How to Calculate UCL (Upper Control Limits) and LCL (Lower Control Limits)

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K

KCIPOH

#13
I agree, but you have to start somewhere. If you have been tasked with charting a process, you often need to get on with it since your boss is not always willing to wait for you to gain the necessary knowledge to be an expert. I would hope that then that individual would recognize that their needs goes beyond the mechanics and must extend to the level of understanding. That understanding is not going to be found in this forum, as statistics need some fairly extensive study and training however we can help folks by giving folks a taste of what the statistics can tell them. :agree1:
Hello iamtroll,

Thanks for your helping explanation and you are right, as the first thing i ask these question is because i dont have any idea of how to calculate it and just want, in the first place to know how to calculate it first, because by knowing how to calculate it, then only i can get an idea of it, after that only i get my self deeper into the statistics of it, without knowing how to calculate, it wont get me further.

I believe many cove members, especially beginner in the statistics, would like to get their calculations solve in the first place before want to go further into what, how, when etc the data is use for as for beginner like me, they are not understand up to that extent yet and therefore wish their calculations to be solve in the first place and need expert cove members to do a favor on this.

After solve the calculations, i think they will see the picture and continue to come up with questions to go further.

No hard meaning, Thanks everyone :)
 
K

KCIPOH

#14
Sorry for deleting the previous response, I attached a file for powerpoint 2007 and saw that the file posted was on a previous version, so it can be seen, change it to 2003.
Hello Darius and Bev D,

Thanks for showing the details of the calculations. For your information, i just want to know how to calculate the UCL and LCL for data in a subgroup and come across a website showing how to do it but i dont understand how they calculate the Std Dev for this case of data. http://www.wikihow.com/Create-a-Control-Chart

Another thing is why they are using different calculations than yours (i mean they are not doing the Xbar-R chart for this data) but instead only calculating the Std Dev, Xbar bar and straight getting the answer for UCL and LCL with the formula below :

UCL = CL + 3*S
LCL = CL – 3*S

Can you show me how to do the calculations for the Std Dev (are they using Population Std Dev (N) or Sample Std Dev (N-1)) as in the link and why they use this approach instead of yours (Xbar-R charts)? i'm really getting myself more confuse in statistics :confused:
 
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D

Darius

#15
Another thing is why they are using different calculations than yours (i mean they are not doing the Xbar-R chart for this data) but instead only calculating the Std Dev, Xbar bar and straight getting the answer for UCL and LCL with the formula below :
UCL = CL + 3*S
LCL = CL – 3*S
Well the formulas are just the same, but the question here is: What does "S" stand for?

If we say: UCL = CL + Average_Range * A2

So
3S = Average_Range * A2
S= Average_Range* A2/3
S= Average_Range *(3/Sample_Size^0.5/d2)/3

reordering and simplifying:

S= Average_Range /Sample_Size^0.5/d2

being: ds_Within_Sample= Average_Range /Sample_Size^0.5/d2
UCL = CL + 3*ds_Within_Sample
LCL = CL – 3*ds_Within_Sample

There are diferent kind of estimates for different statistical calculus, but SPC uses ds_Within_Sample wich is the variation inside the subgroup

Theorically: ds_Total = ds_Within + ds_between

There are also other kind of charts like "Average and s", but it's another story, they are used for sample sizes >10:lol:, and a big NO, they SHOULDN'T using Population Std Dev (N) or Sample Std Dev (N-1), don't believe all that can you seen on the NET, that site is cute, nice displays but WRONG.

One question that arrived to me is: ¿why 4 as sample size?, remember that samples are rational subgroups, not just to use a nice number but by a reason.

ACLARATION TO THE SITE'S CALCULATION:

http://www.wikihow.com/Create-a-Control-Chart

Is wrong in many ways, first the variation estimate, :lmao::lmao::lmao:, it's the stdev of all data (without subgrouping):lol::lol::lol:

Second, the use of colors to make SPC look like a precontrol chart

Third, the use of rules to determine patterns without advice that most of them not always apply, depend on the process and variable behaviour.

But al least, they try to show how and it's a nice looking site.
 
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bobdoering

Stop X-bar/R Madness!!
Trusted Information Resource
#16
Second, the use of colors to make SPC look like a precontrol chart

Third, the use of rules to determine patterns without advice that most of them not always apply, depend on the process and variable behaviour.

But al least, they try to show how and it's a nice looking site.
Wow...they really dwell on trends. That is a great way to train operators to overcontrol.
 

Bev D

Heretical Statistician
Staff member
Super Moderator
#17
yes that site is rife with errors.

As Darius said - you should NEVER use the direct calculation of either the SD for the individual values or the SD of the subgroup average.

If you really want to understand SPC don't use the internet for your research, get yourself a copy of Donalald Wheeler's book, "Understanding Statistical Process Control", on SPC and read it. An alternative to Wheeler is the book "Statistical Quality Control" by Grant and Leavenworth.
 

bobdoering

Stop X-bar/R Madness!!
Trusted Information Resource
#18
Thanks for your helping explanation and you are right, as the first thing i ask these question is because i don't have any idea of how to calculate it and just want, in the first place to know how to calculate it first, because by knowing how to calculate it, then only i can get an idea of it, after that only i get my self deeper into the statistics of it, without knowing how to calculate, it wont get me further.
We absolutely encourage you to understand the statistics and their associated calculations. You are to be commended for being motivated to look that deep into the process and your courage to join us for help.

I believe many cove members, especially beginner in the statistics, would like to get their calculations solve in the first place before want to go further into what, how, when etc the data is use for as for beginner like me, they are not understand up to that extent yet and therefore wish their calculations to be solve in the first place and need expert cove members to do a favor on this.
That is understandable, but we are trying to help you understand the entire process. To chart and calculate control limits is not the starting place, but closer to the middle point. To make the effort effective, there is up front work that should be done. Check this out to help understand these steps.

So, if we seem like we are being critical, we are only trying to do our best to be helpful and help you avoid the mistakes that plague many SPC implementations. Please don't mistake our passion for the topic for being critical. We want people to succeed! Also, as you can tell, unlike some web sites, this forum is truly peer reviewed! (Not hand "hand-picked" journal peers, either, real peers!) Luckily, as you can tell, we have many experienced people here to help.
 
K

KCIPOH

#19
Hello Darius, Bob and Bev,

Thanks for alert me at this point, i'm sorry if offended you guys in my sentence as my English are quite poor :( i think i really need to get myself the book of SPC to understand it from scratch first. You all have been helpful to me.

Thank you all and will post again soon for SPC related doubt :)

HAPPY NEW YEAR 2012
 
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