Should I treat my data as time series?

Question

I am in doubt whether or not I should treat my data as a time-series. I have a dataset on airplane engines for which I am asked to develop a predictive model for the RUL (Remaining useful life). It contains data on 100 full life-spans of engines.

I have included some actual rows of the dataset to help with interpretation. The dataset contains data of 100 engines. The interpretation of the data rows are as follows. For example, the engine with engine id 1, was working for 192 cycles and then it failed. So, at cycle 191 the RUL for engine with engine id 1 was equal to 1. At cycle 190 the RUL for engine with engine id 1 was equal to 2.

1 1 -0.0007 -0.0004 100.0 518.67 641.82 1589.70 1400.60 14.62 21.61 554.36 2388.06 9046.19 1.30 47.47 521.66 2388.02 8138.62 8.4195 0.03 392 2388 100.00 39.06 23.4190  
1 2 0.0019 -0.0003 100.0 518.67 642.15 1591.82 1403.14 14.62 21.61 553.75 2388.04 9044.07 1.30 47.49 522.28 2388.07 8131.49 8.4318 0.03 392 2388 100.00 39.00 23.4236  
1 3 -0.0043 0.0003 100.0 518.67 642.35 1587.99 1404.20 14.62 21.61 554.26 2388.08 9052.94 1.30 47.27 522.42 2388.03 8133.23 8.4178 0.03 390 2388 100.00 38.95 23.3442  
1 4 0.0007 0.0000 100.0 518.67 642.35 1582.79 1401.87 14.62 21.61 554.45 2388.11 9049.48 1.30 47.13 522.86 2388.08 8133.83 8.3682 0.03 392 2388 100.00 38.88 23.3739  
1 5 -0.0019 -0.0002 100.0 518.67 642.37 1582.85 1406.22 14.62 21.61 554.00 2388.06 9055.15 1.30 47.28 522.19 2388.04 8133.80 8.4294 0.03 393 2388 100.00 38.90 23.4044 

...

1 188 -0.0067 0.0003 100.0 518.67 643.75 1602.38 1422.78 14.62 21.61 551.94 2388.31 9037.91 1.30 48.00 519.79 2388.23 8117.69 8.5207 0.03 396 2388 100.00 38.51 22.9588  
1 189 -0.0006 0.0002 100.0 518.67 644.18 1596.17 1428.01 14.62 21.61 550.70 2388.27 9044.55 1.30 48.08 519.58 2388.33 8117.51 8.5183 0.03 395 2388 100.00 38.48 23.1127  
1 190 -0.0027 0.0001 100.0 518.67 643.64 1599.22 1425.95 14.62 21.61 551.29 2388.29 9040.58 1.30 48.33 520.04 2388.35 8112.58 8.5223 0.03 398 2388 100.00 38.49 23.0675  
1 191 -0.0000 -0.0004 100.0 518.67 643.34 1602.36 1425.77 14.62 21.61 550.92 2388.28 9042.76 1.30 48.15 519.57 2388.30 8114.61 8.5174 0.03 394 2388 100.00 38.45 23.1295  
1 192 0.0009 -0.0000 100.0 518.67 643.54 1601.41 1427.20 14.62 21.61 551.25 2388.32 9033.22 1.30 48.25 520.08 2388.32 8110.93 8.5113 0.03 396 2388 100.00 38.48 22.9649  

Obviously, for this dataset it is very easy to obtain the RUL; One can simply count back from the last cycle. However please note that this data contains only full life-span data; so engines that have been taken out of circulation already. The new engines for which my model will be predicting are not yet at the end of their lives, and therefore I should make a model to predict the RUL. I have now two options to create a model. The first one is I treat every row seperately, which results in 20630 rows of different sensor settings/sensors, from which I build a model to predict the RUL on new (unseen) engines. The other option is I treat the data as time-series, since observations within an engine (So with the same engine id) are clearly related. This would lead to 100 engines with time-series data.

Can somebody explain me what would be the difference between the two options, and which one is most favourable in this case? TLDR; Should I treat the data as a time series or not?

Answer 1

This is a longitudinal study dealing with "survival data". At first instance I would suggest looking at mixed-effects model; this will directly account for the "within-engine" clustering effects. Following that, it would be reasonable to progress with joint modelling techniques that combine longitudinal and survival data. Joint models improve on traditional survival models as they use the longitudinal observations of various explanatory variables to predict the final event of interest (in this case a machine taken out of circulation). Ultimately, this is a time-to-event analysis (i.e. a survival analysis). As a separate avenue one might want to consider an accelerated failure time model instead of a "standard" Cox proportional hazards model used in most joint modelling techniques.