Deming's funnel: Difference between revisions

[[wp:W. Edwards Deming|W Edwards Deming]] was an American statistician and management guru who used physical demonstrations to illuminate his teachings. In one demonstration Deming repeatedly dropped marbles through a funnel at a target, marking where they landed, and observing the resulting pattern. He applied a sequence of "rules" to try to improve performance. In each case the experiment begins with the funnel positioned directly over the target.

 

* Further [http://blog.newsystemsthinking.com/w-edwards-deming-and-the-funnel-experiment/ explanation and interpretation]

* [https://www.youtube.com/watch?v=2VogtYRc9dA Video demonstration] of the funnel experiment at the Mayo Clinic.

 

=={{header|D}}==

{{trans|Python}}

 

auto mean(T)(in T[] xs) pure nothrow @nogc {

experiment("Rule 3:", dxs, dys, (z, dz) => -(z + dz));

experiment("Rule 4:", dxs, dys, (z, dz) => z + dz);

{{out}}

<pre>Rule 1:

Mean x, y: 3.1341, 5.4210

Std dev x, y: 1.5874, 3.9304</pre>

 

=={{header|Elixir}}==

{{trans|Ruby}}

def funnel(dxs, rule) do

{_, rxs} = Enum.reduce(dxs, {0, []}, fn dx,{x,rxs} ->

Deming.experiment("Rule 2:", dxs, dys, fn _z, dz -> -dz end)

Deming.experiment("Rule 3:", dxs, dys, fn z, dz -> -(z+dz) end)

 

{{out}}

Mean x, y : 3.1341, 5.4210

Std dev x, y : 1.5874, 3.9304

</pre>

 

=={{header|Haskell}}==

{{trans|Python}}

import Text.Printf

 

experiment "Rule 2:" dxs dys (\_ dz -> -dz)

experiment "Rule 3:" dxs dys (\z dz -> -(z+dz))

 

{{out}}

=={{header|J}}==

 

dx=:".0 :0-.LF

_0.533 0.270 0.859 _0.043 _0.205 _0.127 _0.071 0.275

smoutput ' Rule 4 (x,y):'

smoutput ' Mean: ',":dx ,&mean&Rule4 dy

 

Displayed result:

Translation of [[Deming's_Funnel#Python|Python]] via [[Deming's_Funnel#D|D]]

{{works with|Java|8}}

import java.util.Arrays;

import java.util.function.BiFunction;

return sqrt(Arrays.stream(xs).map(x -> pow((x - m), 2)).sum() / xs.length);

}

 

<pre>Rule 1:

Mean x, y: 3,1341, 5,4210

Std dev x, y: 1,5874, 3,9304</pre>

 

=={{header|Kotlin}}==

{{trans|Python}}

 

typealias Rule = (Double, Double) -> Double

experiment("Rule 3") { z, dz -> -(z + dz) }

experiment("Rule 4") { z, dz -> z + dz }

 

{{out}}

Std Dev : 1.5874, 3.9304

</pre>

 

=={{header|PARI/GP}}==

:''This is a work-in-progress.''

my(v=vector(drops),target=0);

v[1]=rule(target, 0);

print()

)

 

-0.533 0.270 0.859 -0.043 -0.205 -0.127 -0.071 0.275

1.251 -0.231 -0.401 0.269 0.491 0.951 1.150 0.001

0.024 -0.386 0.962 0.765 -0.125 -0.289 0.521 0.017

0.281 -0.749 -0.149 -2.436 -0.909 0.394 -0.113 -0.598

0.136 0.717 0.459 -0.225 1.392 0.385 0.121 -0.395

0.490 -0.682 -0.065 0.242 -0.288 0.658 0.459 0.000

-0.729 0.650 -1.103 0.154 -1.720 0.051 -0.385 0.477

1.537 -0.901 0.939 -0.411 0.341 -0.411 0.106 0.224

 

 

{{out}}

 

=={{header|Python}}==

{{trans|Racket}}

 

dxs = [-0.533, 0.27, 0.859, -0.043, -0.205, -0.127, -0.071, 0.275, 1.251,

experiment('Rule 2:', lambda z, dz: -dz)

experiment('Rule 3:', lambda z, dz: -(z+dz))

 

{{output}}

 

'''Alternative''': [Generates pseudo-random data and gives some interpretation.] The funnel experiment is performed in one dimension. The other dimension would act similarly.

from math import sqrt

from pprint import pprint as pp

for rule, comment in rcomments:

printit(rule)

 

{{out}}

=={{header|Racket}}==

The stretch solutions can be obtained by uncommenting radii etc. (delete the 4 semi-colons) to generate fresh data, and scatter-plots can be obtained by deleting the #; .

(require math/distributions math/statistics plot)

 

(experiment "Rule 2:" (λ (z dz) (- dz)))

(experiment "Rule 3:" (λ (z dz) (- (+ z dz))))

 

{{output}}

Std dev x, y: 1.5874, 3.9304

</pre>

 

=={{header|Ruby}}==

{{trans|Python}}

x, rxs = 0, []

for dx in dxs

experiment('Rule 2:', dxs, dys) {|z, dz| -dz}

experiment('Rule 3:', dxs, dys) {|z, dz| -(z+dz)}

 

{{out}}

Std dev x, y : 1.5874, 3.9304

</pre>

 

=={{header|Sidef}}==

a.sum / a.len

}

printf("Mean x, y : %.4f %.4f\n", x̄(z.map{.re}), x̄(z.map{.im}))

printf("Std dev x, y : %.4f %.4f\n", σ(z.map{.re}), σ(z.map{.im}))

{{out}}

<pre>

Std dev x, y : 1.5874 3.9304

</pre>

 

=={{header|Tcl}}==

{{works with|Tcl|8.6}}

{{trans|Ruby}}

namespace path {tcl::mathop tcl::mathfunc}

 

experiment "Rule 2:" $dxs $dys {{z dz} {expr {-$dz}}}

experiment "Rule 3:" $dxs $dys {{z dz} {expr {-($z+$dz)}}}

The first stretch goal:

{{tcllib|math::constants}}

{{tcllib|simulation::random}}

package require simulation::random

 

experiment "Rule 2:" $dxs $dys {{z dz} {expr {-$dz}}}

experiment "Rule 3:" $dxs $dys {{z dz} {expr {-($z+$dz)}}}

{{out}}

<pre>

Mean x, y : -6.3314, -4.0168

Std dev x, y : 3.2387, 4.4825

 

</pre>

=={{header|zkl}}==

{{trans|Ruby}}

x:=0.0; rxs:=L();

foreach dx in (dxs){

"Std dev x, y : %7.4f, %7.4f".fmt(stddev(rxs),stddev(rys)).println();

println();

1.251, -0.231, -0.401, 0.269, 0.491, 0.951, 1.150, 0.001,

-0.382, 0.161, 0.915, 2.080, -2.337, 0.034, -0.126, 0.014,

experiment("Rule 2:", dxs, dys, fcn(z,dz){ -dz });

experiment("Rule 3:", dxs, dys, fcn(z,dz){ -(z+dz) });

{{out}}

<pre>