Solve the Problem $\bar { s }$ (The Mean of the Sample Standard Deviations) and Control Limits

Essay

Solve the Problem.
-A control chart for monitoring variation and center can be based on standard deviations instead of on ranges. An s chart for monitoring variation is made by plotting sample standard deviations with a center line at $\bar { s }$ (the mean of the sample standard deviations) and control limits at $B _ { 4 } \bar { s }$ and $B _ { 3 } \bar { s }$ , where $B _ { 4 }$ $\bar { s }$ and $B _ { 3 }$$\bar { s }$ are found in the Control Chart Constants table. Construct an s chart for the data below.

A manufacturer of lightbulbs picks 10 lightbulbs at random each day for quality control. The mean, standard de and range (in hours) of the lifetimes of the 10 lightbulbs are calculated. The results for 12 consecutive days are sh the table below.
$\begin{array}{lcll}\text { Day } & \bar{x} & \text { Range } & \text { s } \\\hline 1 & 201.1 & 3.4 & 1.2 \\2 & 203.4 & 4.7 & 1.7 \\3 & 200.9 & 3.1 & 0.9 \\4 & 205.6 & 6.2 & 2.3 \\5 & 201.3 & 4.7 & 1.3\\6 & 200.5 & 3.7 & 1.7 \\7 & 205.8 & 5.8 & 2.1 \\8 & 203.7 & 6.2 & 2.9 \\9 & 199.8 & 2.1 & 0.8 \\10 & 202.7 & 4.4 & 1.6 \\11 & 200.0 & 2.7 & 0.7 \\12 & 204.6 & 7.8 & 3.0\\\end{array}$