Table $7.1$
Factors for Calculating Three- Sigma Limits for the $\bar { X }$ - chart and $R$ - chart

-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 1.. What is the value of LCL$\bar { X }$ ) if the sample size is increased to 6?
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

Question

Table $7.1$
Factors for Calculating Three- Sigma Limits for the $\bar { X }$ - chart and $R$ - chart

-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 1.. What is the value of LCL$\bar { X }$ ) if the sample size is increased to 6? 
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

Quizplus · Accepted Answer

The LCL (Lower Control Limit) for the sample mean is calculated using the formula LCL = $\bar{X}$ - A2 * R, where A2 is a constant that depends on the sample size. For a sample size of 6, A2 is approximately 0.483. Given $\bar{X}$ = 0.005 and R = 0.0015, LCL = 0.005 - (0.483 * 0.0015) = 0.004275, which falls in the range greater than 0.0030 but less than or equal to 0.0049.

Table 7.17.17.1 Factors for Calculating Three- Sigma Limits for The Xˉ\bar { X }Xˉ

Table $7.1$ Factors for Calculating Three- Sigma Limits for The $\bar { X }$