Claim Game 

Copyright ©2014 by Paul Niquette. All rights reserved.

What is your explanation?
1.     Length of Flight................................... Longer vs Shorter
2.     Destination Airport............ North vs South,  East vs West
3.     Arrival Time.....Daytime vs Nighttime, Evening vs Morning
4.     Season .....................Summer vs Winter, Spring vs Autumn
5.     Weather ..................................Hot vs Cold, Rain vs Shine
6.     Something Else
As described in the puzzle formulation, a certain large airline company 50 years ago conducted a  Grand Experiment, which called for withholding baggage to facilitate  measurements of the time interval between flight arrival and first “complaint”  in Baggage Claim.  An astonishing bimodal distribution was found.

As depicted below, an interpretation of the Actual Distribution is that statistically two distinct populations were acting in superposition.  One population accounts for about 70% of the total number of measurements and appears to conform reasonably well to the Projected Distribution in the hypothesis, with its mode at 45 minutes after arrival. 

The remaining 30% of the measurements are shown above as the Discovered Population, having its mode at 65 minutes after arrival.  Another exclamation point may be appropriate, but let’s save it for the actual discovery.

Of the five factors offered by the puzzle, none were determined by Terminal Operations to be the explanation.  The data from the Grand Experiment was organized in what we call today a 'database' which could be disaggregated on a "computer," using special software, which in 1964 took some doing.  The statistics associated with each factor were analyzed and found to account for spreading the interval measurements longer and shorter with no correlations evident – in both populations. 

For example, long-duration flights produced both earlier and later complaints.  Same for short-duration flights. 

One variable was not controlled:  the time when 
the conveyer system was turned on at each airport!  

If the conveyer system with its carousel in Baggage Claim was inadvertently powered up early, arriving passengers will apparently stand there watching and waiting without complaining – for an additional 20 minutes.  One might suppose, therefore, that the carousels should always be turned on before the first passengers arrive in Baggage Claim.  Doing that would effectively eliminate the 70% of cases in Projected Distribution and add them to the 30% of cases in the Discovered Population as indicated here…

Finally, as shown below, the cumulative distribution for the Discovered Population tells an interesting story... 

Notice with the carousels turned on, as much as 20 minutes can be added to the available time for baggage handling without producing complaints.
Caution is advised.  Terminal Operations for that airline did take advantage of the "Proposed Service Coverage," thereby exploiting the "pacification" effect of running empty conveyer systems.  The airline realized considerable savings in requisite resources at every airport.

As a consequence, though, there was a risk.  Neglecting to turn on the conveyer system for a given flight could result in a 60% chance of producing passenger complaints for that flight.

Solvers who are interested in the history of this puzzle
are invited to read The Grumble Factor.

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