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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Definitions:

Overload Theory

A concept in psychology and organizational behavior referring to the state where an individual or system is overwhelmed by tasks or information, leading to reduced performance or stress.

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The phenomenon where teams or individuals perform worse in their own environment or venue, contrary to the expected home field advantage.

Hostile Surroundings

Environments characterized by antagonism or adversity that can impact individuals' performance and well-being.

Supportive

Providing encouragement, comfort, or assistance, often in a context of a relationship, group, or social setting.