00368 Ed86c193cea200625a236afd2833554

372

Obenchain

denominator of the ratio that we will use to convert an observed regret, R(X), into the corresponding performance index for that X value:

I(X) = R(X) / ER    [8]

Notę that ER needs to be strictly positive to be of any use in defining an index via equation [8]. The Quality Measurement Plan (QMP) of Hoadley (1981,1986) uses this index scalę for quality trend monitoring. Notę in particular that smali (rather than large) numerical values of our index represent desirable performance. Detailed information on QMP is also provided by Bellcore (1986,1987), Brush, Hoadley and Saperstein (1990), and Barlow and Irony (1992).

Like R(X), I(X) is non-negative and I(T) = 0. After all, we have simply rescaled R(X) by dividing it by a constant to form I(X). Notę that the index value I(X) = 1 is pivotal in the sense that

INDEX < 1 [or R(X)<ER] implies BETTER than standard performance, while

INDEX > 1 [or R(X)>ER] implies POORER than standard performance.

We use the following simple numerical example to give concrete illustrations of common data-analysis problems faced when setting ąuality standards, ER (and VR), for various regret functional forms.

Fill-Volumes Numerical Example Attendees at a March 1991 seminar of minę at Lilly participated in a "fili volume" experiment. We asked each participant to fili a styrofoam cup with water at a drinking fountain, attempting to fili as close as possible to a 75 ml (milliliter) mark drawn on the outside of the cup. We then used a graduated cylinder to measure the volume of each sample to the closest ml; the following 31 sorted values resulted:

51, 62, 62, 63, 65, 65, 69, 69, 70, 72, 72, 72, 73, 73, 73, 73, 74, 75, 75, 75, 76, 76, 76, 76, 78, 78, 79, 80, 82, 91, and 98.

Figurę 6 displays a histogram of these raw fill-volumes, and the four parts of Figurę 7 display histograms for performance indices based upon