Calculating Control Limit for an S Chart (CQE sample question)

R

RACHJAIS

Hello,

I am not too familiar with how to post a question in this forum but i have a cqe exam on this coming saturday and i am desperately looking for a solution to the following problem. Can anyone help me out? May be even post this question at the right place???

Compute the upper control limit for an s chart, based on a sample size of 10, if the process is in control with a mean of 40 and a sample standard deviation of 7.​
A. 11.7 B. 13.3 C. 15.7 D. 21

Answer is A ... but i dont know how do u calculate it??

Thanks,

howste

Thaumaturge
Super Moderator
Re: Help needed calculating control limit (CQE sample question)

Welcome to the Cove Forums! I moved your post to it's own thread so it will get the attention it needs.

I'm just heading to bed now or I'd help with this. If someone hasn't answered by morning I can jump in to help.

howste

Thaumaturge
Super Moderator
I can see why you're confused. Is that the whole question? It seems like there's information missing. In order to calculate the S Chart UCL, you need the average standard deviation, not just the sample standard deviation. The formula for the S chart UCL is B4(s-bar)

B4 is a constant, usually looked up in a table. Here's a table of constants for an S chart:

Code:
`````` n A3    B3    B4
2 2.659 0     3.267
3 1.954 0     2.568
4 1.628 0     2.266
5 1.427 0     2.089
6 1.287 0.030 1.970
7 1.182 0.118 1.882
8 1.099 0.185 1.815
9 1.032 0.239 1.761
10 0.975 0.284 1.716
11 0.927 0.321 1.679
12 0.886 0.354 1.646
13 0.850 0.382 1.618
14 0.817 0.406 1.594
15 0.789 0.428 1.572
16 0.763 0.448 1.552
17 0.739 0.466 1.534
18 0.718 0.482 1.518
19 0.698 0.497 1.503
20 0.680 0.510 1.490
21 0.663 0.523 1.477
22 0.647 0.534 1.466
23 0.633 0.545 1.455
24 0.619 0.555 1.455
25 0.606 0.565 1.435``````
If you use the standard deviation given (7) you would end up with 7*1.716 = 12.012. Working backwards from the answer (11.7), it looks like the average s would be 6.8, but it's not given.

Maybe someone else can correct me if I missed something...

Jim Wynne

Super Moderator
Hello,

I am not too familiar with how to post a question in this forum but i have a cqe exam on this coming saturday and i am desperately looking for a solution to the following problem. Can anyone help me out? May be even post this question at the right place???

Compute the upper control limit for an s chart, based on a sample size of 10, if the process is in control with a mean of 40 and a sample standard deviation of 7.

A. 11.7 B. 13.3 C. 15.7 D. 21

Answer is A ... but i dont know how do u calculate it??

Thanks,
Have a look at the NIST/Sematech Handbook of Engineering Statistics. The formulae are there.

Statistical Steven

Statistician
Staff member
Super Moderator
Hello,

I am not too familiar with how to post a question in this forum but i have a cqe exam on this coming saturday and i am desperately looking for a solution to the following problem. Can anyone help me out? May be even post this question at the right place???

Compute the upper control limit for an s chart, based on a sample size of 10, if the process is in control with a mean of 40 and a sample standard deviation of 7.​
A. 11.7 B. 13.3 C. 15.7 D. 21

Answer is A ... but i dont know how do u calculate it??

Thanks,
It is clear that the question you have has been pulled from the exam. It is poorly written and well pretty hard to follow. The formula for the UCL of an s-chart when the standard deviation is known is B6*S-bar. B6 for n=10 is 1.669 so 1.669*7 is 11.7

howste

Thaumaturge
Super Moderator
It is clear that the question you have has been pulled from the exam. It is poorly written and well pretty hard to follow. The formula for the UCL of an s-chart when the standard deviation is known is B6*S-bar. B6 for n=10 is 1.669 so 1.669*7 is 11.7
You're absolutely right. The question should state the population standard deviation, not the sample standard deviation.

Here's a table for B5 and B6 values:
Code:
`````` n  B5     B6
2 0     2.606
3 0     2.276
4 0     2.088
5 0     1.964
6 0.029 1.874
7 0.113 1.806
8 0.179 1.751
9 0.232 1.707
10 0.276 1.669``````

R

RACHJAIS

Oh... I did not know we should be looking at B6 value instead of B4... so the catch was if its the population standard deviation.....we have to multiply the SD*B6.....

Thanks for ur help!

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