Several years ago, I was flying the C-17 across the Atlantic Ocean in the middle of a cold winter night. Almost a hundred US Army troops, complete with combat gear, were catching a hop to Europe on their way downrange. We were several hundred miles southwest of Iceland when we received the first indication that this wouldn’t be a normal night.
A master caution light illuminated. We quickly began to diagnose the situation by searching our panels and systems, but the master warning light–indicating a more serious problem–quickly followed, and its aural tone sounded like a claxon in our headsets. Our engine instruments showed a failure on engine number two, the left inboard engine. As we began an emergency descent to the altitude indicated in the emergency performance pages of our mission computer, we tried to figure out what caused the failure, to no avail.
There was no malfunction indicated–the engine RPM was simply rolling back to zero.
I began to advise the passengers, using the public address system, to return to their seats. I apprised them of the situation and informed them that we would attempt to restart the engine once we leveled at the lower altitude, and that the loss of an engine would result in a slower cruise speed. Our arrival into the airbase would be delayed by forty minutes.
As we leveled off and began to reset systems on the failed engine, in order to attempt a restart, the master caution and warning lights illuminated again–a second engine was failing. This time, it was engine number one, all indications rolling back to zero.
The thought of the icy Atlantic far below me crossed my mind–with only one failed engine, we could have easily limped all the way to Europe on the remaining three operating engines. A second engine failure was really beginning to worry me.
Because we only had troops and no heavy cargo, though, the mission computer emergency performance pages indicated that we could still maintain altitude and make it to Europe. Again, I relayed the information to the loadmaster and passengers, indicating a further delay–our arrival would be eighty minutes late. There was some grumbling amongst the soldiers about the delay–but at this point, I don’t think they fully understood the gravity of the situation.
I began to suspect that the problem was fuel contamination–this is one of the few possibilities that can cause multiple jet engines to fail with no other symptoms. As I started to explain my thoughts to the copilot, the third engine failed.
With a frantic voice, I announced this fact to the loadmaster over the public address system. (He knew implicitly that I needed him to begin emergency preparation actions in the cargo compartment.)
As I turned around to see if the loadmaster heard me, looking for his thumbs up from the back, I saw two troops peering in to the flight deck and overhead them talking, seemingly concerned about the delay. The older one turned to the soldier next to him and said, “if that last engines fails, we’ll be up here all night.”
When (Statistical) Predictions Fail
Our friend, the unsuspecting solider, realized that each time an engine failed, the delay was forty additional minutes. We can all see the ridiculous proposition of using this prediction to estimate the aircraft’s flight time for a third and fourth engine failure–airplanes don’t stay up very long when they become gliders. This fact is obvious.
This silly story suggests a fundamental rule about analytical tools of mathematics and statistics (ATOMs): With a limited knowledge of ATOMs, we can easily fall into the same trap.
It is very easy to misuse, abuse, or apply analytical principles to the wrong situation. You and I would not use a Nashville street map to navigate our way across the Atlantic Ocean by air, nor would we expect to stay airborne with no propulsion. However, it is easy to find examples of statistical “buffoonery” equivalent to this silly story, and we must sharpen our own intellectual saws to defend against them.
Where Do We Go From Here
How do we find our way then, when we are exploring the unknown, blazing a trail into uncharted territory? How do we apply elementary statistical principles to transform uncertainty into decisive action? What is to prevent us from making a preposterous application of ATOMs when we deal with very complex situations, those in which our intuition fails?
This question is not much different from that faced by Chuck Yeager before he ever broke the sound barrier or Neil Armstrong as he took that first step on the moon. Neither of these men, nor anyone around them–with hundreds or thousands of highly educated, very scientific people on these teams–none of these people knew what to expect. Or did they…?
ATOMs is a monthly column that introduces analytical tools of mathematics and statistics and illustrates their application. To read more about ATOMs, you can read Where Do We Go From Here, or view the online workbook here.
There is a legend (and a delightful poem) about six blind men who examine an elephant. The first finds the elephant’s side and declares that an elephant is like a wall. The second feels its tusk and compares it to a spear. And so on and so forth it goes…with observations of its trunk, ears, tail and knee.
