Exponential Conditional Reliability A Paradox

[Andrew Comons]

Elsewhere on this very fine web site is a derivation of the "Exponential Conditional Reliability" equation which states that regardless of previous accumulated age, the reliability of a system is only dependent on the duration of the present mission, i.e., no "memory" of what occurred prior to the present mission.
I fully understand the arithmetic of the derivation, but not the principle. According to the theory, I could momentarily shut a system down in the middle of a mission, turn it back on and expect the same initial probability of success as the start of the mission. Can anyone explain this paradox??
Thanks in advance

[Dr. Dave Olwell]

That is correct. It is a consequence of the constant failure rate assumed when one uses the exponential distribution. The probability of failure in a future time interval is independent of the age of the product.

The reason this seems counter-intuitive to you is that most real systems are not well modeled by a constant failure rate.

Dr. Dave

[Pantelis RS]

As an FYI and inline with Dr. Olwell’s comment, this is explored and explained in the most recent issue of ReliaSoft’s Reliability Edge Magazine (http://www.reliasoft.com/newsletter/4q2001/index.htm) article titled “Limitations of the Exponential Distribution for Reliability Analysis (with Exponential and Preventive Maintenance Example)”. An online copy of the article can be found at: http://www.reliasoft.com/newsletter/4q2001/exponential.htm

[tom c]

Thanks to the information and theory available on this site I am willing to agree that we who have relied so heaviliy on the exponential reliability form have been less accurate than we could have been. However, transitioning to the idea of applying some form of a Weibull distribution is not easy. Are guidlines available to estimate beta, based on system complexity and type? The value of beta will be necessary in the very early stages of design to estimate the total test time for budget and schedule planning.