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 control limits for the s-chart, we first need to calculate the sample standard deviation (s) for each sample. Using the given data, we get the following sample standard deviations:

s1 = 0.316
s2 = 0.282
s3 = 0.179
s4 = 0.209
s5 = 0.244
s6 = 0.265

Next, we calculate the average of all the sample standard deviations:

sbar = (0.316 + 0.282 + 0.179 + 0.209 + 0.244 + 0.265) / 6 = 0.2382

Finally, we use the formula to determine the control limits:

LCL = 0
UCL = sbar * 3 = 0.7146

Therefore, the correct answer is B, with LCL = 0.0994 and UCL = 0.6006.

Six Samples of Size 10 Were Collected