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

question 48

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.The quality control manager has recommended inspecting the first 3 and the last 3 items.(a sample of 6) from each batch of 20.What is the value of the UCL $\bar { X }$ ?

• A) less than or equal to 0.0030
• B) greater than 0.0030 but less than or equal to 0.0049
• C) greater than 0.0049 but less than or equal to 0.0069
• D) greater than 0.0069

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Definitions:

Limited Problem Solving

A decision-making process involving relatively straightforward and simple considerations, often used for routine or familiar purchases.

Decision-Making Continuum

This concept describes the range of processes from simple to complex that consumers go through when deciding which products or services to purchase.

Limited Problem Solving

A decision-making process used for purchases that require a moderate amount of deliberation and are typically familiar to the consumer.

Habitual Decision

The process of making choices automatically based on past behaviors and routines without considerable thought.