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I am interested to learn if it is possible to use a survival analyses approach when, in the middle of the study, there "gaps."

Specifics: does oiling a motor increase the "time until death" or failure of the motor. The wrinkle is that the motors are shut off for some period of time each day. There are, as a result, two "times": 1) the amount of time the motor was running and 2) the amount of clock time the motor existed in an operational state (running or not-running but not broken; this is important because oil can influence the state of the motor even if it is not running. That said, oil is less effective as time goes on whether the motor is running or not).

Here are the relevant facts:

  • some motors are oiled (randomly in time) and others are never oiled
  • motors generally only last for a maximum of several hours before failing, however it is possible for them to go for several days
  • motors are shut down and restarted twice per day
  • fact: benefits of oil decrease with time

Example: imagine two brand-new motors.

-Motor 1 is turned on at 1:00

-Motor 1 fails at 2:00

*Motor 2 is turned on at 2:45

*Motor 2 is powered down at 3:00

*Motor 2 is oiled at 4:00

*Motor 2 is powered on at 6:00

*Motor 2 fails at 6:45

Both motors only ran for 1 hour however it will appear that Motor 2, the oiled motor, lasted for 4 hours in the survival model.

Can a survival model be used in this case? If so, how should one deal with the gaps? (I use R)

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    $\begingroup$ There is a concept of time on test. In that case you just use the cumulative time on test (i.e. simply ignoring the gaps) for calculating the time until failure or the time until censoring. $\endgroup$
    – Michael R. Chernick
    Aug 17, 2018 at 2:26
  • $\begingroup$ for maintenance purpose, the military trained us in the concept of "run time" or cumulative operating hours. Gaps in equipment use had little or no effect on spare parts replacement before failure, but run-time hours most certainly did so. $\endgroup$
    – James Phillips
    Aug 17, 2018 at 10:48
  • $\begingroup$ @james: Thank you so much for your response! Unfortunately, the example with motors I gave is a simplified version of a more complex problem. In my case time-since-oiling makes a difference regardless of if the motor was running or not... $\endgroup$
    – trilobite
    Aug 17, 2018 at 22:42
  • $\begingroup$ @MichaelChernick: Thank you also for your response! As I mentioned in response to James Phillips, because the time-since-oiling matters do you think it would make sense to right censor any instance when the motor is first turned on and then is turned off rather than fails? Similarly, I could right sensor when a (previously running) motor was powered back on to the time it fails? $\endgroup$
    – trilobite
    Aug 17, 2018 at 22:57

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