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

R

RACHJAIS

#1
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??

Please help!
Thanks,
 

howste

Thaumaturge
Super Moderator
#2
Re: Help needed calculating control limit (CQE sample question)

Welcome to the Cove Forums! :bigwave:

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
#4
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. :confused:


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
#5
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??

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

Statistical Steven

Statistician
Staff member
Super Moderator
#6
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??

Please help!
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
#7
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

#8
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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