# Process Z

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• #37699

redo
Participant

See I am trying to calculate the capability of a process and Minitab spits out a Process Z value (after a Binomial Capability Analysis) that now I have to explain.  What is it in the scheme of things, and what value is good/bad.
Thank you!

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#111462

mjones
Participant

The Process Z that Mtb is giving you is the equivalent to the Std Normal Z for the given per cent defective from your process.
Example: If your Binomial Capability Analysis gives you an avg p = 0.03 = 3%, the Process Z = 1.8808. In other words, if you assume the proportion defective = 3% is a valid value (and your review of the Binom Cap Analysis tells you this), your process is equivalent to a “1.88 Sigma”
[Or, if it is your custom, call this “long term data” and add the 1.5 sigma for shift and drift so you have a 3.38 Sigma Process to be equivalent to the ‘short term’ data from other processes. PLEASE NOTE: I mention this as it is an approach used by some organizations — not necessarily one I suggest.]
What value is good/bad? If you have a very high Process Z (hence, high Process Sigma), you may be in great shape — or you may not… It all depends on what your customer is happy with, and what else is happening in your process, competition, number of steps in your process, risk/cost factors, etc., etc…
I’d be happy with a Z = 3 for loss of checked luggage with an airline, but I’d want a Z = 7+ for likelihood of dying during a flight.

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#111464

Tim F
Member

Did you try Minitab help?Process Z
Process Z is computed by finding the Z-value using standard normal distribution for Average P. The larger the process Z, the better the process performance.Average P
“Best guess” of the proportion of items in your process that are defective, assuming you have collected enough samples to have a stable estimate.Does that help? Tim F

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#111477

redo
Participant

This is a fab forum.
I dug up an old forum that discussed Process Z value and translated it to a Equivalent Cpk.
Equivalent Cpk = (equivalent Z Value + 1.5 sigma shift) / 3
example: I have a plastic injection molding process hat has returned a z value of 2.14 for a pass fail study for short shots with two hour sample size of 60 pieces.  (2.14 +1.5) / 3 =1.21 Cpk not too bad for who its for.
(I understand Stan LOVES the 1.5 sigma shift, ask him about it.)

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#111480

Mikel
Member

The good news is that z > 3 for baggage handling and has been for decades.
The bad news is z < 7 for liklihood of dying during a flight and has been for decades.
There is data on both that has been available since at least the 80’s and nothing significant has happened to impact either under Six Sigma.

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