Predicting the time to failure of a complex system is basically the aim of reliability analysis. I mean If at the end of the day I cant tell when a system would fail its stupid of me to study that system.
Frankly I think the probability approach is not suitable because it takes data with a bias. MTBF must fit a probability curve. We twist and turn trying to fit a curve with substantial data falling out. Its not a nice way for PROGNOSIS. If I cant tell you weather the toss will be a heads or tails , What use is of the word '50%' probability.
My hypothesis of diagnosing a fault is this:
Suppose we line up the times between failures on a strainght line . With breaks consisting of up times and solid lines consisting of failure times , can we find a pattern? Can we find some scaling? Can we find repetative patterns of small failures inbetween big failures? Can we find a fractal dimension of the pattern of failures? and Can we extrapolate this? I mean if I find that the MTBF line of say a pump is say of .76 dimension, can I make a guess about how it is going to be in next ten years?
My central question is this...Is there a pattern or scaling in failure times? It could be possible that the pattern squezes as we near the death of the system but central idea is this..IS there a pattern? Is there a rythm to way things go down?
I dont kno..but I strongly feel that there is . there is a song of systems going duff..Its a song with not-random beats. Its a song we havent analysed. We hear just random beats and try and fit a curve ..but fitting a curve doest take into account the sequence :
For example say the time to failures is : 1,3,4,2,3,2,3,3,3
Now by probabilty analysis the points are just points,they are taken and fitted around a weibull distribution and parameters are taken out. Where do we take into account weather it was 1>3>4>2..? or 1>4>3>2?
What matters is cumulative time and time to failure..We never study the pattern. do we?