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Regret Indices and Capability Quantification

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Probabi lity Plot of Regret Order Statistics and GaNMa Quantiles at Equioalent Expectancy -    1.647

FigurÄ™ 12. Gamma Q-Q Probability Plot for Logistic Fill-Volume Regret.

EN(X)

EE

R(X)

ER

= I(X)

[22]

In other words, a regret index can also be viewed as the ratio of an equivalent nonconformance, EN, to its expected value, EE. In fact, this new point-of-view allows us to use the so-called "additivity" theorem for Poisson and standardized gamma distributions to form composite regret indices. These additivity properties are:

If Zi follows a Poisson distribution with intensity parameter EEi, Z2 follows a Poisson distribution with intensity parameter EE2, and Zi and Z2 are statistically independent, then Zi + Z2 follows a Poisson distribution with intensity parameter EEi + EE2, even when EE] and EE2 are different intensities.

If Zi follows a gamma distribution with shape parameter EEi, Z2 follows a gamma distribution with shape parameter EE2, and Zi and Z2 are statistically independent, then Z\ + Z2 follows a gamma distribution with