We are establishing a quality control program for a process and need to establis
ID: 3229787 • Letter: W
Question
We are establishing a quality control program for a process and need to establish the mean and standard deviation for the process. The first 10 batches had samples of size 5 taken, and the following data were recorded.
Which of the following are the upper and lower control limits for an x control chart?
A) (37.545, 51.915)
B) (42.313, 47.147)
C) (37.086, 52.374)
Batch x s 1 43.6 2.56 2 45.4 1.90 3 43.0 1.96 4 46.2 2.67 5 43.5 3.09 6 43.0 2.55 7 45.0 2.01 8 47.6 2.35 9 46.6 1.90 10 43.4 2.96Explanation / Answer
UCL = Average(Xbar) + 3*Sigma(Xbar)
= ( 43.6+45.4+43.0+46.2+...43.4 /10) + 3 * (2.56+1.9+....+1.9+2.96 / 10) = 44.73 + 3*2.395 = 51.915
LCL = Average(Xbar) - 3*Sigma(Xbar) = 44.73 - 3*2.395 = 37.545
option A is right
Control limit equations are based on three sigma limits. Just remember, it is three sigma limits of what is being plotted. So, what does that mean? If you are plotting individual values (e.g., the X control chart for the individuals control chart), the control limits are given by:
UCL = Average(X) + 3*Sigma(X)
LCL = Average(X) - 3*Sigma(X)
where Average (X) = average of all the individual values and Sigma(X) = the standard deviation of the individual values.
If you are plotting subgroup averages (e.g., the Xbar control chart), the control limits are given by:
UCL = Average(Xbar) + 3*Sigma(Xbar)
LCL = Average(Xbar) - 3*Sigma(Xbar)
where Average(Xbar) = average of the subgroup averages and Sigma(Xbar) = the standard deviation of the subgroup averages.
If you are plotting range values, the control limits are given by:
UCL = Average(R)+ 3*Sigma(R)
LCL = Average(R) - 3*Sigma(R)
where Average(R)= average of the range values and Sigma(R) = standard deviation of the range values.
So for each set of control limits, there is a location parameter and a dispersion parameter. The location parameter simply tells us the average of the distribution. The dispersion parameter gives us the amount of variation in the data. The average is an estimate of the location parameter. The standard deviation is an estimate of the dispersion or variation parameter.
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