Table 5.1
Factors for Calculating Three-Sigma Limits for the Chart and R-Chart
Source: 1950 ASTM 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 5.1.What is the value of lower control limit for the x-bar chart 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 5.1
Factors for Calculating Three-Sigma Limits for the  Chart and R-Chart
  Source: 1950 ASTM 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 5.1.What is the value of lower control limit for the x-bar chart 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 lower control limit (LCL) for the x-bar chart is calculated using the formula: LCL = X̄ - A2 * R̄. Given the average thickness (X̄) is 0.005 inch and the average range (R̄) is 0.0015 inch, and using the A2 factor for a sample size of 6 from Table 5.1, the LCL falls in the range greater than 0.0030 but less than or equal to 0.0049.

Table 5.1 Factors for Calculating Three-Sigma Limits for the Chart and Chart