Limit (LCLR)= mm (round your response to two decimal pleces). e) If the true diameter mean should be 155mm and you want this as your center (nominal) line, what are the new UCL; and LCL; Upper Control Limit (UCL)= mm (round your response to two decimal places). Lower Control Limit (LCLj)= mm (round your response to two decimal places)