Hi all,

I am currently using Cp and Cpk in our process, im just wondering what the definitions of CPU and CPL are and what they can be used for and how it can be efficient to use them? i've tried searching but all i get is central processing unit which is not what i want in this case :).

Thanks for your time everyone.:thanx:
Omeil

I am not aware of a specific definition, only the equations. Cpl and Cpu are only intermediary calculations for Cpk as shown below.

Cpl = (Mean - LSL) /3s
Cpu = (USL - mean) /3s

Cpk = Minimum (Cpl, Cpu)

You can easily calculate Cpk without either Cpl or Cpu as follows:

Cpk = |Mean - nearest spec limit| /3s; where | | means absolute value.

Thanks for the equations miner i was able to calculate the Cpu and Cpl accurately, a manager was asking me for information on the subject your equations was perfect oh and i also found a website which leads to a list of SPC definitions but i can't post the link due to me only have 4 posts. but i will post it once i have a higher count.
:thanx:

Here's the link to the website with SPC definitions:

http://www.quality-control-plan.com/spc-definitions.htm

If you would like to understand the definitions of CPU and CPL you have first understand the difference between Cp and CPK (min {CPU, CPL), where Cp is a capability index, it compares the process capability to the max allowed variation as indicated by the tolerance. This index provides a measure of how well the process will satisfy the variability requirements, Cp is calculated by
Cp = {(USL-LSL)/6 σ}
While Cpk is a capablity index, it takes the process location as well as the capabiltiy into account. For bilateral tolerances Cpk is always be less than or equal Cp.
Cpk well be equal to Cp only if the process is centered
Cpk is calculated as the minimum of CPU or CPL where:
CPU= (USL - mean)/3σ
CPL= (mean - LSL)/3σ
Cpk and Cp should always be evaluated and analyzed togather. A Cp value signficantly greater than the corresponding Cpk indicates an opportunity for improvement by centrering the process.

Exactly what Miner said.

Plus: They are good indicators of what you need to work on in your process. If your CpU is very low and your CpL is high...you very likely need to shift your process down if possible...and vice versa if they're switched. If they're both low, you're in trouble and you've got to eliminate as much variability as possible (measurement systems/set-up variation/operator consistency) and if those still don't help...you'll need higher technology or wider spec limits.

(Cp is very useful in that way too...in that it tells you how your process would do if it is perfectly centered. If your Cp is a good deal higher than your CpK...you've got a good shot at a nice process if you can center it. If Cp and CpK are close to equal and are both lower than 1.0...you've got a lot of work to do...or a lot of scrap to account for)

I am splitting this thread (http://elsmar.com/Forums/showthread.php?t=32118) off because the topic is sufficiently different from the original thread.