Table 61
Factors for Calculating Three-Sigma Limits for The The \bar

Table 6.1
Factors for Calculating Three-Sigma Limits for the $\bar { X }$ -chart and R-chart
$$\begin{array} { | c | c | c | c | } \hline \begin{array} { c } \text { Size of } \\\text { Sample } \\( n ) \end{array} & \begin{array} { c } \text { Factor for UCL } \\\text { and LCL for } X \text { - } \\\text { Charts } \\\left( A _ { 2 } \right) \end{array} & \begin{array} { c } \text { Factor for } \\\text { LCL for } R \text { - } \\\text { Charts } \\\left( D _ { 2 } \right) \end{array} & \begin{array} { c } \text { Factor for } \\\text { UCL for } R \text { - } \\\text { Charts } \\\left( D _ { 1 } \right) \end{array} \\\hline 2 & 1.880 & 0 & 3.267 \\3 & 1.023 & 0 & 2.575 \\4 & 0.729 & 0 & 2.282 \\5 & 0.577 & 0 & 2.115 \\6 & 0.483 & 0 & 2.004 \\7 & 0.419 & 0.076 & 1.924 \\8 & 0.373 & 0.136 & 1.864 \\9 & 0.397 & 0.184 & 1.816 \\10 & 0.308 & 0.233 & 1.777 \\\hline\end{array}$$
Source: 1950 Manual on Quality Control of Materials, copyright
American Society for Testing Materials. Reprinted with permission.
-Historically,the average diameter of the holes drilled has been 0.25 cm and the average range has been 0.1 cm.Determine the central line and upper and lower control limits for an $\bar { X }$ - and an R-chart,assuming samples of size 8 will be taken.Use Table 6.1.For the-chart,what is the value of UCL $\bar { X }$ ?

A) less than or equal to 0.100
B) greater than 0.100 but less than or equal to 0.200
C) greater than 0.200 but less than or equal to 0.300
D) greater than 0.300