# Overall Process Capability - Simple question if you know how to answer it!

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#### Brian Hunt

This is something that I last needed to do about 20 years ago but can't remember how to do now. It's part of a case study. Details as follows:

Process A mean is 3 hours, standard deviation is 0.25 hours
Process B mean is 4 hours, standard deviation is 0.25 hours
Process C mean is 5 hours, standard deviation is 0.01 hours
Process D mean is 14 hours, standard deviation is 2.00 hours

How do I calculate the overall process capability and deviation?

Last edited by a moderator:

#### Steve Prevette

##### Deming Disciple
Super Moderator
Re: Overall process capability - simple question - if you know how to answer it!

Do need to know a few details:

Do these processes exist in a series? That is you do Process A first, and then at the completion of A do B, then C, then D? If so, AND IF the processes are independent from each other the general answer would be the total average would be 3+4+5+14, with a standard deviation of sqrt(.25^2 + .25^2 + .01^2 + 2^2).

The answer would be different if there are dependencies between processes, or if the processes are not in series (parallel for example). You can always brute force your way through with a Monte Carlo simulation, especially if you know the distribuiton of the data, not just the mean and standard deviation.

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#### statdoug

Re: Overall process capability - simple question - if you know how to answer it!

I started to assume parallel processes, as in 4 similar machines putting out a standard product, but the obviously significant differences was a little befuddling. It didn't occur to me that it might be the outcome of 4 sequential processes. So in that case, we would be looking for the average time for a part to make it through the system, and the variation we could expect. The mean times in processes A to C would be significant, but the effects of their variances would be negligible (contributing a about 3% to the total variation.) Still, easy enough to do the math.

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#### Brian Hunt

Re: Overall process capability - simple question - if you know how to answer it!

Thanks Steve, Statdog. Yes, it is sequential set of processes e.g. as in manufacturing. I understand it now

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