War games

These first encounters with probability theory occurred when I was attending lectures at a college situated in the middle of a British Government research establishment. Part of this five year course, involved every student spending three month periods in various of the research establishment laboratories.

Not long after my card suit races experience, I was assigned to a laboratory where they were testing electronic components under various environmental conditions. Batches of components would be left for hours on shaker tables. They'd be left for days in humid ovens or in deep freezes.

Before and throughout the different environmental exposures, the components were tested to see if the extreme environmental conditions caused any failures. By testing a hundred similar components at a time, the number of failures gave a direct indication of the probable failure rate for the type of component being tested.

A probability of failure was measured in this way, for every type of component used in a piece of equipment installed in a fighter plane. It was then possible to use probability theory to work out the overall probability that one or other of the components would fail during a critical mission. Such a failure would render the equipment inoperable, so, this calculation was vital to the strategic use of aircraft in a war operation.

The chief scientific officer in charge of this laboratory took the trouble to explain the logic of these tests and calculations. He explained that, for some pieces of critical electronic equipment, there were so many components that although the failure rate of any particular component was low, adding them all together would result in the probability of a fatal failure occurring within as little as two hours. "It is something like a chain being as strong as its weakest link", he explained. "The first component to experience a random failure would result in the failure of the whole equipment".

He further explained that missions expected to last for longer than two hours would have to arrange for spare equipment to be taken along to allow substitution if and when failure occurred (note: the piece of equipment being tested at the time was a radio set; and this was at a time before transistors and microchips: when notably unreliable thermionic tubes were used in all electronic equipment).

Being acutely conscious of my recent experience with the card suit races, I pointed out that an unfavourable run of luck could see equipment failing much sooner than two hours and in some cases even the back up equipment failing as well. "Surely", I asked, "To ensure that the mission would not fail, there would have to many duplicate backups to allow for a bad run of failures during a particular mission".

Patiently, the scientific officer explained that the probability of double failures would be taken into consideration. They could calculate, using probability theory once again, the likelihood of double equipment failures and so predict how many of a squadrons planes would likely be out of action through this effect. The mission would thus be planned with more planes than were necessary to allow for those that were expected to become inoperable through random failure of components.

He then proceeded to explain how this anticipation of probable failure rate allowed a mission to be planned to ensure that a correct number of planes would be in operation over a target area, even though the target might be many hours of flight time away.