Deming, Wald and Boyd: cutting through the fog of analytics

This article is a quick appreciation of some of the statistical, analytic and philosphic techniques of Deming, Wald and Boyd. Many of these techniques have become pillars of modern industry through the sciences of statistics and operations research.

We start with W. Edwards Deming. Deming was a statistician who designed many of the production methods of post-war occupied Japan. Deming’s work on quality quantification, measurement and continuous improvement formed the fundamental basis of Japan’s later rise as a respected manufacturing super power. Many of the further improved techniques were later imported into the United States as “eastern wisdom.” However, some of the lesser ideas were perverted by eager followers into destructive cargo-cult rituals like “six sigma” (we must remember that it was the depth and power of Deming’s ideas that attracted the imitators).

One of Deming’s most fundemental ideas was the “PDCA loop.”


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The PDCA loop is cycle of conceptual and analytic effort that sequences repeatedly through the stages Plan, Do, Check and Act. The cycle starts with a plan and the next cycle’s plan is influenced by results of the previous cycle. The explicit Check and Act steps show the presumption that the Do step will always need measurement and correction. This cycle is designed to help mitigate Clausewitz’s observation that “no campaign plan survives first contact with the enemy.” Deming’s idea is essentially the systematic application of the scientific method (“propose/test”- or Francis Bacon’s Novum Organum of 1620) to adaption and implementation of plans.

While Deming was teaching planning and “statistical process control” to boost US wartime production a number of other statisticians were having great success in developing reactive strategies. One of the best stories is that of Abraham Wald. Wald became interested in allied aircraft mortality during World War II. He prepared a number of studies and charts of surviving aircraft, tabulating where bullet and shrapnel damage was most extensive. He could, for example, combine inspections of many returning bombers to determine where the returning bombers had the most damage (say the bulk area of fuselage and the leading edges of the wings):


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Wald then had the genius idea of proposing additional armor on the parts of the aircraft that never showed any hits on surviving aircraft (reasoning that aircraft routinely took damage everywhere so the undamaged areas in surviving aircraft must be the areas more often damaged in the unobserved, non-returning lost aircraft). From the above diagram we might propose to add more armor near the pilots, engines and trailing control surfaces. Wald later published sophisticated statistical techniques for imputing the distribution of hits (and therefore the distribution of vulnerabilities) on the unobserved aircraft: “A Method of Estimating Plane vulnerability Based on Damage of Survivors,” Abraham Wald, Center for Naval Analyses (1943).

This art of reactive observation was later systematized by Colonel John Boyd. Boyd invented what he called the “OODA loop.”


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This loop cycles similarly to Demings’s through a pattern of Observe, Orient, Decide and Act. The OODA loop differs from the PDCA loop in that it assumes a world that looks back and adapts against your actions. Boyd added ideas of tempo and pace such as “short cutting the loop” (skipping from act to orient or even act to decide) to adapt faster than nature or than your enemy.

Boyd is also famous for applying his and Wald’s ideas in the design of the A-10 Warthog. The A-10 is a unique non-stealth, sub-sonic close air support plane. It is considered one of the ugliest things to every fly. The A-10 was not state of the art when it was introduced but it was scientifically designed for survival in the style of Wald. The engine intakes are partially protected by the wings, there is extra titanium armor around the pilot and a primitive direct lever control system in addition to the traditional hydraulics. The A-10 is known for its “lingering ability” or ability to stay near troops under fire to deliver support. It has also allowed pilots like Major Kim Reed-Campbell to fly for an hour and return to base after losing pieces of wing and all hydraulics. Here is a picture Reed-Campbell inspecting her damaged A-10 in 2003 after safely landing:


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Deming, Wald and Boyd were able to move statistics and analytics beyond description and use mathematics for prescription. The techniques they developed for planning, measurement and reasoning remain relevant to this day.


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