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# CPk

Jeorge

CPk | 6 December, 1999

How to calculate CPk of a chip shooter or a pick and place machine? And what's the right CPk? Want to have a rough understanding about CPk.

Bob Smith

Re: CPk | 6 December, 1999

CPk is a measure of the process variance with respect to the acceptable upper and lower limits. In your case it would be the accuracy of placement. The exact position of a chip ideally would be dead centre on the pads however in real life that position will vary. The distibution of the measurements of all chip placements with respect to dead centre should approximate a normal (bell) curve. If the +/- 3 sigma points on the normal curve are just barely within the allowable limits, the CPk will be approximately 1 - this means that there can be no variation of the process centre or some scrap will be produced. Normally you should try for a CPk of 1.5 to 2 which will allow for some variation of the process centre while still producing good parts. The idea is that the CPk is monitored and trends away from the proper process centre can be detected and corrected BEFORE scrap is produced. CPks less than 1 will always produce a percentage of scrap.

Bob

Andy Yates

Re: CPk | 6 December, 1999

Mathematically, measure the component offsets from nominal then calculate the average and the SD of the offsets in x and y. You can then use the following equation to calculate the CpK:

CpK = (Process Width - Abs(Average offset)) / (3 * SD offset)

Note that this assumes that you are using a 6 sigma process.

A more meaningful measure (to my mind) is to assume that you have a CpK of 2 and calculate what your current process is:

Process = (6 * SD) + Abd(Average offset)

Andy

Russ

Re: CPk | 6 December, 1999

The best way that I have found to calculate CPk for placement machines is to buy the kit that is usually provided by the manufacturer of machine. It usually consists of a glass plate and glass components that are scaled. You simply program the machine to place the component at the precise XY location and then perform measurements of the placement variance. This will give you your range of placement accuracy which is necessary to calculate the CPk. You also need to know what your limits are in regards to how much offpad can a component be. CPk in a nutshell is the capability of a process to meet the target value and the distribution of this variable within the spec. limts. A CPk of 1.3 is usually accepted. The higher the number the better however.

Russ

Brian W.

Re: CPk | 6 December, 1999

Cpk is sometimes referred to as the voice of the process because it is measuring how tight your process is in relation to the specification limits. A Cpk of 1 means that you are running a 3 sigma process (plus or minus 3 sigma). This means that your calculated control limit equals your specification limit, and that 99.73% of your product will fall inside the +-3sigma control limit (meaning a defect ppm of 2700ppm). Usually, a minimum of 1.33Cpk is required to get a process validated. A Cpk of 2 means that your calulated control limits are 1/2 of your specification limits, getting you to that wonderful place known as 6 sigma (or in Motorola terms, a defect of 3.4ppm) How I got there with component placement... Using a coordinate measurement system, I measured different components in relation to the x-y center from the CAD data. I made the specification limits the IPC placement limits (calculated a high and low value) based on the 50% requirement. You have to be careful to check the component size vs. the pad size or your will get an erroneous reading. I found the averages and used the formulas: Cpk=(USL-Xavg)/3sigma or (Xavg-LSL)/3sigma The Cpk is the smaller of the two numbers.

Most of the placement equipment can get to high Cpk's, but you have to make sure you do everything you can to redcue any possible variation. This includes, but is not limited to: machine preventative maintenance, good part shape definitions, feeder setups, feeder maintenance, and various and sundry other factors. Before you try calculating Cpk's, define all the factors in the process and insure that you have minimized the variation in each one. The process must be in statistical control prior to calculating Cpk.

If you want more information on this, please feel free to e-mail me. There are several sources of training I can recommend.

Brian W.

Michael Stewart

Re: CPk | 6 December, 1999

Have you ever tried using a vision system for measuring the part placement accuracy and then clacualting the Cpk's from these results, or do you strictly use the machine vision itself? My concern with using the machine vision is that it it is biased and you may not ge a true represenative of your process.

Thanks Mike

Brian W.

Re: CPk | 6 December, 1999

I have not used a vision inspection system for this. We used a digital x-y coordinate measurement system. With this, we could find the center of the part and then measure where it was in relation to a fixed point, like a fiducial. Some of the systems even allow you to program what you want to do, and then all you have to do is switch out the boards, hit go, print the results, and do the calculations. We just had an in-line vision inspection machine for evaluation, and it does not actually calculate where the part is placed (ie, center of R54 is placed at 3.54 in).

Brian W.

Jerry Stafford

Re: CPk | 8 December, 1999

Michael, You need to know the measurement capability of whatever system you use to do your CpK measurement. Ideally you would do an error of measurement study of the measurement process. It is hard to imagine a measurement system that would err on the side of the machine manufacturer. Measurement will introduce more variability in your measurements, the key is to know how much variability is caused by your measurement system.

There will be variation introduced by the measurement process, by the placement process and by your measurement sample. Have the vision system measure the same part repeatedly. The idea is to measure as close as possible to a perfect part over and over and see how much variation the vision system introduces.

Jerry

Andy Yates

Re: CPk | 9 December, 1999

I would suggest that as well as repeatedly inspecting the same board and looking at the standard deviations of the measurements, you should perform some form of accuracy test either by measuring a known glass plate or by inspecting a board at 0 and 180 degrees and examining the offsets between the two results. The 0/180 test is not a test of true accuracy, but it will show any systematic error in the vision system's measurement.

Andy