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

question 208

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.
-A milling operation has historically produced an average thickness of 0.005 inch with an average range of 0.0015 inch.Currently,the first three items from each batch of 20 are inspected.Use Table 6.1.What is the value of the UCL $\bar { X }$ ?

• A) less than or equal to 0.00200
• B) greater than 0.00200 but less than or equal to 0.00399
• C) greater than 0.00399 but less than or equal to 0.00599
• D) greater than 0.00599

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