00388 ™ad1b2790a36746189e398f860be172

392

Obenchain

shape parameter EEi + EE2, even when EEi and EE2 are different, as long as both gamma distributions have the same scalÄ™ parameter, b. (For example, this property implies the well known additivity of independent chi-squares and of their corresponding degrees-of-freedom.)

Additivity immediately suggests that composite indices are most reasonably formed as follows:

ZEN,(X₍)

Composite Index =    â– =- [23]

2^EEj

Only in cases where all EE's are equal does EÄ…uation [23] reduce to the simple arithmetic average of the individual regret indices, [8].

The Hallmark of Continuous Improyement The EE = ER^/VR corresponding to individual measurements madÄ™ on the process will continually drop. On the other hand, statistically significant lack-of-fit in discrete Poisson approximations is common in cases where EE is smali (0.5 or less) and data are plentiful. After all, the Poisson integer "step-size" then balloons to 2 units or greater when re-expressed on the regret index scalÄ™. The rounded and un-rounded regret index values (corresponding to integer or non-integer ENs) can thus be quite different numerically.

An appropriate strategy in Iow expectancy cases is thus to accumulate Ä…uality information across multiple measurements! Relationship [23] is sufficiently generaÅ‚ to allow us to combine measurements of either the same type or of completely different types, as long as we have confirmed that all components to be combined are at least approximately Poisson (or gamma) distributed. When measurements are madÄ™ on multiple samples from a production batch or are taken over a seÄ…uence of consecutive time points, regret accumulation is straight-forward because each measurement has a common target, regret function, and EE. But relationship [23] also allows us to combine equivalent nonconformances across diverse measurements from the same or related production processes, ...each with its own, distinct target value, regret functional form, and EE.

An Enyironmental Monitoring Eiample

Monitoring of "bio-burden" contaminant counts in a non-sterile