Table 6.1
Factors for Calculating Three-Sigma Limits for the -chart and R-chart
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 0.015 inch.Currently,the first three items from each batch of 20 are inspected.Use Table 6.1.What is the value of the LCL ?
A)less than or equal to 0.00100
B)greater than 0.00100 but less than or equal to 0.00299
C)greater than 0.00299 but less than or equal to 0.00499
D)greater than 0.00499

Question

Table 6.1
Factors for Calculating Three-Sigma Limits for the  -chart and R-chart
  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 0.015 inch.Currently,the first three items from each batch of 20 are inspected.Use Table 6.1.What is the value of the LCL  ?
A)less than or equal to 0.00100 
B)greater than 0.00100 but less than or equal to 0.00299 
C)greater than 0.00299 but less than or equal to 0.00499 
D)greater than 0.00499

Quizplus · Accepted Answer

Using Table 6.1, with n=3, the factor A2=0.729. The control limits for the X-bar chart are calculated as:
Upper Control Limit = X-double bar + A2* R-bar = 0.005 + 0.729*0.015 = 0.01664
Lower Control Limit = X-double bar - A2* R-bar = 0.005 - 0.729*0.015 = 0.00336
Therefore, the LCL for the X-bar chart is 0.00336, which is greater than 0.00299 but less than or equal to 0.00499.

Table 6.1 Factors for Calculating Three-Sigma Limits for the -Chart and -Chart