Tip:
Highlight text to annotate it
X
Minitab is the leading global provider of
software and services for quality improvement
and statistics education.
Quality. Analysis. Results.
For more information visit Minitab.com
This podcast is available at KeithBower.com
Hello, today I'm going to talk about the capability index Ppk, and its relationship with Cpk.
Now I recommend that you check out the Podcast: "What is Cpk?" first.
Let's give a quick overview of what Cpk is...
It takes into account where the distribution is centered,
and the value for Cpk is the minimum value of the
upper spec limit minus the mean, divided by 3 standard deviations
and the mean minus the lower specification limit, again divided by 3 deviations.
So what's the difference between Cpk and Ppk?
It's the denominator. It's exactly the same formula [for Ppk] as for Cpk,
but that standard deviation that's being used in the denominator, for Ppk, is...
well, people sometimes give it different terms, they sometimes call it the
"overall" level of variation, or sometimes the "long-term" variation.
So lets distinguish between the two ["long term" vs. "short term"].
With Cp and Cpk, that estimate of variation (that standard deviation that we use)
is supposed to come from common causes of variation.
In other words, the amount of variation that is inherent to the system itself.
So if you think of control chart limits, when we go plus/minus 3 standard deviations,
that's the standard deviation that we're employing,
and we use the same mathematical computation.
What sometimes people want to do is consider how capable a process is going to be even when it is unstable.
So what they'll do is, maybe they will take a very long period of time
and just use this "overall" standard deviation - the "big old" standard deviation [S],
instead of using, let's say, the average moving range to come up with this common cause variation estimate.
Of course, if you're process is stable, then the amount of variation within the subgroup
and the overall variation is going to be pretty much exactly the same,
because your between-subgroup variation is going to be very small.
So, of course, if your process is stable then (Cp and Pp); (Cpk and Ppk),
will be very close to each other so this is a moot point [in that situation].
If , however, your process is unstable, and you do use this overall estimate of variation
then the two values could be markedly different.
Pp and Ppk are highly controversial because we are assuming that we can estimate the capability of a process when it is unstable.
Many people out there (including myself) would argue that Pp and Ppk are disingenuous estimates
of capability, and this goes to the very core of how we can use applied statistics in my opinion.
Think of what W. Edwards Deming once said: a process only has measurable capability if it is in statistical control.
I agree with that. So if we are trying to put our hand on our heart and say we know what a process is going to give us
because we've looked at periods of time when it's unstable as well [as stable]...
we can't make that argument. I think it's an invalid estimate of variation.
I know there are people out there who would disagree with that, but I think we should only be reporting estimates
of means and standard deviations if we really have a good handle as to what these estimates truly are.
For more information on this topic I strongly recommend you to go onto my website, and I'll point you to
some articles where certain experts go into much more detail on this and really give you the warning signals.
So I hope this has been helpful. Of course, if you have any questions on this or anything else,
please feel free to email them to me through my website, KeithBower.com
For more information on statistical methods for quality improvement
visit KeithBower.com