# Modified Control Limits - Process that has points out of control

D

#### DJN

I have a process that has points out of control. However,the CP figure is 2.29, which I believe is a six sigma process. I understand that modified control limits may be applied in this instance, but have been unable to find any information on the subject. Can anyone help on this subject?

David

D

#### Darius

DJN said:
I have a process that has points out of control. However,the CP figure is 2.29, which I believe is a six sigma process. I understand that modified control limits may be applied in this instance, but have been unable to find any information on the subject. Can anyone help on this subject?

David

Es far as I know, the calculus of Capability or Performance Index have nothing to do with the calculation of Control Limits.

Most of statiscians say that you shouldn´t calculate Cp when is out of control, and some recommend to use performance index in that case (Pp, Ppk).

I tink as I read in some posts "One size doesn´t fit all", that some patterns doesn't apply to some process, if the process is a continuos ones, it's obvious that runs will appear, don't use out of control rules without tinking if they must apply or not.

If you are using IX (individual ond moving range), The autocorrelation could be a problem, I tink the control limits affected by an autocorrelation factor are called "modified control limits ", Don Wheeler show this on "Advanced Topics in Statistical Process Control".

****************

Sorry, I want to add something, I readed, Modified Control Charts use

Upper Spec - 3 Sigma(X) + 3 Sigma (X_average)
Lower Spec - 3 Sigma(X) + 3 Sigma (X_average)

The try to fuzze the spec limits to obtain action limits, the fuzzed limits are called Reject Control Limits. It is thought that as long as the subgroup averages are within these limits the process will be producing conforming product.

:thedeal:

#### Attachments

• spc_detection_rules.pdf
259.2 KB · Views: 913
Last edited by a moderator:
D

#### DJN

Darius said:
Es far as I know, the calculus of Capability or Performance Index have nothing to do with the calculation of Control Limits.

Most of statiscians say that you shouldn´t calculate Cp when is out of control, and some recommend to use performance index in that case (Pp, Ppk).

I tink as I read in some posts "One size doesn´t fit all", that some patterns doesn't apply to some process, if the process is a continuos ones, it's obvious that runs will appear, don't use out of control rules without tinking if they must apply or not.

If you are using IX (individual ond moving range), The autocorrelation could be a problem, I tink the control limits affected by an autocorrelation factor are called "modified control limits ", Don Wheeler show this on "Advanced Topics in Statistical Process Control".

****************
Thanks Darius.
Sorry, I want to add something, I readed, Modified Control Charts use

Upper Spec - 3 Sigma(X) + 3 Sigma (X_average)
Lower Spec - 3 Sigma(X) + 3 Sigma (X_average)

The try to fuzze the spec limits to obtain action limits, the fuzzed limits are called Reject Control Limits. It is thought that as long as the subgroup averages are within these limits the process will be producing conforming product.

:thedeal:

Thanks for replying Darius. I realise that CP has nothing to do with control limits, it is just that the variability of the process is much smaller than the spread in the specification limits. The LSL is 10 and the USL is 10.2 but the sigma is 0.01 The distance is 20 sigma which is much greater than the 6 sigma natural tolerance, which in turn is a six sigma process. I am sure you are right about using the 3 sigma value. Many thanks Darius
David

A

#### Atul Khandekar

David,

Modified Xbar control charts are used in case of highly capable processes, where the process average can be "allowed" to vary within a certain range without affecting the quality. You want the chart to detect ONLY when the mean shifts to a position where the process produces a certain fraction nonconforming.

To quote Douglas Montgomery (Introduction to Statistical Quality Control):
The modified XBar control chart is concerned only with detecting whether the true process mean is located such that the process is producing a fraction nonconforming in excess of some specified value "delta".

The Lower limit up to which process mean can vary= LSL + (Zd*sigma)
The Upper limit up to which process mean can vary= USL - (Zd*sigma)

where Zd is the upper Z value where delta nonconforming would be produced and sigma=process std dev

The control limits are calculated as:

LCL = LSL + [Zd - (3/sqrt)]*sigma
UCL = USL - [Zd - (3/sqrt)]*sigma

I would recommend you refer to Douglas Montgomery's book for detailed explaination.

Also take a look at these PPT demos:

https://www47.homepage.villanova.edu/joseph.pigeon/pp_files/chap09.ppt

Hope this helps.

-Atul.

L

#### lday38

Calculatign control limits

I have been using modified control limits with a sample of 5. To make it safer and easier to calculate, I am taking 4 std dev from the usl and adding 4 std
to LSL. The r chart reflectrrs normal limits
I now need to change to a sample size of 2 pcs and use the data more for process control. I am having a discussion with my boss that to calculate the inital control limits , you must eliminate the out of control points. He wants to see that in writign. Perhpas, I should have siad you cant calculate the control limits unless the process is in control and variation is removed.
He would liek to see that in print. Anyone have a recognized source they could recomend for me and my boss. The toolmakers will have a fit if they were to try and hold normal control limits, they say I am taking away there spec.

R

#### Rob Nix

I can see Steve P's heart rate going up already, but I'll jump in ahead of him.

1. I have some concern or question about your use of "modified" control limits that seem to be attached to spec. limits. Control limits are independent of any specification. I'm not a fan of ANY use of "modifiers" anyway. Can you explain how and why you are using that method?

2. Changing the sample size from 5 to 2 just means a change in the constant; but why do you say that change 'uses the data more for process control'?

3. Many, many publications on quality and SPC clearly state that for a process to be capable, it must first be in a state of statistical control. I'll look something up for you.

AIAG's SPC Manual, page 13 says "the process must first be brought into statistical control... then its performance is predictable, and its capability... can be assessed".

4. Tool makers should have NO PROBLEM with whatever legitimate control chart scheme (i.e. sample size, intervals) you use since, if in control, simply reflects their normal activity. In other words, they don't "hold normal control limits", the limits conform to THEIR process.

Last edited by a moderator:
L

#### lday38

explanation

I understand your concern and may even agree with it in some cases. Let me explain. Process capability has been proven -both CP and CPk is way over. These parts have a minimum of .008 up to .012 tolerance. The customer's requirement is CPK of 1.33 and they donot want parts out of spec. Consistency from lot to lot is not the objective to date. The raw material is a tolerance of .0035 to .004. These machines have both warm up and tool wear. I am just trying to use spc to prevent parts from going out of tolerance, maintain a Ppk of 1.33 on lots going out. If you do a search on economic control limtis or modified limits-this topic is covered.

G

#### Graeme

Rob Nix said:
AIAG's SPC Manual, page 13 says "the process must first be brought into statistical control... then its performance is predictable, and its capability... can be assessed".
Which is also approximately what Shewhart said in 1928 or so ...

When a process is in a state of statistical control, that simply means that only random variation is present -- all identifiable systematic variations have been eliminated or corrected for. The description of the natural state of the process as shown on the control chart does not have any relationship at all to the product specifications.
• The product specifications describe what the designer would like to have.
• The process control chart describes what the process is actually doing.
In addition, the most common sample size is 5, although 3 is sometimes used as well. A sample of 2 is rarely used because the Student's t distribution value for that sample size (1 degree of freedom) is so huge as to make it just about useless in most applications. For example, for a 2-tail 95% probability, t for a sample of 2 is 12.706; it is 4.303 for a sample of 3 and 2.776 for a sample of 5.

#### Steve Prevette

##### Deming Disciple
Super Moderator
Rob Nix said:
I can see Steve P's heart rate going up already, but I'll jump in ahead of him.

Good post by Rob.

In Dr. Wheeler's words, there is the voice of the customer (USL/LSL) and then there is the voice of the process (UCL/LCL about the average).

If you start confusing the two, you end up with the Funnel Experiment.

Good luck.

#### bobdoering

Trusted Information Resource
It sounds like the OP is trying to control machining processes with traditional X-bar -R controls. The problem is they do not apply to machining - it yields a non-normal distribution. Its control limits ARE related to the specifications!

For more details, see:

Statistical process control for precision machining

As far as the tool makers having their "specs" taken away from them, they never had those specs to begin with. The only way they would have the total design specification (print spec) as their process specifications is if:

1. No sampling error (100% inspection of their dimensions)
2. No gage or measurement error

No chance, huh?