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

question 160

Multiple Choice

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 $\bar { X }$ -chart,what is the value of the LCL $\bar { X }$ ?

• A) less than or equal to 0.10
• B) greater than 0.10 but less than or equal to 0.19
• C) greater than 0.19 but less than or equal to 0.29
• D) greater than 0.29

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