Recently a colleague sent me a published copy of the first CRE exam. Scanning through the document suggests that a few things have changed and many have not changed at all. I often comment my enjoyment of the reliability engineering profession, as it doesn’t change too fast and even I can keep up.
Occasionally, I’ll pull a question from this vintage exam and work out the solution with you. Here’s one that caught my eye this morning.
25. The reliability of a device comprised of various parts functionally in series is the
1. sum of the probabilities of the unreliabilities
2. product of the unreliabilities
3. sum of the reliabilities
4. product of the reliabilities
5. sum of the combinations and permutations
The first thing I think of is the function, ‘sum’ or ‘product.’ Reliability is the probability of success over some period of time, or the fraction still functioning. Also, reliability is defined as between zero and 1, there for adding reliabilities is not appropriate. And, as a gut check, for a series system, the system reliability is less than any of the individual component reliability.
Addition is a common practice for failure rates or lambda. Today we often have FIT rates, and also use addition to tally up the system failure rate. Therefore, I’m ruling out the three answers with ‘sum.’
That leaves number 2 and 4.
Unreliability is 1 – reliability and reflects the probability of failure over a point in time. Since we would have to convert the result back to reliability, this probably isn’t the right response. The product of unreliability is one technique that is useful for parallel system calculation.
Therefore, let’s look at answer 4. If you know the basics about series system reliability calculations, then this selection is obvious. We multiply reliabilities for a series system, add failure rates, and since the question is looking for reliability and not unreliability, we select answer 4.
There is a post with more information about series system reliability here.
Related:
Common formulas (article)
Exponential Reliability (article)
CRE in Application (article)
Of course there is the important unstated assumption of independence among the failure times of the individual components.
I recall, perhaps 30 years ago, a colleague from the College of Engineering brought me a copy of some of the questions from the CQR exam to ask my opinion on some of the questions. I recall that at least a couple of the questions (in order to be answerable) had the unstated assumption that the underlying failure time distribution was exponential. This was at a time when it was beginning to be well known among engineers that correct use of the exponential distribution was rare in describing the failure time distribution of system components. I hope thatr those faults have been removed by now.
HI Bill,
Thanks for the note. And, alas, many of the issues related to unstated assumptions and exponential distribution, independence, etc. are still around and in full force. As you may know the site, nomtbf.com, is devoted to clearing up mis-understanding and point out dangers.
I think a major problem with the CRE exam is the seeming inability to test at this assumption level. The mark of great reliability professional is to understand the implications of all assumptions including in the analysis.
cheers,
Fred