# Question on Xbar R chart control limits

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• #52147

LVL
Participant

I have what maybe is a basic question about control limit formulas.
I am in the automotive industry, and would like to know if it is acceptable to use the formulas of sigma, UCL and LCL together with the target cpk to derive a theoretical UCL (for Xbar and R) and LCL (for Xbar) which will satisfy the cpk requirement. So if all the points on the xbar and R charts are inside these limits (assuming there are no special causes in the graph), the cpk would meet the customer requirement.
I have not seen anything on the net about this being done, and am curious if this is logically sound.
Please advise, thank you.

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#183031

Severino
Participant

Based on the fact that you asked this question in the first place, your answer is no.  Don’t try and reinvent the wheel.  Collect data and plot the normal +/- 3 sigma limits and establish whether your process is in control.  Once it is in control, then you can worry about capability and adjusting your average or variation to meet your customers requirements.
If you try and set limits based on specifications (which is what you would be doing if you calculated anything off of cpk) you will likely have a whole bunch of points which plot outside the arbitrary limits you set and no idea whether it is likely they are due to common cause or special cause variation.  You will then run around like a chicken with your head cut off trying to crowbar the process which you have gained no knowledge of due to your arbitrary limits into these two lines on your chart and you will fail miserably.
The whole purpose of setting the UCL and LCL as is normally done is to allow you to gain a true understanding of your process.  If you try and cheat the system you will only cheat yourself.

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#183035

LVL
Participant

Thank you Jsev, that clarified the main function of the Xbar R chart for me. I’m off to collect data now.

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#183037

Gary Cone
Participant

Jsev607 is a smart guy and he is giving you good advice on the proper
use of control charts, but the answer to your question is yes. You can
know in advance what your target (X-bar) and your UCL and LCL
should be to achieve a specific capability. I have done this often when
starting a new process.I will write a simple example and post it this morning.

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#183042

Gary Cone
Participant

Lets take a very simple example.I have a specification of 10 +/- 2 units.I have a customer imposed capability requirement of Cp > 2 and
Cpk > 1.67. 2 and
Cpk > 1.67. 2 and
Cpk > 1.67. 1.67. 1.67.Ive done all the proper front-end work of qualifying my process
and my measurement system. I have also chosen my equipment
wisely to, at least in theory, be capable. I have also taught my
people SMED and practices to assure I start my process on target
instead of just to spec.Part of qualifying the process included a tool which we know
historically contributes to >90% of the mean of this critical spec
and found the mean to be 9.7 when using known best practices for
this type process. The tool is expensive to modify and it has been
decided to accept the tool as is.90% of the mean of this critical spec
and found the mean to be 9.7 when using known best practices for
this type process. The tool is expensive to modify and it has been
decided to accept the tool as is.90% of the mean of this critical spec
and found the mean to be 9.7 when using known best practices for
this type process. The tool is expensive to modify and it has been
decided to accept the tool as is.With that I know exactly what my control chart needs to look like to
be able to achieve the capability demanded by the customer.A Cp of 2 says my Standard Deviation cant be bigger than 0.33.
Knowing that my mean is offset from nominal by 0.3 demands less
of my standard deviation to achieve the Cpk 
I am 1.7 from the nearest spec, which demands a standard
deviation of 0.34.Assume I will do SPC with subgroup sizes of 4 (I just choose 4 for
the ease of computations), I can set up a chart with X-bar of 9.7
(known from the tool qualification) and UCL of 10.2 and LCL of 9.2.
The Range chart will be set up with R-bar of 0.68 with a UCL of
1.55. This represents what I know about where I know the process will
be targeted based on tool qualification and what I need to see to
achieve capability.The advantage of this approach is traditional wisdom says start SPC
with 25  30 subgroups and then compute mean and control limits.
If your process starts with an issue, would you rather know soon or
after 25  30 subgroups? I have been doing this since 1988 and
been able to address potential issues within the first hour of
running vs doing an analysis several days later.This approach should be taught as part of any DFSS curriculum.

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#183043

Gary Cone
Participant

Sorry about the repeated stuff following greater than signs.Must be something with coding of the messages.

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#183063

MBBinWI
Participant

Gary:  You’re absolutely right that this should be part of DfSS curriculum.  And if the dimension is coming from existing machinery, some historical data should be available to compare with to see if you are going to be able to get close.
Also, during the development, the factors should be evaluated for sensitivity to variation.  Factors should be desensitized to variation, and any that cannot be reduced sufficiently should be prioritized for process variation data gathering/monitoring.

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#183067

Severino
Participant

I’d prefer to see the op go through the learning experience of the traditional approach until they had enough knowledge from application of spc and capability studies to answer this question for themselves.  I guess you could say I’m conservative… at least as far as quality goes.

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#183071

LVL
Participant

Thank you all for your inputs. Gary’s example is what I was referring to, but I agree with Jsev607 that the operator should know the basics as far as reading the charts.
Actually what I have resolved is to begin the charts by placing the ‘theoretical’ limits, but then still go and analyze the data after collection and treat it separately from the limits. I just want the limits to serve as guidelines for the operator to take action even before the performance reaches near the plant tolerances. And for continuous improvement, maybe even use the calclulated limits (as the new guide) if process control is better than the customer requirement.

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#183077

Fontanilla
Participant

Jsev607, Gary’s right.  You can set up the limits in advance.  I’ve done it too, and it does show you very quickly if you have a shot at success, or need to stop and revise things, before you make a bunch of scrap.  It works.  Calculate based on your customer requirements, your known process performance (or bench marked performance if a new process), and set your reaction plan based on the limits you derive.  When the first point falls outside of the limits, better start to pay close attention.
You’re right too.  You need to look at the chart of the data and look for special cause indicators in the shape of the histograms, run charts, etc.  The theoretical limits are a starting point for you to quickly know if you have a problem, but they don’t substitute for the true limits created by the process itself.
Good work guys!

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#183078

Gary Cone
Participant

Just remember, it’s not just the operator.It’s the supervisor, it’s the planner, it’s the support engineers, …They do more damage to an SPC program than any operator I’ve ever
met.

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#183079

Gary Cone
Participant

I agree except if we wait for the knowledge to be ingrained it will
never be done.We have been waiting since at least the 1930’s.If the operation took the use of charts seriously, there would be no
problem with the operator. This includes limited and judicious use of
charts.

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#183179

Ravnold
Participant

Dear LVL,
while others have already told you how to proceed, I would like to tell you something different. Try doing this along with the conventional tools.
Use of Pre control charts.
The advantage is that it is very simple. But the major disadvantage is that it is not statistically supported.
Step 1: Multiply the tolerance value (USL-LSL) with 0.25.
Step 2: Substract the resulting value from the USL to get the Upper Pre Control limit. and add it to LSL to get the Lower Pre control Limit.
Step 3: If the first part is outside the limits adjust the process. If it is inside measure the next part. if two are out, adjust the process, if five sucessive points are inside, then you can switch to less frequent measuring.
Caution: Friend pls do this with the conventional method what Gary and other friends have told you, once you gain confidence then you can consider using this.
Regards

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#183241

LVL
Participant

Thank you for this tip, as a starting point it does seem practical.. Actually, what I did was to use the Cpk requirement of 1.33 to get the required Zmin, and then work my way back to a formula of UCL for Xbar and R, as well as LCL for Xbar which is a function of the upper or lower spec limits. Using the constants for my sample size, I did arrive at a simple equation. I will try this out and see what my results look like.

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#183242

Cone
Participant

Ravold,Could you clarify the steps, they don’t make sense.

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