Cartons of Plaster of Paris are supposed to weigh exactly 32 oz. Inspectors want to develop process control charts. They take ten samples of six boxes each and weigh them. Based on the following data, compute the lower and upper control limits and determine whether the process is in control.
$133.81.1234.60.3334.70.4434.10.7534.20.3634.30.4733.90.5834.10.8934.20.41034.40.3\begin{array} { | c | c | c | } \hline \text { Sample } & \text { Mean } & \text { Range } \\\hline 1 & 33.8 & 1.1 \\\hline 2 & 34.6 & 0.3 \\\hline 3 & 34.7 & 0.4 \\\hline 4 & 34.1 & 0.7 \\\hline 5 & 34.2 & 0.3 \\\hline 6 & 34.3 & 0.4 \\\hline 7 & 33.9 & 0.5 \\\hline 8 & 34.1 & 0.8 \\\hline 9 & 34.2 & 0.4 \\\hline 10 & 34.4 & 0.3 \\\hline\end{array}$

Question

Cartons of Plaster of Paris are supposed to weigh exactly 32 oz. Inspectors want to develop process control charts. They take ten samples of six boxes each and weigh them. Based on the following data, compute the lower and upper control limits and determine whether the process is in control.

133.81.1234.60.3334.70.4434.10.7534.20.3634.30.4733.90.5834.10.8934.20.41034.40.3\begin{array} { | c | c | c | } \hline \text { Sample } & \text { Mean } & \text { Range } \\\hline 1 & 33.8 & 1.1 \\\hline 2 & 34.6 & 0.3 \\\hline 3 & 34.7 & 0.4 \\\hline 4 & 34.1 & 0.7 \\\hline 5 & 34.2 & 0.3 \\\hline 6 & 34.3 & 0.4 \\\hline 7 & 33.9 & 0.5 \\\hline 8 & 34.1 & 0.8 \\\hline 9 & 34.2 & 0.4 \\\hline 10 & 34.4 & 0.3 \\\hline\end{array}

Leigh Memunatu · Accepted Answer

Final Answer :

n = 6; overall mean = 34.23;

Rˉ\bar { R }

= 0.52.

33.978840\begin{array} { | l | r | r| } \hline \text { Upper control limit } & 34.48116 & 1.04208 \\\hline \text { Center line } & 34.23 & 0.52 \\\hline \text { Lower control limit } & 33.97884 & 0 \\\hline\end{array}

$n = 6; overall mean = 34.23; \bar { R } = 0.52. \begin{array} { | l | r | r| } \hline \text { Upper control limit } & 34.48116 & 1.04208 \\ \hline \text { Center line } & 34.23 & 0.52 \\ \hline \text { Lower control limit } & 33.97884 & 0 \\ \hline \end{array} The mean values for samples 1, 2, 3, and 7 fall outside the control limits on the x-bar chart and sample 1 falls outside the upper limit on the R-chart. Therefore, the process is out of control.$ The mean values for samples 1, 2, 3, and 7 fall outside the control limits on the x-bar chart and sample 1 falls outside the upper limit on the R-chart. Therefore, the process is out of control.

Definitions

Learning Objectives

Learning Objectives

Related questions