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

rikkyyee,

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.

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?:)

rickyyee-
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?

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?:)

Al

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)

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

Sam-
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)


:D

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.

Darius and Sam -
Thanks for the replies.
I guess I'll have to try and locate that edition unless you can summarize any explainations it has.

The problem I see is if we take samples of 2,20,200,and 2000 and fail respectively 1,10,100 and 1000 as non-conforming, the fraction defective is always 0.5 but the % capabilities per this formula are 40,94,99.4 and 99.94 %

Obviously, the more we sample the better our capability even if our non-conforming fraction remains the same.

What's wrong with this picture? Any insights?

Percent capable on an attribute chart is a good measure, but it does not tell you if the process is centered (Cpk), or how much of the process is being used (Cp). :)

Al, as Donald Wheeler said, the use of attribute charts (p,np,u,c) assume relationship between location an dispersion, and other conditions, that if wrong, then the limits will be wrong, he sugest to use individual control charts (XmR).

From Advanced topics in Statistical Process Control

"If the data saisfy the conditions for Poisson model, then c-chart or a u-chart may be used. If the data satisfy the conditions for binomial model, then np or p-chart may be used. In any case an XmR chart may be used as long as the average count por sample exceeds 1.0".

What i try to say is that, it's OK about the use of Cp, Cpk , but also i recommend the use of XmR charts

Dave

I used the formula and obtained: %Capability= 100* (1 - (F+0.7)/N)
Sample,Non-conforming,%Capability
2,1,15
20,10,46.5
200,100,49.65
2000,1000,49.965

In the text they said something about Ford, and a sample size of 250 minimum with none out of specs, so given 99.73% inside tolerance.

They said also that the formula if non is out of the specs limits

%Capability = 100* (0.5)^(1/(N+1))

and if one or more values are out

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

In my oppinion the last formula is just the percentage of conforming units minus a some value that depend on the sample size 0.7/N

% non-conforming = 100 * F/N
% conforming = 100*(1- F/N)

Where does 0.7/N come from, may be from distribution assumptions.:confused:

I tink that the value with sample size of 2 is very different from the others just because the sample is to small to the formula (or the 0.7/N factor).

Hi,

For calculating the CP or CPk in this case you need only sigma vlaue, rest of the values are knows. As per the central limit theorem if your sample size is reasonable you can calculate your sigma as

sigma = sqrt(np_bar*(1-np_bar))

which can be used for calculating the Cp and Cpk values.

just a thought

best regards
A.Sridhar

So many reply and so many formular

I am a bit confuse already which should i use...?

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

for this formular which given by Darius
i think is more convicing but do it have any minimum sample size recomended to be used..?

Hi rikkyyee,

I dont know how this formula has come from, lets have some observations from the above formula

If you neglect 0.7/N then you are left with 100(1-F/N) which is nothing but a simple percentage of Confiming units out of sample size N. Does this equal to process capability. I may be wrong but i dont think that process capablity will be same as percentage of confirming units.

I may be wrong because i dont know the backgroung of this formula. Please correct me if i am wrong.

regards
A.Sridhar

sridhar

In review of all the last posts of this topic

The problem can not be solved by the Cp, Cpk, pp, ppk, Cpm, Cpkm capability or performance index because the lack of Specification Limits.

Sam came with

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

from:

Juran Quality Control Handbook 4th edition
Page 16.25 Design for production

As I said in my last post, I am agree that % Capability is just the % of conforming units minus a strange factor of 0.7/N (that I don´t know where came from), but the lack of Specification limits does not leave any other way.:frust:


rikkyyee

As I said in the last post

In Juran Quality Control Handbook 4th edition

"In the text they said something about Ford, and a sample size of 250 minimum "

I tink is a good rule of thump, but I will add another rule on my own(not written in any book), "It should be that in the sample size must include at least 5 non conforming units", Why 5?, I tink is a good number (but you could fix your own) and because if the capability is too small, there will not be any non conforming unit in the sample, the minimum non-conforming rule will assure the stability of the estimate, or use the case of non-conforming units in sample from Juran book.

So N at least 250 (Juran book) and at least 5 non-conforming units (my own), for example you may require 10000 units for 5 non-conforming if the % conforming = 100*(1-5/10000).

:smokin: