Why is Cpk = lower of (USL-Xbar)/3sig & (Xbar-LSL)/3sig ?

K

krishna_sadas

#1
We are considering Cpk=(USL-Xbar)/3sig , CpK=(Xbar-LSL) which one is the lower value in our SPC study,

What is the reason for choosing the lower value?

Pl. help me
 
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Manix

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#2
Re: cpk

We are considering Cpk=(USL-Xbar)/3sig , CpK=(Xbar-LSL) which one is the lower value in our SPC study,

What is the reason for choosing the lower value?

Pl. help me
You choose the lower value because this is the actual capability of your process. Depending on where your process is centered you may not be able to fit 3 std deviations between the Xbar and and the lower spec limit which would result in non-conformance and hence your process is not capable. Visa versa, you may not be able to fit 3 std deviations between the Xbar and USL and again, this means the process is in capable. You need to be able to fit 3SDs with room to spare between your USL and LSL in order for the actual process capability (Cpk) to be high enough to have confidence.
 

antoine.dias

Quite Involved in Discussions
#3
In fact, the lower of the two gives an indication of the highest risk of producing parts outside of tolerance.

Best regards,

Antoine
 

Stijloor

Staff member
Super Moderator
#4
We are considering Cpk=(USL-Xbar)/3sig , CpK=(Xbar-LSL) which one is the lower value in our SPC study,

What is the reason for choosing the lower value?

Pl. help me
A picture is worth a thousand words.

Look at this simulation Cp & Cpk that Marc (the owner of this site) put on the very bottom of this page.

Stijloor.
 
D

Darius

#5
Why?:confused:

Simple....., just because where the cpk is lower, you are farther from the middle of the spec limits (that could be your target), desto easer to have non conforming parts.:D

In such indicator, there is no pretention to measure, but to penalty your process capability (Cp) for such behabiur.:whip:
 

Bev D

Heretical Statistician
Staff member
Super Moderator
#6
you know I have the same question as the OP. (perhaps for a different reason)

Why take just the lower value? what if you have parts out of spec both high and low? are the defects that are less frequently out of spec not of any importance? won't they feel left out?

what if there are 2 machines making the same parts: both have the same Ppk value for the high end of the spec (.5) but one has a very good Ppk value (>2) for the low end of the spec and the other machine has a poor Ppk (.9) for the low end of the spec. How do we judge these two machines? They certainly aren't equal...
 
D

Darius

#7
what if you have parts out of spec both high and low?
Parts out of Lower and Upper specs affect to the stdev, desto to Cp, not to the penalty of cpk calculations (both cpk formaulae have 3*stdev).

Are the defects that are less frequently out of spec not of any importance? won't they feel left out?
If it is the case your specs are wrong.

what if there are 2 machines making the same parts: both have the same Ppk value for the high end of the spec (.5) but one has a very good Ppk value (>2) for the low end of the spec and the other machine has a poor Ppk (.9) for the low end of the spec. How do we judge these two machines? They certainly aren't equal...
It's true that cpk is affected by two events; one is less variation, the other is the process position. This makes possible to happen this scenario. I take better cpmk (to penalty because of not centering your process to it's target).

Even going into the same direction, some guys say that it's better to chart the process than rely on the index (ie. boxplot or run charts), but is a standard, most of the companies expect a cpk..... And as I readed somewhere "If you don't measure you can't manage".
 

Bev D

Heretical Statistician
Staff member
Super Moderator
#8
Darius - first I don't think my sarcasm came thru in translation.
of less importance is the fact that just because customers ask for Cpk/Ppk doesn't mean they are right.

and I do believe that you can't manage without measuring but poor measurements only lead to poorer decisions. I've stated my distaste for trying to reduce the beautiful complexity of variation to a single number in previous posts. Manager's who can't interpret simple charts like run charts, multi-vari charts and control charts need to be taught as do our customers. WE need to be intellectual leaders, not lemmings who follow the priests of simplistic off the cliff.
 

Caster

An Early Cover
Trusted Information Resource
#9
you know I have the same question as the OP. (perhaps for a different reason)

Why take just the lower value? what if you have parts out of spec both high and low? are the defects that are less frequently out of spec not of any importance? won't they feel left out?

what if there are 2 machines making the same parts: both have the same Ppk value for the high end of the spec (.5) but one has a very good Ppk value (>2) for the low end of the spec and the other machine has a poor Ppk (.9) for the low end of the spec. How do we judge these two machines? They certainly aren't equal...


Hi Bev D

Your questions seem designed to provoke a response, so if I was your customer I'd be "unhappy"

For parts out of spec I hope you are sorting (not shipping me the OOS) and working hard to get in spec or negotiating with me the customer to open up the spec?

For two machines it comes down to the overall out the door capability, and it will be pretty bad when you combine two processes, one targeted and high and the other targeted low.

The customer gets all these parts, so again I hope you are working to target both machines, or get customer relief on the spec....

All this assumes the customer even knows anything about capability and that they have actually put tolerances on the print that make sense.

Sometimes customers just copy old prints without understanding. It is always good to talk to them to understand.
 

Caster

An Early Cover
Trusted Information Resource
#10
What is the reason for choosing the lower value? Pl. help me
I was taught the "truck and tunnel" approach to SPC

Your process is the truck, and it is not in the center of the road

Steer your truck (process) back to the center line for a safer trip through the tunnel

People seem to get this example easily

The center line of the road is the target, the rumble strips are your control limits, and the tunnel walls are the customer specs

The truck is your process, I'd rather drive a normal truck through a tunnel than a wide load

Good luck
 
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