# Thread: Need Help Understanding Calculation of Printed Circuit Board Design Time

1. ## Need Help Understanding Calculation of Printed Circuit Board Design Time

First post here. If it's not appropriate or needs moved, I apologize. FWIW, this is not a homework problem...

I'm in need some help understanding a statistics process or calculation.

I'm in the process of trying to understand how to properly estimate the number of hours required to design a printed circuit board (PCB) based on a few key pieces of data. I came across a paper that has looked into this and they used some statistics calculation, including R-code, to estimate hours based on three pieces of data. I tried to follow it, but I do not know how they produced these results.

Here is the paper: https://users.soe.ucsc.edu/~renau/docs/wced06.pdf

The three variables that they ended up using are: # Passives, Component Density, and Pin Density. With these three values, how are they calculation hours (uPCBComplexity)?

Here is the data for designs B1 through B11 (variables is red, results in green), calculations, and R-Code:

The (1/rho) value is ignored in this example.

# non-linear model
nls(log(Effort) ˜
log(w1*stat1 + w2*stat2)
,start=list(w1=0.1,w2=0.1)
,data=traw)

I ultimately want to have a calculation to be able to reproduce their results so I can estimate hours for any job with these three variables. I've downloaded R and tried processing their code, but I don't have their data file (traw). I'm not sure how they organized traw and how the code references the variables within traw.

Any help would really really be appreciated!

2. ## Re: Need Help Understanding Calculation of Printed Circuit Board Design Time

Bump.

Can someone at least tell me what this R-code does mathematically for the data in the table above?

# non-linear model
nls(log(Effort) ˜
log(w1*stat1 + w2*stat2)
,start=list(w1=0.1,w2=0.1)
,data=traw)

3. ## Re: Need Help Understanding Calculation of Printed Circuit Board Design Time

That fits a non-linear model via least squares. The model is

where and are the parameters to be estimated. The line start=list(w1=0.1, w2=0.1) tells the model which "starting values" to use. Basically the way this model is fit is by guessing a value for the parameter and then trying to a better fit in the area around there and it keeps trying to find better and better values but it needs a place to start its search.

4. ## Re: Need Help Understanding Calculation of Printed Circuit Board Design Time

Originally Posted by Dason
That fits a non-linear model via least squares. The model is

where and are the parameters to be estimated. The line start=list(w1=0.1, w2=0.1) tells the model which "starting values" to use. Basically the way this model is fit is by guessing a value for the parameter and then trying to a better fit in the area around there and it keeps trying to find better and better values but it needs a place to start its search.

So, using the example in the original post, we are trying to estimate uPCBComplexity (which would be w1, correct)? If that was the only estimated value, we wouldn't need w2, w3, ect, right?

Where do the three variables come in (#passives, component density, and pin density)? Are those "stat"?

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