@dnaviaux 

I should note that the example code in JacobianVsSEA is not well documented (I'm a newbie).  In summary:

1. It first develops an expression for a microcontroller ADC reading of the output of a roll-your-own differential amplifier that is monitoring the electircal current through an LED.
2. Evaluates the statistical and worst case ADC reading uncertainty using the Jacobian
3. Evaluates the statistical uncertainty using the SEA package.

@mmcdara 

Thanks again.  I'm anxious to examine your code in more detail.  I have never used the Monte-Carlo techniques to determine worst case results.  I expect that it will result in a more realistic worst case analysis compared to the way I am doing it with the Jacobian.

If you are interested, here is a worksheet that I put together that allows me to compare the SEA package to the brute force Jacobian techniques.  I have not incorporated the code that you posted to analyze the individual parameter contributions to the total uncertainty yet, but I will.

JacobianVsSEA.mw

I greatly appreciate the time you have take to answer my questions and your contributions.  Being new to Maple, the examples are very valuable.  I have learned quite a bit in the past few days due to MaplePrime.

@dnaviaux 

In my context, I could have used "parameter" in place of contributor, oh well...  I think it is clear though. 

@mmcdara 

I see that I have so much more to learn!  Thank you so much for the detailed answer and the example worksheet.  I have been evaluating my electrical designs for years using Jacobian matricies to calculate the total uncertainty and the "Effect" of each of the contributors so that I could verify that my design meets my design goals. By examining the "Effect" of each contributor, I could then make appropriate component changes as required to meet my goals (e.g. change a resistor from a 1% to a 0.1% resistor, use a better opamp, etc.) or change the design specifications.  

Using the Jacobian matricies, I am able to predict an uncertainty that matches the value returned by the SEA combine(f(),errors) function:

Using the Jacobian I am essentially calculating the following:

uncertainty = sqrt( (diff(y, a) * s_a)^2 +  (diff(y, b)* s_b)^2 + ...) 

Using the Jacobian I can also calculate the worst case uncertainty as follows:

worst case uncertainty = abs(diff(y, a) * s_a) + abs(diff(y, b) * s_b) + ...)

In generally I list both of the results for my clients.  The worst case results are exceedingly conservative since in practice it is unrealistic to expect every parameter to be at its worst case value. 

I really like the SEA app and by your explanation, I can see how I can also use it to see the effects of each contibutor.  My next step (after I review a bit of statistics that you response alerted me to) will be to compare the SEA vs Jacobian matricies implementation efforts.

@mmcdara 

Are you refering to giving credit to the person that developed the code?  

@mmcdara 

I have tried the Tolerance package but is seems that my equations are too complicated for it to work properly.  However the ScientificErrorAnalysis package works great and rerturns the same results that I get from my analysis code.  However, I can only see how I can analyze the total error.  My existing code examines the contributing error of each error source.  Is it possible to do this with SEA?

@acer 

Thank you for re-posting the old link.   It took a while, but I think that I understand it.  If I only need a few special symbols and I know their decimal equivalent Unicode, I could do this to create the printfable symbols:

plusmn := nprintf("&#%a;", 177);
Omega := nprintf("&#%a;", 937);

printf("%g %s %s %g%%\n", 2200, Omega, plusmn, 1);
2200 Ω ± 1%

It's a little clunky but a lot better than not being able to printf symbols.

Thanks

@Carl Love 

Thank you!

@acer 

I'm new to MaplePrime.  I will "Comment/Reply" in the future. 

@Carl Love 

The output example is what I could figure out how to do from Maple.  I would like the various component values to show their units and tolerances, e.g.:

rgp = 1000.1 Ω ± 0.01%

I know that it might seem unimportant, but 6 months from now 'rgp' might not mean much to me and having the units and tolerance shown is important to me since it shows what design parameters applied to the output results (I often experiement with other resistance tolerances in the design phase).

I realize that I can use the code that you posted in another thread and will likely do that. 

Thank you!

@mmcdara 

Here some information that might help.

I realize that the comments in my StandardValues package are slim to say the least.  The only proc in it at the moment is the CalcStdRes proc which does the following:

In addition to setting the value of some global variables (in parentheses) the proc takes a desired resistor value and standard resistor tolerance and returns a 5 element vector containing (in the following order):

the closest standard value to the specified resistance (EQ)

the closest standard value less than the specified resistance (LT)

the closest standard value greater than the specified resistance (GT)

the closest standard value less than or equat to the specified resistance (LTEQ)

the closest standard value greater than or equal to the specified resistance (GTEQ)

The specified tolerance sets what standard values are available (i.e. 1% resistors have different values than 5% available).

@acer 

Thanks again. I have so much more to learn before I have much proficiency with Maple and have appreciated all those that have helped. 

@acer 

Thank you.  In addition to Greek letters, I frequently use other symbols that I see I could add to the listed code.  I would stick to the Latex names for the simbols to keep things simple. 

@mmcdara 

Matlab does have a really nice conversion to html if instead of "running" the script, you "publish" it.  It is the only way to get graphics into any Matlab script output.

Because I want to understand what I did some time in the future, I need graphics incorported into the output that maple does very well.  Of course, I am able to automatically output some very useful infomation (without the special symbols yet). Example:

rgp = 1000.1  
rfp = 27697.2  
rgn = 999.9
rfn = 27702.8
rsens = 0.02
vofs = 0.06
vpos = 5
vref = 2.5
LED current = 0.4A

4000D IMON Uncalibrated Uncertainty
typical uncertainty = 1.4265[%]
maximum uncertainty = 3.0953[%]

 Parameter  Contribution
       rgp: -0.2152[%]
       rfp:  0.2152[%]
       rgn:  0.2052[%]
       rfn: -0.2052[%]
     rsens:  0.9999[%]
      vofs:  0.9026[%]
      vpos: -0.1742[%]
      vref: -0.1010[%]
       ibp: -0.0125[%]
       ibn:  0.0125[%]
       vos:  0.0518[%]
    olgain:  0.0000[%]

@mmcdara 

Thank you for the detailed explanation.  I have posted the code that produced to design and analyze a simple differential amplifer.  In analyzing the effects of component and parameter variations, I am taking the elemental product of the Jacobian matrix (well vector) and a vector holding the maximum various component variations. The result being a vector where each element contains how much the output is affected by the associated parameter.

I have always done it this way, but welcome any other suggestions.