Curiosities in choosing system components: a Bayes analysis

A Bayes-decision problem in which the incorrect interpretation of unobservable parameters leads to counter-intuitive choices is introduced. A system is to be built and the engineers in charge must choose between two different brands of components with the same average chances of failure. Results show that under certain conditions, if the system has two components, one should choose the brand whose chance of failure has the largest standard deviation. Moreover, if the system has more than two components, the best choice might depend on the number of components in the system. These counter-intuitive choices, and the value of an informative test, are explained. One must be careful when defining unobservable parameters in modeling situations. Their role in the model ought to be well understood, and the actual average utility to be maximized must be well defined