MaplePrimes - answers and comments on Question, Behavior of "Tolerances" package

evalr

acer — Mon, 08 Feb 2010 12:42:36 Z

The Tolerances package uses evalr.

> R1:=INTERVAL(76.0 .. 84.0):
> R2:=INTERVAL(114.0 .. 126.0):
> Req:=R1*R2/(R1+R2):

> evalr(Req);
                     INTERVAL(41.25714285 .. 55.70526317)
 
> evalr(1/(expand(1/Req)));
                     INTERVAL(45.59999998 .. 50.40000003)

Now, that second result was just lucky. Terms simplified and repeated instances of R1 and R2 vanished before evalr got its hands on them.

Are you trying to bound the behaviour of the system, given bounds on the capabilities of the components? If so, then I can imagine that a Tolerances package that functions well could be useful.

If not, then are you trying to characterize behaviour given physical measurements of the resistances (with of course have an associated measurement error)? In that case, is the ScientificErrorAnalysis package of any use? Note that for that package, the error does not represent an interval, but rather a distribution.

> restart:

> R1:=ScientificErrorAnalysis:-Quantity(80.1,4.0)*Unit(ohm):
> R2:=ScientificErrorAnalysis:-Quantity(120.1,6.0)*Unit(ohm):

> Req:=combine(R1*R2/(R1+R2),errors);
           Req := Quantity(48.05199800 [Omega], 1.730531812 [Omega])

acer

SEA vs Tolerances

herclau — Mon, 08 Feb 2010 20:10:21 Z

restart;
R1 := ScientificErrorAnalysis:-Quantity(80.0, 4.0)*Unit(ohm);
R2 := ScientificErrorAnalysis:-Quantity(120.0, 6.0)*Unit(ohm);
Req := combine(R1*R2/(R1+R2), errors);

restart;
with(Tolerances);
R1 := `&+-`(80.0, 4):
print(`output redirected...`); # input placeholder
R2 := `&+-`(120.0, 6):
print(`output redirected...`); # input placeholder
R := 1/(1/R1+1/R2);

48.0 `&+-` 2.40

restart;
R := 1/(1/R1+1/R2):
print(`output redirected...`); # input placeholder
dR := sqrt(((diff(R, R1))*dR1)^2+((diff(R, R2))*dR2)^2):

subs(R1 = 80.00, R2 = 120.00, R);
48.00000001

subs(R1 = 80.0, R2 = 120.0, dR1 = 4.0, dR2 = 6.0, dR);
1.730664613

Behavior of "Tolerances" package

andreasr — Thu, 11 Feb 2010 05:36:22 Z

Thanks for your responses and explanations. As herclau noticed the issue can be resolved for this case with some algebra.

My intent was to use this package to figure out required or resulting tolerances for dimensions/specifications of components or assemblies. It can be done of course, but it's a rather tedious bookkeeping exercise. Unfortunately it's also a very frequent exercise for a mechanical engineer like me. I'll try using the package keeping in mind its restrictions.

The SEA package would be more useful to bound measurements and calculations with measurements as mentioned.