An intense discussion among LinkedIn UAV group members involves several important topics, including the source of a one-out-of-a-billion requirement for probability of a mishap.  The source is thus far unidentified.

I can shed some light on the genesis of another related requirement.  From within RTCA SC-195 (GPS Integrity) Working Group for FDI/FDE (Fault Detection and Isolation / Fault Detection and Exclusion) in the 1990s, parameters were used to establish the Missed Detection requirement as follows:
* From records obtained as far back as possible (1959) there were over 333 million flight-hours nationwide between 1959 and 1990.
* In the (inevitably imperfect) real-world, the maximum allowable number of hull-loss accidents in 30 years cannot be specified at zero; so that maximum allowable number was set to one, producing 3 billionths per flight-hour
* The number used for mean time between loss of GPS integrity was 18 years.
* Probability of an unannounced SV (satellite) malfunction is then  1 – exp{ -1/18x365x24 } = approx. 6 millionths per hr per SV.
* Since 6 SVs are needed for FDE, that probability is multiplied by 6, producing 36 millionths per hour as the probability of an unannounced SV malfunction in any SV among those chosen for FDE.
* Probability of an undetected unannounced SV malfunction is then  36 millionths per hour multiplied by Missed Detection probability.
* With an incident/accident ratio slightly below 1/10, a value of 0.001 for Missed Detection probability satisfies the 3 billionths per flight-hour requirement.

None of this is intended to signify thoroughness in the genesis of decisions affecting flight safety requirements. Neither demands for rigorous validation in early 1994, nor an attempt to facilitate meeting those demands — via replacement of GO/No-GO testing by quantitative assessment — met the “collective-will” acceptance criteria. History related to that, not reassuring, is recounted on page 5 of a synopsis offered here and page 127 of GNSS Aided Navigation & Tracking. The references just cited, combined with additional references within them, address a challenging topic: how to substantiate, with high confidence, satisfaction of very low probabilities.  There are methods, using probability scaling, not yet accepted.

Returning to the original question that prompted this blog: It might be uncovered — possibly from some remote source — that the number with a mysterious origin was supported, at one time, by some comparable logic.

Elmen C. Quesinberry

Earlier this year I wrote a belated tribute to a well-known pioneer in strapdown. Now I must write another tribute, even more belated, to a pioneer who was less well-known — but with a legacy equal to any other whose work helped mine to come alive.

Over three decades (Feb 1961 to Nov 1993) I was a full-time employee of Westinghouse (division names varied from AirArm to DESC to …) — but what I want to express here is first of all a salute to many of the people whose paths crossed with mine. That word “many” is no exaggeration; one recollection that stands out occurred during a chance conversation with Tim Gunn, at about lunch hour, near the cafeteria. Over and over again, seemingly everyone-&-their-brother walking by, was saying “Hi” to me. Tim was flabbergasted at how many people I knew, whether they were from the shop (in some of those cases, from barbershop quartet or other music activities) or — in many other cases — from one department or another of engineering.

In recollection it is crystal clear that, during that time period, I was privileged to work with many of the best. That includes names like Joe Dorman, Jim Mims,  … And when position/velocity/acceleration gains had to be set for track at lock-on over 7 octaves of range with 16-bit words, George Axelby and John Stuelpnagel helped show the way — and who could forget the Schafer/Leedom/Weigle triumvirate or, from TIR, Bill Hopwood or, from software, names like Heasley + Landry + Kahn + Clark (who as a techie was among the best, as was another from his group — working with me on A12 when John crossed into management) — plus others, too numerous to mention. Many of the latter names are more obscure, it is realized; in some ways that’s the most important part of this effort, to give credit where credit is overdue. Of all the best-and-brightest named &/or unnamed here, no one stands higher in my memory than Elmen C. Quesinberry. His contribution to Westinghouse’s collection of achievements over time is realized by only very few. I guess what’s important is that he realized it himself; he earned every bit of his salary, and much more.

This revisit-of-history isn’t intended to imply that all was sunshine + roses; in fact, we encountered some major opposition. No need to go into detail now, but many had peripheral (or less) understanding. I made my peace with those long ago and have no desire to retract it. For doubters, flight-validated results appear elsewhere on this site. Enough said; of central importance here is the lasting legacy of a truly great engineer. Elmen C. Quesinberry, a true Christian gentlemen, was an outstanding engineer whose collaboration gave me benefits unsurpassed by any other over three decades at Westinghouse.