Table 1-Statistical Process Control (SPC) Problem Data for Service Waiting Times
$\begin{array} { | c | c | c | c | } \hline \begin{array} { c } \text { Sample } \\\text { Number }\end{array} & \multicolumn{3}{|c|} { \text { Observation Number } } \\\hline & 1 & 2 & 3 \\\hline 1 & 9.6 & 10.2 & 9.8 \\\hline 2 & 9.4 & 10.0 & 10.4 \\\hline 3 & 9.9 & 9.6 & 9.0 \\\hline 4 & 9.3 & 10.5 & 9.9 \\\hline 5 & 9.7 & 9.2 & 9.7 \\\hline\end{array}$
-In Table 1, the sample values represent service waiting times in minutes. For the R-chart, what is the value of UCL_R?

Question

Table 1-Statistical Process Control (SPC) Problem Data for Service Waiting Times

\begin{array} { | c | c | c | c | } \hline \begin{array} { c } \text { Sample } \\\text { Number }\end{array} & \multicolumn{3}{|c|} { \text { Observation Number } } \\\hline & 1 & 2 & 3 \\\hline 1 & 9.6 & 10.2 & 9.8 \\\hline 2 & 9.4 & 10.0 & 10.4 \\\hline 3 & 9.9 & 9.6 & 9.0 \\\hline 4 & 9.3 & 10.5 & 9.9 \\\hline 5 & 9.7 & 9.2 & 9.7 \\\hline\end{array}

-In Table 1, the sample values represent service waiting times in minutes. For the R-chart, what is the value of UCL_R?

Quizplus · Accepted Answer

The UCL for an R-chart is calculated using the formula UCL_R = D4 * R-bar, where D4 is a constant that depends on the sample size. For a sample size of 3, D4 is approximately 2.114. The average range (R-bar) is calculated as the average of the ranges of each sample. The ranges are 0.6, 1.0, 0.9, 1.2, and 0.5, with an average of 0.84. Thus, UCL_R = 2.114 * 0.84 = 1.776, which falls in the range greater than 1.5 but less than or equal to 2.0.