Table 1 Statistical Process Control (SPC) Problem Data*
$\begin{array}{|c|c|c|c|c|c|}\hline \text { Sample } & \begin{array}{c}\text { Observation } \\\text { Number }\end{array} & \begin{array}{c}\text { Observation } \\\text { Number }\end{array} & \begin{array}{c}\text { Observation } \\\text { Number }\end{array} \\\hline \text { Number } & 1 & 2 & 3 & \begin{array}{c}\text { Row } \\\text { Average }\end{array} & \text { Row Range } \\\hline 1 & 10.1 & 10.6 & 9.6 & 10.1 & 1.00 \\\hline 2 & 9.7 & 9.4 & 9.0 & 9.37 & 0.70 \\\hline 3 & 10.1 & 9.1 & 10.3 & 9.83 & 1.20 \\\hline 4 & 10.1 & 10.3 & 10.9 & 10.43 & 0.80 \\\hline 5 & 10.2 & 9.8 & 9.0 & 9.67 & 1.20 \\\hline 6 & 10.6 & 10.2 & 9.5 & 10.10 & 1.10 \\\hline 7 & 9.5 & 10.2 & 10.2 & 9.97 & 0.70 \\\hline\end{array}$ *The range and row average help you avoid simple math errors and quicken the time to complete the SPC analysis but you have to know what to use when.
-Using Table 1, for the R-chart, what is the value of LCL_R?

Question

Table 1 Statistical Process Control (SPC) Problem Data*

\begin{array}{|c|c|c|c|c|c|}\hline \text { Sample } & \begin{array}{c}\text { Observation } \\\text { Number }\end{array} & \begin{array}{c}\text { Observation } \\\text { Number }\end{array} & \begin{array}{c}\text { Observation } \\\text { Number }\end{array} \\\hline \text { Number } & 1 & 2 & 3 & \begin{array}{c}\text { Row } \\\text { Average }\end{array} & \text { Row Range } \\\hline 1 & 10.1 & 10.6 & 9.6 & 10.1 & 1.00 \\\hline 2 & 9.7 & 9.4 & 9.0 & 9.37 & 0.70 \\\hline 3 & 10.1 & 9.1 & 10.3 & 9.83 & 1.20 \\\hline 4 & 10.1 & 10.3 & 10.9 & 10.43 & 0.80 \\\hline 5 & 10.2 & 9.8 & 9.0 & 9.67 & 1.20 \\\hline 6 & 10.6 & 10.2 & 9.5 & 10.10 & 1.10 \\\hline 7 & 9.5 & 10.2 & 10.2 & 9.97 & 0.70 \\\hline\end{array}

*The range and row average help you avoid simple math errors and quicken the time to complete the SPC analysis but you have to know what to use when.
-Using Table 1, for the R-chart, what is the value of LCL_R?

Quizplus · Accepted Answer

The LCL for the R-chart is calculated as D₃ * σ_R, where D₃ is a constant that depends on the sample size and σ_R is the standard deviation of the sample ranges. For a sample size of 3, D₃ = 0 and σ_R = 0.886 * σ, where σ is the standard deviation of the process. Therefore, LCL_R = 0 * 0.886 * σ = 0.

Table 1 Statistical Process Control (SPC) Problem Data *The Range and Row Average Help You Avoid Simple Math