Pareto Distribution
Pareto’s Law
Pareto’s Principle

Generally understood as the 80/20 rule.

Inaccurately attributed yet popular.

Before the late 1930’s Joseph M. Juran observed at Western Electric quality losses to concentrate in a “few major defects” [1960]. In search of a shorthand name for the rediscovered phenomenon, he resorted to the Vilfredo Pareto who postulated a law of income distribution [1906] – not the concentration of defects.

Juran visualised the relationships with Lorenz Curves [1905] and coined the terms Vital Few and Useful Many.

Juran [1960] began to use the phenomenon in business in the 1930’s. It spread from the 1940’s. He established it as an industry standard with his book Quality Control Handbook in 1951.

effectus assumes a pareto distribution to be present if the given cause-effect relationship is equal or stronger than 60 percent of effects stemming from 40 percent of causes.

80/20 Rule

Phenomenon that a few values derive their power from their weight while most other derive it from their frequency. In many cases the Vital Few contribute more to the total than most others, the Useful Many, do.

Named after Vilfredo Pareto who observed that a 20 percent of England’s population received the 80 percent of income. Felix Auerbach [1913] found it in the concentration of population, Gutenberg and Richter [1949] in the amount of energy of earthquakes, Liljeros [2001] in the sexual relationships of humans. Newman [2005] gives other examples.

Rule 50/5

A majority of causes provoking only a minority of effects. While it might overlap with the Useful Many, it usually it only a subset of it.

A rule 50/5 is present if 50 percent of causes with least effects make up only 5 percent of all effects.

the_rule() determines it or any variant of it.

Vital Few
The minority of causes provoking a majority of effects. This is the printable representation of Effects(). The representation is the best estimate, the actual relation is stored in effectus.Effects.actual.
Useful Many
Trivial Many
The counterpart to the Vital Few. Originally coined Trivial Many by Joseph M. Juran but later renamed to Useful Many to emphasize its usefulness.
The Focused Factory

Concept of Wickham Skinner [1974] we continuously violate. Therein he states any system trying to accomplish two similar yet different things can not be optimised for one thing. If it was, it would not accomplish the second thing. Consequently, any system trying to accomplish more than equal things, requires more effort to effect less results.

If one removes the second thing, one will gain in saved effort and increased result that in sum could outweigh the lost contribution by the second thing. Alternatively, the additional setup and maintenance cost for a second system could be well surpassed by the saved costs and increased results by both systems.

Lorenz Curve
Diagram introduced in [1905] relating cumulative causes and cumulative effects to each other. The axes were originally not logarithmic.
Measures of Central Tendency
Measure Characteristic
Arithmetic Mean Equal sum of deviations
Median Equal number of deviations
Peak Value Surrounded by most values
Arithmetic Mean

Value of equal sum of deviations smaller and greater to it. The sum of the deviations is minimal with the arithmetic mean.

The arithmetic mean of constant causes follows the Law of Error: The more measurements of the height of the same house the nearer the arithmetic mean will come to the true height of the house.

The arithmetic mean of heights of different houses is only a an abstract concept.

Value of equal number of deviations smaller and greater to it. It is the middle value in the ordered series of values.
Peak Value
The value surrounded by most other values. In other words the most dense value or the most likely. It is found by classifying all values into classes of equal bandwidth and taking the middle of the class or the arithmetic mean of its values.
Standard Deviation
The sum of the squared difference of each value to the standard, that is the arithmetic mean, divided by the number of values, eventually the squared root of the latter.
Law of Error
Applies when deviations from the arithmetic mean distribute normally. Then the arithmetic mean is the most likely value, coinciding with Scheitelwert.
Law of Large Numbers
The more often a measurement of constant causes is repeated, the nearer the Arithmetic Mean comes to the true value.
[1905](1, 2) Lorenz, M. O. Methods of Measuring the Concentration of Wealth. American Statistical Association Publication. 9, 209-219.
[1960](1, 2) Juran, Joseph M. Pareto, Lorenz, Cournot, Bernoulli, Juran and others. Industrial Quality Control 17 (4), 25.
[1906]Pareto, Vilfredo. Manuale d’Ecomonia Politica.
[1913]Auerbach, Felix. Das Gesetz der Bev√∂lkerungskonzentration. Dr. A. Petermanns Mitteilungen aus Justus Perthes’ Geographischer Anstalt, 59, 74-76.
[1949]Gutenberg, B.; Richter, C. F. Seimicity of the Earth and Associated Phenomena. Princeton University Press.
[2001]Liljeros, F.; Edling, C. R.; Amaral, L. A. N.; Stanley, H. E.; Aberg, Y. The web of human sexual contacts. Nature 411, 907-908.
[2005]Newman, M. E. J. Power laws, Pareto distributions and Zipf’s Law. Contemporary Physics 46, 323-351.
[1974]Skinner, Wickham. The Focused Factory