50%25 Confidence is no confidence

[Geoff]

[Originally Posted: 6/6/00--Transferred by ReliaSoft Moderator]

The two preceding postings refer to calculating 50% confidence bands. My understanding is that this is effectively "no confidence" because one has the same confidence (50%) of the band having excluded the population parameter as having included it.

Could someone confirm/reject the above? When, if ever, is there is any value in using 50% confidence intervals?

[RS Support]

[Originally Posted: 6/7/00--Transferred by ReliaSoft Moderator]

50% confidence represents the "best guess" estimate of your parameters, reliability, time to failure, etc. There isn't really a "50% confidence band" because the values for the upper and lower bound would be same as the value being estimated. In other words, the estimate of the parameter etc. represents the 50% confidence and the bounds can be widened from there. For example, for a certain dataset the estimate for the B10 life is 21.8 hours. This is the 50% confidence estimate for the B10 life. We can calculate the bounds around this estimate the 60% 2-sided confidence bounds around this estimate as being (20.1 hours, 23.6 hours). That is to say we are 60% certain that the "true" value of the B10 life for this product is between 20.1 hours and 23.6 hours.

[Geoff]

[Originally Posted: 6/8/00--Transferred by ReliaSoft Moderator]

At the risk of getting in over my head, I take it that what you are referring to is that the "best guess" estimate of your parameters, reliability, time to failure, etc falls at 50% within the expected sampling distribution of population parameters. i.e. you have 50% confidence that the population parameter may be below your estimate and 50% confidence that it may be above.

However, you have "no" confidence that your estimate is precisely correct.

Just as there is a there are "60% 2-sided confidence bounds around this estimate" there are also 50% 2-sided confidence bounds. The values for the upper and lower bound would NOT be same as the value being estimated. My understanding is that one can indeed generate 2-sided confidence bounds from 0% (the initial estimate of the parameter) to 100% (+/- the mathematical limits of the parameter e.g. +/- infinity).

Is this correct?

[James H. Vallem]

[Originally Posted: 6/21/00--Transferred by ReliaSoft Moderator]

My experience with this subject is that a lot of confusion exists around the terminology. First of all, there is subjective confidence ("I'm very confident the new design will meet the reliability requirements"), which is NOT what we are dealing with. We're talking about objective, statistical confidence, as it relates to estimates of some value (say, reliability at some point in time), based on testing a group of parts (the entire group is a "sample") from the entire population of parts. If we tested the entire population, we would know the reliability, and would not need to use statistical confidence at all. So confidence is really a sampling issue (parts don't have confidence!). If we were to test a different sample, we would get a different estimate of the true (but unknown) population value, as well as different confidence lines.

There are upper and lower confidence bounds, each of which defines a one-sided interval. You would expect the true (but unknown) population value to be above a 75% lower bound about 75% of the time if you kept repeating your testing plan with a new sample each time. This is an example of a ONE-sided interval.

A TWO-sided interval (or band) falls between a lower and an upper bound. You can make a 50% two-sided interval as the values between the 75% lower (one-sided) bound and the 75% upper (one-sided) bound. There is a 75% chance of being above the lower bound, a 75% change of being below the upper bound, and a 50% chance of being between them -- thus, a 50% two-sided interval. This is NOT the same as a 50% lower bound, which is also the 50% upper bound, as well as your "best" estimate of the true (but still unknown) population value.

In the reliability arena, we don't much care if the population reliability is greater than our estimate, but we do worry about the possibility of the population reliability being less than the estimate. That's why with reliability, we generally talk about lower bounds only, that is, one-sided lower intervals. We don't often state that specifically, which is perhaps part of the reason for confusion in this area.

Incidently, if we are using the success-run formula to determine a sample size for success testing, the confidence value used is for a lower bound on the reliability being demonstrated.