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Mis-Application of the Exponential Distribution


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Many basic quality textbooks use the exponential distribution when dealing with reliability problems.  Also, many textbooks often start the solution to a reliability problem with the phrase "assuming an exponential time to fail distribution".  The reason for this is that the exponential distribution is very easy to use.  Reliability problems can be worked quickly and easily, and other distributions are considered too difficult for the beginner.

An important topic in reliability engineering is parameter estimation when there are items that have been tested and have not failed (censored data).  For the exponential distribution parameter estimation when censored data is encountered is a relatively simple task.  For other distributions parameter estimation is extremely difficult when some of the data are censored.  Because of this, many texts describe parameter estimation in detail for the exponential distribution, but neglect to present parameter estimation techniques for other distributions.

An excellent source for the mathematics involved in parameter estimation is the Reliability Engineering Handbook.  This book is easy to read; it focuses on examples and does not contain derivations and proofs.

The exponential distribution is not very useful in modeling data in the real world.  The exponential distribution is only useful for items that have a constant failure rate.  This means that the population has no wear-out or  infancy problems.  Many sources will state that electronics have a constant failure rate, but this is not true in most cases.  Electronics will have a decreasing failure rate if:

  1. there are any manufacturing defects,
  2. there is any damage during shipping,
  3. if there is any damage during final assembly, or
  4. if the final assembly is not done correctly.

Electronics will have an increasing failure rate if they are subjected to environments that induce mechanical failures of the components and the circuit boards.  Examples are vibration, temperature cycling and contamination.

Click here for the technical details of the exponential distribution in Adobe Acrobat format.  For the same article in Microsoft Word for Windows 95 format click here.


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