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 find the upper and lower control limits for an s-chart, we first calculate the average range using the formula:

Average Range = (Range1 + Range2 + ... + Range6) / 6

= (0.32 + 0.38 + 0.28 + 0.44 + 0.36 + 0.40) / 6

= 0.35

Next, we calculate the control limits using the formula:

UCL = Average Range * A2 
LCL = Average Range * D3

A2 and D3 values can be found in statistical tables. For a sample size of 10, A2 = 0.577 and D3 = 0.0.

Plugging in the numbers, we get:

UCL = 0.35 * 0.577 = 0.201 
LCL = 0.35 * 0.0 = 0

Therefore, the upper control limit is 0.201 and the lower control limit is 0. For the given options, only option B has the correct UCL and LCL values.

Six Samples of Size 10 Were Collected