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(a) Find trial control limits forand charts_Control Limits:UCLLCLR Control Limits:UCLLCL(b) Assuming that the process is in control, estimate the process mean and s...

Question

(a) Find trial control limits forand charts_Control Limits:UCLLCLR Control Limits:UCLLCL(b) Assuming that the process is in control, estimate the process mean and standard deviation

(a) Find trial control limits for and charts_ Control Limits: UCL LCL R Control Limits: UCL LCL (b) Assuming that the process is in control, estimate the process mean and standard deviation



Answers

A process that is in control has a mean of $\mu=12.5$ and a standard deviation of $\sigma=.8$
$\begin{array}{l}{\text { a. Construct the } \overline{x} \text { control chart for this process if samples of size } 4 \text { are to be used. }} \\ {\text { b. Repeat part (a) for samples of size } 8 \text { and } 16 .} \\ {\text { c. What happens to the limits of the control chart as the sample size is increased? Discuss }} \\ {\text { why this is reasonable. }}\end{array}$

Here gives us a mean of 5.42 and a value on average are here off two point. Oh, and it wants us to estimate the computer for some of the control limits and then estimate the standard deviation. So the upper control limit can be first of all found by taking the mean plus a two art, and then the lower control limit can be taken by the mean minus 82 Um, are so from table 19.3, we can find the values of A to where we're given that the value is gonna be 0.577 here. So once we substituted in, we know that our upper control them in here is going to be 6.57 and our lower control of it here is gonna be 4.27 So these are gonna be the control limits for our particular sample. So that is going to be the answer for this particular question here

All right. So for number four, we have our experts report five hours, 1.6, uh, and it's eight. So you're gonna need table 14.3. You go to sample size eight. That's gonna give you all things that need to plug in in order to get your our chart started. So the our chart requires you to get a UCO and an L CEO. And so how that will end up working is you do your are times D four, which is in your table and then our times d three. So are our is 1.6, and then you go toe the table, plug in it, look for eight and go across the D four. You should see 1.8641 point six times 1.64 is gonna be 2.98 and then you do 1.6 times 0.136 of getting the 0.136 at d three with end is eight. And so that's gonna get us 80.22 And so, since I Ennis 20 basically, you would have this go. Maybe by fives. So 5 10 15 20 eur R goes here and then you have your say three and zero. And I'm just getting a little bit above 0.22 Box it up and over to the three. Almost. That's the me too. 0.98 and ours right down the middle. All right, then we're asked to make the X chart, so that's gonna involve a U. C. L and L CEO Equalling the ex far. Plus, you're a to which is also in the chart time the are, and it'll be also minus ing the 82 times the are. So with that being said, you're gonna have 28.5 r x bar plus and minus are a three or a two offenders. A two is in the char e goto sample size and eight and that over to where the A two is, and you should see 20.373 It's gonna go in both spots times the are 1.6. So when it's all said and done, you should see 29.10 and you'll then see 27 point. So then you've got your sample size going from, uh, it happened 20 times, So you're gonna have all those results you got 5, 10 15. 20 You've got your ex is 28.5 year in the middle, and then right below and right above. We're going to have your box 27.1 29.1, okay?


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