0.3 Jack: the good zoroastrian, by nozer d. singpurwalla

(This module helps introduce The Good Book: Thirty Years of Comments, Conjectures and Conclusions, by I.J. Good . The book is available for purchase from the Rice University Press Store . You can also visit the Rice University Press web site .)

Irving john good: the man

Humata, Hukhta and Hvarshta are the three guiding principles of Zoroastrianism, a philosophical conception of deity that came out of Persia before the timeof Christ. Translated from the ancient language of Avesta , these words mean Good Thoughts, Good Words, and Good Deeds.

Jack Good, a mathematician, a statistician, a computer scientist, a philosopher, and a chess expert, is well known for his good thoughts. Oneonly need read Good (1983) on Good Thinking: The Foundations of Probability and Its Applications . On the matter of Good Words, those of us fortunate to know Jack cannot recall having heard him utter an unkind wordor a disparaging comment about anyone. A possible exception could be Good (1990), wherein he calls R. A. Fisher “... a great practitioner but amediocre philosopher.” Finally, on the matter of Good Deeds, what can be better than a Good-like deed of generously citing the work of othercolleagues, no matter how inconsequential the work? Jack therefore fully deserves the accolade of being called “The Good Zoroastrian,” orparaphrasing Rudyard Kipling, “You are a better Zoroastrian than I, Irving John.”

Jack good: an appreciation

David Banks wanted of me an “appreciation” of Jack's work. By this I am presuming that David wanted me to reflect on the impact of Jack's writingson reliability, survival analysis, and quality control, broadly labeled the assurance sciences. I am grateful to David for this opportunity because it motivated me to re-visit some of Jack's writings, beginning with his earliest on Probability and the Weighing of Evidence (1950), to one of his latest on “Subjective Probability” (1990). Sandwiched betweenthese is an impressive list of over two thousand articles and books, some of the more notable ones (to me) being “Rational Decisions” (1952), “A Theoryof Causality” (1959), “The Estimation of Probabilities” (1965), “A Subjective Evaluation of Bode's Law” (1969), “Dynamic Probability, ComputerChess, and the Measurement of Knowledge” (1977), “Some History of the Hierarchical Bayesian Methodology” (1981), and then of course suchtitillating titles as “Quantum Mechanics and Yoga” (1963), and “Good Saw That It Was God(d)” (1975). But since my present charge is to focus onthe assurance sciences, I will, in what follows, say a few words about this.

Traditionally, and up until recently, the point of view adopted by most reliability theorists and life data analysts is that reliability is aprobability. The fact that there could be different kinds of probability has been an alien concept, and continues to be so in survival analysis. In Good(1965), the different interpretations of probability are carefully articulated. These are: chance or propensity (a physical probability),psychological probability, subjective probability, and credibility (or a logical probability). In Good (1990), the focus is on subjective probability;also given there is a dendroidal classification of the different kinds of probability and usages of the term. A consequence of these writings,together with those of de Finetti, Savage, and Lindley, is that reliability is now seen as an unknown chance (or propensity), and one's uncertaintyabout the reliability, expressed as a personal probability, is labelled survivability [cf. Singpurwalla (2006), “Reliability and Risk: A Bayesian Perspective”].

This distinction between reliability and survivability has far-reaching ramifications. For one, it makes survivability assessments dynamic. Foranother, it brings into play the hierarchical nature of probabilities (first via chance, and then via a subjective probability imposed on chance).Finally, it imparts a sense of truthfulness in the context of life-time assessments, because in actuality one ends obtaining an item'ssurvivability, not its reliability. The former is personal and subjective; the latter is abstract and unobservable. Hierarchical probabilities alsocome into play when assessing network and system integrity. Good has commented on the hierarchical and dynamic nature of probability as early as1965 and perhaps earlier.

The impact of Good's other works on the assurance sciences pertains to acceptance sampling based on life-test data using the weighing of evidenceconcept via Bayes' Factors, information gleaned from life test data and the design of life testing experiments, and the classification of interdependentfailures as being cascading or causal. Good's discussion of rational behavior and the utility of a distribution [Good (1968)]takes a tangible form when one needs to apportion reliability between the nodes of a networkand when one needs to choose systems with competing designs. For a flavor of these topics, see Singpurwalla (2006) and the references therein.

All in all, Good's writings are so plentiful and so diverse that one canfind their impact on a wide variety of topics in mathematics, statistics, operations research, philosophy, psychology, parapsychology, physics, andeven yoga! For this broad body of work, Jack deserves deep appreciation from us allfor his contributions to our learning.