Night flying in the mountians in a cessna 150,

"Ron Garret" wrote in message
...
[...]
and have determined the number of trials (flights) in advance.

No. That statement is true regardless of whether N is known.

Knowing that your chances of having an engine failure are 1-(1-P)^N isn't
very useful information if you don't know what N is.

It's not a useful calculation for the purpose of this discussion.

That is a matter of opinion.

Tell me how I'm going to use the information then. Since you think it's so
useful.

No one knows before they've started flying how many flights they will
make
in a lifetime.

That is not necessarily true. My mother, for example, knows exactly how
many flights in GA aircraft she will make during her lifetime: zero.

For a person who will never make a flight in a GA aircraft, why in the world
would I consider at all how many engine failures she'll experience?

It's like trying to figure out how many live births I'll have in my
lifetime. Duh.

And just in case you're too dimwitted to extrapolate from this example
I'll spell it out for you: one can *decide* on the basis of this
calculation to stop flying after some number of flight because flying
more than that results in a cumulative probability of disaster that
exceeds one's risk tolerance.

Only if they make that decision prior to flying those hours. I haven't met
a single person who has ever done such an analysis of their flying career.
I doubt one exists.

If you can find me one, I'll stand corrected. Otherwise, you are without a
point (I'll refrain from any implication that YOU are dimwitted, just 'cause
that's the kind of guy I am).

Pete

Morgans wrote:
"Matt Whiting" wrote

Sure, if the

engine quits it will be ugly, but that is a very remote possibility and
one that I accept every now and again if the trip is important enough.


Matt


Do me a favor, and settle a bet. Would you mind telling us how old you are?

45. Who won the bet? :-)


Matt

wrote:

On Fri, 25 Feb 2005 17:16:35 -0800, Ron Garret
wrote:


That's true, but the longer you fly (or play the lottery) the closer
your probability of experiencing an engine failure (or a lottery win)
some time your career approaches 1.

Of course, you might have to fly/play for a *very* long time before that
probability actually gets close to 1, but sooner or later it will be 1
to any desired degree of accuracy. So the statement "fly long enough and
you will experience an engine failure" is pretty close to being true.
The question is how long is "long enough."

rg



This just ain't so.

Every time you play the lottery, it's like the first time you ever
played it.

It doesn't matter whether you won a jillion yesterday, or haven't won
in 50 years, or never played. The odds are exactly the same.

Yes, for every given play you are correct. However, Ron is correct that
in aggregate, someone who plays more often has a higher overall chance
of winning at some point than a person who only plays once in their
lifetime. At least I think that is the point he was making.


Matt

wrote:

On Fri, 25 Feb 2005 21:27:54 -0500, Bob Noel
wrote:


On Fri, 25 Feb 2005 17:16:35 -0800, Ron Garret
wrote:


That's true, but the longer you fly (or play the lottery) the closer
your probability of experiencing an engine failure (or a lottery win)
some time your career approaches 1.

Of course, you might have to fly/play for a *very* long time before that
probability actually gets close to 1, but sooner or later it will be 1
to any desired degree of accuracy. So the statement "fly long enough and
you will experience an engine failure" is pretty close to being true.
The question is how long is "long enough."

rg


This just ain't so.

Every time you play the lottery, it's like the first time you ever
played it.

It doesn't matter whether you won a jillion yesterday, or haven't won
in 50 years, or never played. The odds are exactly the same.

The odds of winning any particular lottery are (approximately) the same.

The odds of winning a lottery sometime in your lifetime are much better if you
play the lottery every day of your life (assuming a nice long life) than if you
just play the lottery once.

--
Bob Noel
looking for a sig the lawyers will like


Approximately? They are exactly the same.

Of course your odds of having an engine failure with two engines is
double of what it would be with one, and quadruple with four.

No, because the engines aren't completely independent of each other.
Most have at least one common system (fuel).

Matt

In article ,
"Peter Duniho" wrote:

"Ron Garret" wrote in message
...
[...]
and have determined the number of trials (flights) in advance.

No. That statement is true regardless of whether N is known.

Knowing that your chances of having an engine failure are 1-(1-P)^N isn't
very useful information if you don't know what N is.

As I pointed out before (and will point out again later on -- watch for
it) it is useful because you can choose your risk tolerance and then
solve for N (assuming of course you know P).

It's not a useful calculation for the purpose of this discussion.

That is a matter of opinion.

Tell me how I'm going to use the information then. Since you think it's so
useful.

I just did, but here it is again: if you believe that the risk of an
engine failure on any particular flight is P1 and you are willing to
accept a lifetime risk of experiencing an engine failure at no more than
P2, then you can use these two numbers and the formula for cumulative
probability to solve for N. You can then choose to stop flying after N
flights.

No one knows before they've started flying how many flights they will
make
in a lifetime.

That is not necessarily true. My mother, for example, knows exactly how
many flights in GA aircraft she will make during her lifetime: zero.

For a person who will never make a flight in a GA aircraft, why in the world
would I consider at all how many engine failures she'll experience?

It's like trying to figure out how many live births I'll have in my
lifetime. Duh.

No, because in my mother's case the number is zero because she has
*chosen* to make it zero. (Perhaps I should have made it clear that I
am a pilot, and so my mother can, if she chooses, go flying with me any
time she wants.) Your analogy is faulty because you cannot choose to
get pregnant.

And just in case you're too dimwitted to extrapolate from this example
I'll spell it out for you: one can *decide* on the basis of this
calculation to stop flying after some number of flight because flying
more than that results in a cumulative probability of disaster that
exceeds one's risk tolerance.

Only if they make that decision prior to flying those hours. I haven't met
a single person who has ever done such an analysis of their flying career.
I doubt one exists.

Just because you are not personally acquainted with someone who has
chosen to avail themselves of the utility of this calculation does not
mean that such people do not exist. (And even if it were true that no
one in the world has availed themselves of this utility (which it isn't)
that would not prove that the calculation is without utility.)

If you can find me one, I'll stand corrected.

I very much doubt that. You seem not to have noticed, but we've
actually already done that experiment, and you stubbornly cling to your
position regardless.

Not only are you wrong, but you are clearly, demonstrably, and
self-evidently wrong. If you don't believe me, you can actually *do*
this experiment. Don't play the lottery or go flying until your engine
fails. Get a die. Pretend that rolling a six means your engine has
failed. Now ask yourself: are you more likely to roll a six if you roll
it once, or if you roll it 100 times? Clearly if you roll it once your
chances are one in six, and if you roll it 100 times the chances of
rolling AT LEAST ONE SIX in those hundred trials is very close to 1.
(0.99999998792532652 to be precise).

Otherwise, you are without a point

Whereas you seem to have one on the top of your head.

(I'll refrain from any implication that YOU are dimwitted, just 'cause
that's the kind of guy I am).

Hey, if the shoe fits, I'll wear it. Will you?

rg

In article ,
"Peter Duniho" wrote:

wrote in message
...
[...]
Of course your odds of having an engine failure with two engines is
double of what it would be with one, and quadruple with four.

Only approximately. The only reason doubling (or quadrupling) the number of
engines doubles (or quadruples) the chance of an engine failure
(approximately) is that the failure rate is so low. For example, if the
failure rate were 50%, a doubling of that would cause you to expect an
engine to fail each flight (a 100% chance of failure), when in fact the
chance is actually only 75%.

It is somewhat ironic that you should be the one to point this out in
light of the argument we are having in another branch of this thread
because this is precisely the point I was making. The condition of the
probability of failure on a single trial P being low is precisely the
condition that allows you to approximate the formula for cumulative
failure 1-(1-P)^N as P*N. If you think about it, there is absolutely no
difference in the risk calculation between making one flight with four
engines and four flights with one engine (except insofar as the
probability of failure for one engine over four flights are not quite
independent of each other if it's the same engine each time).

rg

In article ,
wrote:

On Sat, 26 Feb 2005 11:45:19 -0500, Matt Whiting
wrote:

wrote:

On Fri, 25 Feb 2005 17:16:35 -0800, Ron Garret
wrote:


That's true, but the longer you fly (or play the lottery) the closer
your probability of experiencing an engine failure (or a lottery win)
some time your career approaches 1.

Of course, you might have to fly/play for a *very* long time before that
probability actually gets close to 1, but sooner or later it will be 1
to any desired degree of accuracy. So the statement "fly long enough and
you will experience an engine failure" is pretty close to being true.
The question is how long is "long enough."

rg



This just ain't so.

Every time you play the lottery, it's like the first time you ever
played it.

It doesn't matter whether you won a jillion yesterday, or haven't won
in 50 years, or never played. The odds are exactly the same.

Yes, for every given play you are correct. However, Ron is correct that
in aggregate, someone who plays more often has a higher overall chance
of winning at some point than a person who only plays once in their
lifetime. At least I think that is the point he was making.


Matt


no, I think his point is that you are more likely to have an engine
failure tomorrow if you have flown 10,000 hours than if you have flown
10 hours.

No, that is NOT the point I was making. (And if you thought it was,
would you please point out what I wrote that made you think so? I
obviously need to hone my pedagogy.)

This ain't so.

Indeed. Matt's restatement of my position is correct.

rg

In article ,
wrote:

On Sat, 26 Feb 2005 09:15:41 -0800, Ron Garret
wrote:

Not only are you wrong, but you are clearly, demonstrably, and
self-evidently wrong. If you don't believe me, you can actually *do*
this experiment. Don't play the lottery or go flying until your engine
fails. Get a die. Pretend that rolling a six means your engine has
failed. Now ask yourself: are you more likely to roll a six if you roll
it once, or if you roll it 100 times? Clearly if you roll it once your
chances are one in six, and if you roll it 100 times the chances of
rolling AT LEAST ONE SIX in those hundred trials is very close to 1.
(0.99999998792532652 to be precise).


Let's look at this another way.

Let's say the probability of an engine failure is 1 every 10,000
hours.

Let's assume that I declare that I intend to fly 10,000 hours in my
lifetime. We would probably agree that my chances of an engine
failure in my lifetime approximates 1. A serious betting man would
not bet against my chances of having a failure.

Now let's say my life is half over, and I've flown 5000 hours without
having had my failure. (a perfectly acceptable supposition).

Now I am looking at the rest of my life, wherein I will fly the
additional 5000, hours. The probability of a failure is still 1 every
10,000 hours (nothing has changed with the equipment, etc., to change
the probability)

Therefore, now the chances of having an engine failure during the rest
of my life has DECREASED.

That's right. Just as if you get half-way through your hundred rolls of
the dice without rolling a six, your chances of rolling a six in your
remaining rolls are now less than they were when you started. In the
extreme, if you get through 99 rolls without rolling a six, your chances
of rolling a six on your last roll are just one in six. And if you get
through all 100 rolls without rolling a six your chances of rolling a
six from then on are zero, just as they would have been if you'd never
started rolling/flying to begin with.

Simply put, it's how much flying time you got in front of you, not
behind you, that determines your likelihood of experienceng a failure.

Obviously.

rg

In article ,
wrote:

On Sat, 26 Feb 2005 09:25:40 -0800, Ron Garret
wrote:

no, I think his point is that you are more likely to have an engine
failure tomorrow if you have flown 10,000 hours than if you have flown
10 hours.

No, that is NOT the point I was making. (And if you thought it was,
would you please point out what I wrote that made you think so? I
obviously need to hone my pedagogy.)



rg

This is what made me think so:


"That's true, but the longer you fly (or play the lottery) the closer
your probability of experiencing an engine failure (or a lottery win)
some time your career approaches 1.

Of course, you might have to fly/play for a *very* long time before
that
probability actually gets close to 1, but sooner or later it will be 1
to any desired degree of accuracy. So the statement "fly long enough
and
you will experience an engine failure" is pretty close to being true.
The question is how long is "long enough."

rg"

Well, gee, you and Peter are both making it challenging to frame
respectful responses here. You wrote:

"I think his point is that you are more likely to have an engine failure
tomorrow..."

but that is clearly not what I said. What I said was that you are more
likely to have an engine failure "SOME TIME IN YOUR CAREER". Not
"tomorrow". Big difference.

It's as if I said, "The sky is blue" and you responded "I think the
point he was trying to make is that the sky is green." Well, you're
right, the sky isn't green. But I never said that it was.

Let me try this again:

1. The probability of experiencing an engine failure (or any other
improbable event for that matter) AT SOME POINT IN YOUR FLYING CAREER
goes up the more you fly. It goes up monotonically but nonlinearly
according to the formula 1-(1-P)^N, which asymptotically approaches 1 as
N gets large.

2. The probability of experiencing an engine failure (or any other
improbable event) on any one particular flight does NOT depend on how
often you fly. (This is the point that I think you and Peter have been
trying to make, and with which I have never disagreed.)

3. The sky is BLUE (except lately in southern California).

rg

Running out of fuel is not my idea of "engine failure".


Well, statistically, it is THE reason for engine failure.

--
Thomas Borchert (EDDH)