James J. Filliben
Statistical Engineering Division, ITL
Optical Technology Division, PL
As part of its leadership role in the international optical physics community, the Optical Technology Division (844) of the Physics Laboratory will be conducting an extensive interlab experiment to determine the responsivity (power output) and homogeneity of photo-diodes (= photo detectors).
The photo-diode measurements are non-destructive and so diodes can be reused, rechecked, and recirculated. A serious complicating issues is that the diodes themselves may drift.
This experiment design contends with the usual mix of experimental objectives and practical constraints. The experimental objective is to determine the equivalency of participating labs for the above two responses. Practical constraints include: 1) How many diodes NIST could afford to buy? 2) How many diodes NIST could afford to run as a control? 3) How long the experiment was to last in toto?
Statistical issues involve: 1) How many diodes to send to each lab? 2) How many replicates should a lab run? 3) Exactly what diodes a lab should receive? 4) How many recyclings (the diodes get returned to NIST, remeasured, and redistributed)? 5) Should diodes be returned to the same lab or sent to other labs? 6) How to assess within-lab variability problems? 7) How to assess within-lab drift problems? 8) How to assess between-lab bias problems? 9) How to detect and correct for diode drift?
A series of admissible designs were constructed and evaluated. A metric was formulated to evaluate/score a given design: 1) the number of diodes that a given lab sees; 2) the number of labs that a given diode "sees"; 3) the number of replications of a given diode within a lab; and 4) the total number of physical diodes.
The theoretical "ideal design" will have the property that 1) metric 1 is large (to minimize confounding); 2) metric 2 is large (to maximize between-lab discrimination); 3) metric 3 is large (to maximize within-lab discrimination); and 4) metric 4 is relatively small (to be affordable).
An unconstrained optimzation of all 4 metrics is not possible from a practical point of view-tradeoffs exist. A schematic of the final design is presented on the opposing page.
Figure 20: Experiment design for photo-diode interlab experiment.
Date created: 7/20/2001