If it was me I wouldn't necessarily have noticed if a few were blown before putting away without doing an inspection (remember, cognitive bias),...
In most contexts, I would plead very guilty to that possibility, but in this particular case, I don't think it's likely. Because sporadic failures (and visible deteriorations) are relatively common, I make a point of inspecting and checking these things before 'putting them away', and label them "for attention" as necessary!
... but anyway I'm not sure the failure modes of overdriven LEDs but maybe they were cracked or something and the storage let the dampness in (stored in the loft?)
Cellar, actually, so probably worse than a loft! However, we're back to those 'unlikely co-incidences' yet again - for cracks/whatever to be present, and to result in dampness/whatever-related failure, in four
adjacent LEDs would not be very likely 'by chance'!
Anyway you are very surprised but actually the law of expectation shows that there will be a lot of one in a hundred events happening, this has been shown to be the case that one in 1000000 events occur very often many times where common factors are at work that people have no idea about before hand! So the chance of 4 blowing is not the same as the chance of one blowing to the power of 4.
Sure - that's basic probability theory. If the probability of one blowing is 1 in N, then the probability of four blowing will only be 1 in N^4 if the events are
totally independent of one another - and, as you say, that often isn't the case (and, as you also say, factors resulting in non-independence are often not known, or necessarily even suspected).
Indeed, at the other extreme, there are plenty of situations in which the events are totally
non-independent. Sticking close to topic, the functioning of each of a number of bulbs in series is totally dependent upon the functioning of others - hence, if the probability of any one bulb in a string of 20 'going out' in a particular time period is 1 in N, then the probability of all 20 going out in that same time period is much greater than 1 in N (far, far, from 1 in N^20 !)....
.... if the probability of any one of the 20 bulbs failing in a given time period is 1 in N (and if failure of an individual bulb is random and independent of failure of any others), then the probability of 20 'going out' in the same time period is actually roughly (I won't bore you with the technical reason for that!) 1 in N/20 (essentially since there are 20 possible events {single bulb failures} any of which can lead to all 20 going out). In other words if the probability of any one bulb failing in a given period were 1 in 100 (1%), the probability of all 20 going out in that period would be roughly 1 in 5 (20%).
However, since you raised these matters of probabilities, it sounds as if I probably have not been clear enough in what I've been saying about my 'surprise', and "my suspiciousness about what appear to be amazing co-incidences" (and, indeed, the reason for this thread) ....
I suppose I should have been more precise but what I've been trying to say is that
IF the failure of individual LEDs
WERE totally random and totally independent of the failure of any other LED, then I would be extremely surprised by that, and suspicious about the apparent 'amazing co-incidence' of what I was observing -
and therefore that it seemed probable that factors (such as some of those you have suggested) were probably at work, such that failure of one LED was
not independent of failure of others. Hence this thread, in an attempt to see if anyone could think of any such factors which I have overlooked.
This is, in fact, essentially the concept which underlies the entire subject of Statistical Inference, which is central to so must research. If it can be shown that the probability of observed facts being 'due to chance' (random and independent events) is extremely small, then the conclusion is that some 'factor(s)' must be responsible for what has been observed. In the case of carefully controlled experiments (like testing a treatment in a particular disease), one does everything one can to think of and control/eliminate all but one factor which might affect the result - so if one is fairly successful in eliminating all but one possible 'factor' (e.g. 'the treatment'), if the probability of the observed result being 'due to chance' is very low, then this is taken to mean that the observed result was probably due to that one known factor (e.g. the treatment).
Kind Regards, John
