forum 9: week of 12 March: Fisher and the design of experiments
Nicole, Does the above chart copy, and the associated text copy that follows below, that are copied from the experiment described on page 248 of the Boeing Advanced Quality Sytem Tools document, satisfy your concept of significance test methods, and the significance test methods of Deborah Mayo, and Sir Ronald A. Fisher
Robust design: testing process parameters Parts in a heat-treat process were experiencing unpredictable growth, causing some parts to grow outside of the specification limits and be rejected as scrap. It was surmised by the engineering team that irregular growth was due to the orientation of the part in the oven and the part’s location in the oven. Since it was desirable to heat treat a maximum number of parts in each oven load, it was important to be able to determine a set of heat-treat processing conditions that would result in minimum growth for heat-treated parts in both a horizontal and vertical orientation, and at both the top and bottom locations in the oven.
Four process factors were identified: hold temperature, dwell time, gas flow rate, and temperature at removal. The team defined two settings for each of the process factors. The experiment used eight runs of the oven, as shown in figure 2.7 (a fractional factorial design, that is, a particular selection of half of the 16 possibilities defined by all combinations of the process factors at two settings). For each oven run, parts were placed at both the top and the bottom of the oven and in both orientations.
The experimental results indicated an unsuspected effect due to oven location, with parts in the bottom of the oven experiencing less growth than those in the top of the oven. The analysis indicated that a particular combination of hold temperature and dwell time would result in part growth that is insensitive (or robust) to part orientation and part location. Furthermore, the experiment indicated that temperature at removal did not affect part growth, leading to the conclusion that parts could be removed from the oven at a higher temperature; thus resulting in savings in run time.
Unless I have access to the analysis of variance (ANOVA) table, I cannot comment on the last paragraph (pertaining to what the results indicated, or the conclusion that was drawn from the experiment). Also, I should mention that ANOVA (e.g., see http://www.stat.columbia.edu/~gelman/research/unpublished/econanova.pdf) is a separate technique in itself, distinct from the type of significance tests that Fisher introduced in Chapter 2 of his book (i.e., the reading for this past week). To answer your question, page 248 of the Boeing Advanced Quality System Tools document does not satisfy my concept of significance test methods insofar as it not relating at all to the significance test introduced in my presentation earlier this week. I hope this helps. If you have any more questions pertaining to the example you gave me in the Boeing Advanced Quality System Tools document, then I suggest we do not communicate on this forum but in other ways that will not disturb the focus of the discussions in this course.