o AT&T; LTE 12:33 AM blackboard.boisestate.edu 2 of 5 2. Cans of soup are suppos
ID: 443370 • Letter: O
Question
o AT&T; LTE 12:33 AM blackboard.boisestate.edu 2 of 5 2. Cans of soup are supposed to weigh exactly 16oz. Inspectors want to develop process control charts They take eight samples of five bones and weigh them. They ebeain the Sollowing data Sample Mea Range 14.6 3 165 18. 15.2 1.8 0.7 0.5 04 13.202 0.2 04 0.5 0.9 6 160 7 159 8 14 (a) What is the upper control limit for the x-bar chart? (b) What is the lower control limit for the x-bar chart? (c) What is the upper control limit for the R chart? (d) What is the lower control limit for the R chart? (e) Is the process in a state of control?Explanation / Answer
Let,
Xmean= central line of the chart and the average of past sample means, and A2= constant to provide three sigma limits for the process mean
Rmean= average of several past R values and is the central line of the control chart
D3, D2 = constants that provide three standard deviation (three-sigma) limits for a given sample size
From the provided table we get, Xmean = 15.5375, Rmean = 0.675, n = 5 (as we are sampling 5 boxes)
Using the table of control chart constraints,
D4 = 2.114, D3 = 0, A2 = 0.577
a. UCLX= X mean +A2*Rmean = 15.92698
b. LCLX= Xmean-A2*Rmean = 15.14803
c. UCLR = D4*Rmean = 1.42695
d. LCLR = D3*Rmean= 0
e. First we check the R chart if any observation is out of the limits UCLR and LCLR. We see that first observation in R chart is out of limits. If any observation in R chart is out of limit it implies that the process is out of control.
Additionally, we also check the x chart to see if any observation goes out of limits UCLX and LCLX. We see that majority of the observations are out of limit. Thus, the whole process is out of control.
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