Cp, Cpk calculation for np chart - No USL or LSL - SMT Production



Hi all

Recently i am working in the smt production line which use np
chart to monitor the defect level. but i was requested to help
determine the Cp and Cpk for the process.

if i am not wrong for x-bar,R chart the formular are:

Cp = (USL-LSL)/(6 x sigma)

Cpk = min ((USL-mean),(mean-LSL)) / (3 x sigma)

but for the SMT production line there do not have any USL or LSL
so how we calculate the Cp and Cpk...??

pls advise. thank you

Rick Goodson


Showing formula is always difficult never the less, the formula for the upper and lower control limits on an np chart is:

UCL = np-bar + 3*[square root of (np-bar*(1-p-bar)]
LCL = np-bar - 3*[square root of (np-bar*(1-p-bar)]

If after charting with the control limits all points are in control then the Cpk is equal to the process average.

A good reference for control charts is the Statistical Process Control (SPC) Reference Manual from the Automotive Industry Action Group (AIAG). The web site is http://www.aiag.org The cost of the manual is $30.00 for non members.

Al Dyer

I'm confused (as usual),

How can you determine a real Cpk without using spec limits? Given that is possible to be within control limits but still out of spec limits.

Cpk measures the centering of the process within spec limits, Cp measures the amount of process being used.

Could you put an arbitrary USL and LSL on an Np chart then use those to estimate capability?:)

Dave Strouse

If you want a capability index, Cp or Cpk you must be given a specification. Otherwise, the question is capability to produce WHAT?

For attribute data, it is sometimes usefull to find the average ppm defective as per Rick's suggestion. The process should be in statistical control as he indicated and also you ought to examine the distribution by a histogram.

Given statistical control and that the distribution is relatively normal, you can convert the ppm defective into a equivalent sigma or "Z" value. This is the numerator of your formulas you want to use. Divide this by 6 for an estimate of Cp or 3 for Cpk. See "Advanced Topics in Statistical Process Control" Wheeler pages 191 to 196 for more on this.

However, would it not be easier to just report and compare the average per cent defective or ppm from the control chart? Why do you need or want a Cp value at all?

Al Dyer

I seem to remember that somewhere in the PDF files is a form that correlates PPM with capability. If I knew where I would post it, but try the search engine.

Anybody else with a better memory?:)



In my opinion, as Donald Wheeler said (in advanced topics on SPC), the correlation between PPM and capability is a nonsense, because the distribution of the data must be a gausian ones ("normal"), even when the process is a stable ones. Wheeler recomend to count the point outside of the specification limits and show them as as %, insteed of going from capability to ppm with such tables.

But the problem still is after all "THERE ARE NO SPECIFICATION LIMITS" :frust: , so there could not be any ppm to correlate.

The recomendation is to fix the "Specification Limits" (could be yours, inside of the company, if the customer doesn´t have one).

Another way (there are some people that don't like capability index), is to chart it as a box plot to see the behabiur of the process tru the time.

I don't like it :bonk: , but there is the table (page 14)


  • processcapability[1].ppt
    469.5 KB · Views: 866


For attribute data;
capability % = 100(1 - (F + 0.7/N)) ,
Where F is the number of failures,
N is the sample size.

Juran Quality Control Handbook 4th edition

Dave Strouse

Maybe it's the limitations of the software in reproducing formulas, but the formula as given makes no sense.

It gives for a sample of 1 and 1 failure, a % capability of -70. For a sample of 100 and 50 failures the % capability is -4900.7. What could these mean?

I don't have a copy of Juran's 4th edition, but the 5th has nothing like this that I could find.

Is it maybe a transcription error?


Sam and Dave

For attribute data;
ERROR >> capability % = 100(1 - (F + 0.7/N))

Because F in the previous equation must be a fraction of non-conforming units

capability % = 100(1 - (F + 0.7)/N)



Darius, you are correct. I placed the bracket in the wrong position.

Dave, In the 4th edition it is in the chapter on Manufacturing planning.
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