Under Cupboard Halogen Lamps don't last long

[EFLImpudence]

Also -

Is/was the (P/Q)¹² derived from anything other than trial and error?

In other words,

was a lamp that had been designed for 240V then tested at 245V and found to only last 78% as long?

240/245 = 0.98 - mmmmm.
0.98² = 0.96 - no
0.98³ = 0.94 - no ... etc.

0.98¹² = 0.78 - that's it!

Did they just keep clicking until it arrived at 0.78 or was there another way?

 

[JohnW2]

There is an aircraft level of safety, so-called six nines, which is a 99.999% likelihood that the aircraft will not fail during its mission length.
In principle you can work backwards from this 50 hours to figure the mean time between failures of these lights.
If the bulb MTBF is 50 hours there is only a 1/e (.37, 37%) chance of succeeding for a 50 hour mission and a 90% chance for a 5 hour mission.

John W2 When you get a minute

Hmmm - what do you want - the concept, the answers or the maths (or maybe all 3!)?

For many types of components (and organisms), for much of their lifetime the risk of failure follows a roughly exponential distribution – i.e. if you plot the probability of failure against time (the probability that failure will have occurred by that time), the curve starts off very ‘flat’ and becomes progressively steeper and steeper as time goes on. If you think about the lifespan of humans, that should make sense - the longer it is since you were born, the more likley it is that you will not have survived to that point in time, and that risk accelerates as time since birth gets high. The ‘mean time between failures’ (MTBF) is more-or-less what it says – the average (‘expected’) time taken for failure to occur. Because of the shape of the curve (with very flat early portions – i.e. very low probability of early failure), that MTBF will be greater than you might expect. If, for example failure was almost certain by, say, 100 hours, the MTBF might be 70 hours or more. Again, thinking of human life, very few get beyond 100, but the average life expectancy ('MTBF') is something approaching 80 years.

If one assumes that exponential distribution, one can do calculations like Porque did. As he said, with an MTBF of 50 hours, there’s about a 37% chance of not failing by 50 hours, and about a 90% chance of not failing by 5 hours. If he wanted that 99.999% probability of not failing during a mission, he would only be able to have a mission of about 0.0005 hours (about 1.8 seconds)

Working the other way, which is what I think he was talking about, if one wanted a 99.999% probability of the component not failing during a 50 hour mission (do they fly missions that long – would need lots of refuelling ), then one would have to have a MTBF of around 5,000,000 hours. For a 99.999% probability of the component not failing during a 10-hour mission, the MTBF would have to be about 1,000,000 hours.

If you want to know the actual maths (which isn’t all that complicated), just let me know.

Having said all that, it is totally flawed if one takes components straight from the manufacturer (after all the usual testing) and fits them to the aircraft. Most manufactured components (and most organisms, including humans) exhibit a very early phase of relatively very high failure rates (‘teething problems’, perinatal deaths etc.), before the curve settles down to its main exponential part. If one wants Porque’s very demanding level of certainty, one therefore has to run the component ‘on the bench’ for long enough to get beyond that ‘early failure phase’ (and hence weed out any of those ‘early failures’) before fitting it to the aircraft.

The other ‘flaw’ is that inherent in any probabilistic situation. The fact that there is, say, a 99.999% probability of a component not failing during the first 10 hours of service obviously does not mean that it cannot fail two minutes after the aircraft takes off. That’s the nature of probability. People win lotteries!

Hope that helps.

Kind Regards, John

 

[333rocky333]

John, you are amazing

 

[JohnW2]

Also - Is/was the (P/Q)¹² derived from anything other than trial and error? In other words, was a lamp that had been designed for 240V then tested at 245V and found to only last 78% as long?
240/245 = 0.98 - mmmmm.
0.98² = 0.96 - no
0.98³ = 0.94 - no ... etc.
0.98¹² = 0.78 - that's it!
Did they just keep clicking until it arrived at 0.78 or was there another way?

I would assume that it was far more general than that, not the least because the process you have described would only give an answer which was specific to the two voltages one had chosen (240V and 245V in your case), and hence could not necessarily be extrapolated to other voltages. However, I presume that it was determined empirically.

I can but speculate, but I imagine what they will have done is taken a pile of roughly identical lamps and determined their survival times over a wide range of voltages (hopefully several tested at each voltage). They would then have a curve of lifespan vs. voltage and, by mathematical modelling, determine what mathematical function/equation was fairly close to that curve. I'm sure that the 'true' answer would be a function much more complex than (P/Q)¹², but I guess that (if it is correct) that was deemed to be close enough as a 'rule of thumb'.

[P.S. how did you get that superscripted '1'? - I had to copy/paste yours ]

Does that make sense?

Kind Regards, John

 

[EFLImpudence]

Windows character map - system tools.

 

[JohnW2]

John, you are amazing

Nothing particularly amazing. We all have different backgrounds, knowledge, experience, educations etc. - mine are perhaps just a little more 'many and varied' than some people enjoy

Kind Regards, John

 

[mfarrow]

We have 6 MR16 downlights in the bathroom and 5 G4 capsules in under-capinet holders in the kitchen. All are 20W.

The voltage into the house rarely goes lower than 245V, and often peaks above 253V.

The kitchen lights have had maybe 2 dozen lamps replaced in 3 years, the bathroom has had 3 in the same time period.

I have known no reasonable difference between cheap bulbs and expensive bulbs.

 

[ban-all-sheds]

For many types of components (and organisms), for much of their lifetime the risk of failure follows a roughly exponential distribution

And many follow a bathtub curve.

 

[ban-all-sheds]

On reflection (and having now done some sums), that 50% might not be far off - I had forgotten how little reduction in voltage would be necessary to get a 10% reduction in brightness ...

But don't forget that dimming halogen lamps tends to shorten their lives.

 

[JohnW2]

For many types of components (and organisms), for much of their lifetime the risk of failure follows a roughly exponential distribution

And many follow a bathtub curve.

Indeed - in fact, the great majority of things do, to a lesser or greater extent. As I went on to say:

Most manufactured components (and most organisms, including humans) exhibit a very early phase of relatively very high failure rates (‘teething problems’, perinatal deaths etc.), before the curve settles down to its main exponential part.

[for the wider readership, that initial high failure rate, prior to the exponential phase, results in a 'down and up' curve that looks a bit like the cross-section of a bathtub).

Kind Regards, John

 

[JohnW2]

On reflection (and having now done some sums), that 50% might not be far off - I had forgotten how little reduction in voltage would be necessary to get a 10% reduction in brightness ...

<graph of light output against power consumption>

Since that graph shows the relationship between light output and power, it actually very much under-states the very strong relationship between light output and voltage - since (if one assumes constant resistance) power is proportional to voltage squared - i.e. a graph of light output against voltage (which is what I was talking about) would be even more 'dramatic' (Porque suggested that light output was proportional to V^3.5, which sounds credible).

[P.S. you've made the thread too wde for my laptop screen again ]

Kind Regards, John

 

[Porque223]

@EFLImpudence, look up accelerated life testing.

One way to do MTBF is to test many, many light bulbs for a week or so and count the failures, then the MTBF is 168 hours/(# of failures). This method is not without controversy.

MIL-STD-217 deals with reliability and according to http://en.wikipedia.org/wiki/Dennis_Lindley their methods are flawed.

There is also 'burn-in', to weed out infant mortality.

 

[JohnW2]

One way to do MTBF is to test many, many light bulbs for a week or so and count the failures, then the MTBF is 168 hours/(# of failures). This method is not without controversy.

A major problem with what you and I have written about reliability, MTBF etc. is that it has necessarily been a very serious over-simplification of the situation.

The sort of calculations which you (and I) have done, only really relate to relatively early failures (but not very early, 'infant failures'), since the exponential relationship only exists in the 'middle' part of the ('bathtub') curve, between 'infant failures' and 'wearing out failures' - and throughout that middle portion, the 'failure rate' is assumed to be constant (that's what lwads to the exponential curve).

If one is talking about that middle, exponential, part of the curve, where 'failure rate' is assumed to be constant then, yes, one can estimate MTBF on the basis of very short periods of testing - since one would expect to see exactly the same number of failures if one tested, say, 1,000 items for 200 hours (about 1.2 weeks) as one would see if one tested 20 items for 10,000 hours (a bit over a year).

Such an approach is fine for safety critical situations etc (and is hence widely used by the military and aerospace industries), since, in such situations, one would never dream of leaving a component in service until it got anywhere near the 'wearing out phase' - so one is therefore only interested in that 'middle' exponential (constant 'failure rate') part of the curve. However, I'm very much less convinced that such an approach is applicable to things like lamps in domestic service. They are generally left in service 'until they die', and that is often long after the 'middle' part of the curve (and well into the 'wearing out' phase). Calculations based on MTBF, and assuming the exponential curve, are therefore pretty meaningless in relation to the likely lifespan of things such as lamps in domestic service - because of the accelerated, non-exponential, late phase, they are likely to die far sooner than would predict from the MTBF.

If you look around the internet forums, you'll find countless examples of people being confused by this, perhaps most commonly in relation to hard drives. The MTBF for them is often reported as around 500,000 hours (i.e. about 57 years), and people rightly say that they don't believe that hard drives have that long an average lifespan! An MTBF of 500,000 means that, for the first few years (after 'infant failures') the failure rate of a pile of drives will be about 1.75% per year (see below**), but after that first few years (long, long before 57 years!!), 'wearing out' kicks in and annual failure rate becomes very much higher.

[** given 1 year = 8760 hours, with an MTBF of 500,000 hours, the expected annual failure rate is 8760/500,000 = 0.0175 = 1.75%]

Kind Regards, John