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Doc migration done, fixed on-screen errors
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robmoffat committed Jan 31, 2024
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2 changes: 1 addition & 1 deletion docs/complexity/End-Of-Complexity.md
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Expand Up @@ -17,7 +17,7 @@ KubeCon (2022): To start with, a computer ran a program. There was a one-to-one

The problem with this is that it is more complex. Over time, software _always_ gets more complex, because it's always trying to adapt and [model human needs better and better](../estimating/Fractals.md#continuous-refinement).

![The Broccoli Problem](/images/complexity/broccoli.jpg)
![The Broccoli Problem](/img/complexity/broccoli.jpg)

I call this the Broccoli Problem.

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75 changes: 0 additions & 75 deletions docs/complexity/SAME.md
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276 changes: 7 additions & 269 deletions docs/estimating/Fill-The-Bucket.md
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Expand Up @@ -41,86 +41,7 @@ Where we are able to see measurements clustering-around-the-mean, this gives ris

<script defer src="https://cdn.jsdelivr.net/npm/[email protected]/dist/Chart.min.js" integrity="sha256-Uv9BNBucvCPipKQ2NS9wYpJmi8DTOEfTA/nH2aoJALw=" crossorigin="anonymous"></script>
<script defer src="{{ site.baseurl }}/assets/js/mychart.js"></script>
<script type="text/javascript">

function stddev(range, mean, variance) {
const factor = 1 / (Math.sqrt(2* 3.141592 * variance));
return range.map(r => {
const num= ((r - mean)*(r - mean));
const denom = 2 * variance;
const fact = num / denom;

return factor * Math.exp(-fact);
});
}

window.addEventListener("load", () => {
doChart('simulation',
{
'units' : { min: 1, max: 15, value: 10, name: 'Number of Units', step: 1 },
'mean' : { min: 20, max: 120, value: 60, name: 'Mean time to Complete Unit', step: 1 },
'variance' : { min: 1, max:50, value: 30, name: 'Variance In Unit Time', step: 1}
},
[
model => {
var min = 0;
var max = 120;

return {
type: 'line',
data: {
labels: range(min, max, 1).map(r => Math.round(r)),
datasets: [{
label: 'Time To Complete A Single Unit (minutes)',
backgroundColor: [ 'rgba(255, 99, 132, 0.2)' ],
borderColor: [ 'rgba(255, 99, 132, 1)' ],
data: stddev(range(min,max,1), model.mean.value, model.variance.value)
}]
},
options: {
scales: {
yAxes : [{
ticks : {
max : .3,
min : 0
}
}]
}
}
}
},
model => {
var min = 0;
var max = 1000;

return {
type: 'line',
data: {
labels: range(min / 60, max/60, 10/60).map(r => Math.round(r)),
datasets: [{
label: 'Time To Complete All Units (hours)',
backgroundColor: [ 'rgba(132, 99, 255, 0.2)' ],
borderColor: [ 'rgba(132, 99, 255, 1)' ],
data: stddev(range(min,max,10), model.mean.value*model.units.value, model.variance.value * model.units.value)
}]
},
options: {
scales: {
yAxes : [{
ticks : {
max : .05,
min : 0
}
}]
}
}
}
},

]);
});

</script>
<script type="text/javascript" src="/js/fill-the-bucket1.js" ></script>

## Mean and Variance

Expand All @@ -147,96 +68,16 @@ If you paint the first fence panel in 40 minutes, how sure can you be that this

After the first fence panel, you just don't know. After you've painted two or three, you can start to figure out the _sample variance_ $$s^2$$:

$$s^2 = \frac{\sum(x - \bar{x})^2}{n - 1}$$
$$
s^2 = \frac{\sum(x - \bar{x})^2}{n - 1}
$$

The more samples we make, the more precise the sample variance will be, and so the more confident we should be on our expected time to complete painting the fence.

<div id="simulation2"></div>

<script type="text/javascript">
window.addEventListener("load", () => {

function stddev(range, mean, variance) {
const factor = 1 / (Math.sqrt(2* 3.141592 * variance));
return range.map(r => {
const num= ((r - mean)*(r - mean));
const denom = 2 * variance;
const fact = num / denom;

return factor * Math.exp(-fact);
});
}

function random_normal()
{
const M_PI = 3.14159;
return Math.sqrt(-2*Math.log(Math.random())) * Math.cos(2*M_PI*Math.random());
}

var mean = 11;
var variance = 2.5

const samples = range(0, 200, 1).map(i => random_normal()*variance+mean);

function bucket(samples) {
var out = new Array(20).fill(0);
samples.forEach(s => {
var b = Math.round(s);
if ((b>=0) && (b<20)) {
out[b] ++;
}
});
return out;
}
function calcMean(s) {
var tot = s.reduce((a,b) => a+b);
var len = s.length;
return tot/len;
}

function calcVar(s, mean) {
var tot = s.map(i => (i - mean)*(i - mean)).reduce((a, b) => a+b);
var len = s.length - 1;
return tot / len;
}

doChart('simulation2',
{
'samples' : { min: 2, max: 200, value: 3, name: 'Individual Samples', step: 1 },
},
[
model => {
var subsam = samples.slice(0, model.samples.value);
var mean = calcMean(subsam);
var variance = calcVar(subsam, mean);
var buckets = bucket(subsam);
var dist = stddev(range(0, 20, 1), mean, variance).map(r => r* model.samples.value);

return {
type: 'bar',
data: {
labels: range(0, 20, 1),
datasets: [{
label: 'Samples',
data: buckets,
borderWidth: 1,
backgroundColor: 'rgba(132, 99, 255, 0.2)' ,
borderColor: 'rgba(132, 99, 255, 1)' ,
},
{
type: 'line',
label: 'Normal Distribution Fit',
backgroundColor: [ 'rgba(255, 99, 132, 0.2)' ],
borderColor: [ 'rgba(255, 99, 132, 1)' ],
data: dist
}]
},

}}]);

});

</script>
<script type="text/javascript" src="/js/fill-the-bucket2.js"></script>


In the above simulation, we are trying to fit a Normal Distribution, estimated from a number of samples.

Expand Down Expand Up @@ -276,110 +117,7 @@ Let's ignore _all other risks_ and just focus on these monetary ones. What is t

<div id="simulation3"></div>

<script type="text/javascript">
window.addEventListener("load", () => {

function stddev(range, mean, variance) {
const factor = 1 / (Math.sqrt(2* 3.141592 * variance));
return range.map(r => {
const num= ((r - mean)*(r - mean));
const denom = 2 * variance;
const fact = num / denom;

return factor * Math.exp(-fact);
});
}

var days = 60;
var mean = 2;
var variance = 1;


doChart('simulation3',
{
'estimate': { min: 20, max: 80, value: 20, name: 'Estimate', step: 1 },
'records' : { min: 100, max: 700, value: 500, name: 'Records', step: 1 },
'mean' : { min: 1, max: 3, value: 2, name: 'Mean', step: .1 },
'variance' : { min: .5, max: 3, value: 1, name: 'Variance', step: .1 },
'staff' : { min: 1, max: 10, value: 4, name: 'Staff', step: 1 },
'hours' : { min: 1, max: 17, value: 8, name: 'Hours Per Day', step: 1 },

},
[
model => {

var meanEffort = model.records.value * model.mean.value;
var varEffort = model.records.value * model.variance.value;
var manPower = model.staff.value * model.hours.value;
var daysPDF = stddev(range(0,days,1), meanEffort / manPower, varEffort / manPower);

return {
type: 'line',
data: {
labels: range(0, days, 1),
datasets: [{
label: 'Days To Complete',
backgroundColor: [ 'rgba(255, 99, 132, 0.2)' ],
borderColor: [ 'rgba(255, 99, 132, 1)' ],
data: daysPDF
}
]
},

}},

model => {
var penalty = (model.estimate.value - 20) * 300;
var returns = range(0, days, 1).map(d => 10000 - penalty - (Math.max(0, d - model.estimate.value) * 1000));

return {
type: 'line',
data: {
labels: range(0, days, 1),
datasets: [{
label: 'Return',
backgroundColor: [ 'rgba(132, 99, 255, 0.2)' ],
borderColor: [ 'rgba(132, 99, 255, 1)' ],
data: returns
}
]
},

}


},
model => {
var penalty = (model.estimate.value - 20) * 300;
var returns = range(0, days, 1).map(d => 10000 - penalty - (Math.max(0, d - model.estimate.value) * 1000));
var meanEffort = model.records.value * model.mean.value;
var varEffort = model.records.value * model.variance.value;
var manPower = model.staff.value * model.hours.value;
var daysPDF = stddev(range(0,days,1), meanEffort / manPower, varEffort / manPower);
var riskAdjustedReturn = daysPDF.map((v, i) => v * returns[i]);

return {
type: 'line',
data: {
labels: range(0, days, 1),
datasets: [{
label: 'Financial Risk',
backgroundColor: [ 'rgba(255, 132, 99, 0.2)' ],
borderColor: [ 'rgba(255, 132, 99, 1)' ],
data: riskAdjustedReturn
}
]
},

}


}
]);

});

</script>
<script type="text/javascript" src="/js/fill-the-bucket3.js"></script>

## Analysis

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