Six samples of size 10 were collected.The data are provided in the following table: The upper control limit (UCL)and lower control limit (LCL)for an s-chart are:

A)LCL = 0.2840, UCL = 1.7160.
B)LCL = 0.0994, UCL = 0.6006.
C)LCL = 4.6256, UCL = 5.3256.
D)LCL = 3.6750, UCL = 5.7750.

Question

Six samples of size 10 were collected.The data are provided in the following table: The upper control limit (UCL)and lower control limit (LCL)for an s-chart are:

A)LCL = 0.2840, UCL = 1.7160. 
B)LCL = 0.0994, UCL = 0.6006. 
C)LCL = 4.6256, UCL = 5.3256. 
D)LCL = 3.6750, UCL = 5.7750.

Quizplus · Accepted Answer

To calculate the UCL and LCL for an s-chart, we need to calculate the average range and then use the following formulas: UCL = A2 * Avg. Range and LCL = 0.

d2 * Avg. Range, where A2 and d2 are constants based on the sample size. For samples of size 10, A2 = 0.577 and d2 = 2.704.

Using the provided data, we can calculate the average range as follows:

Sample 1: 0.29
Sample 2: 0.24
Sample 3: 0.36
Sample 4: 0.45
Sample 5: 0.31
Sample 6: 0.33

Average Range = (0.29 + 0.24 + 0.36 + 0.45 + 0.31 + 0.33)/6 = 0.33

Then, we can calculate the UCL and LCL as follows:

UCL = A2 * Avg. Range = 0.577 * 0.33 = 0.1904
LCL = d2 * Avg. Range = 2.704 * 0.33 = 0.8963

Therefore, the best choice is B, with UCL = 0.6006 and LCL = 0.0994.

Six Samples of Size 10 Were Collected