The Seven Reasons for Non-Linear Weibull Behavior

1. The Bath Tub Curve
A sample in question may be exhibiting one or more of the stages of the “bath tub curve” while it operates on test. This situation applies equally well to electronic or mechanical components or systems. A variety of failure modes are typically exhibited through the life history. The early life failure stage might exhibit a Weibull slope (Beta) of 0.6, followed by a mid-life stage with a slope of about 1.0. The wear phase has a Weibull slope typically greater than 1.5 and sometimes as high as 5.0. Some of the modes associated with early life failures, or infant mortality type failures, but other failure modes are usually associated with middle-life or end-of-life failures, the data can’t be linear. Further work and investigation is typically required to verify this situation, once a non-linear situation is recognized.
2. A Mixed Population
A sample in question may have been drawn from more than one sub-populations. These sub-populations often have distinct failure modes that are exhibited on Weibull graph as an “S-shaped curve” on the Weibull graph. Not all of the “S curves” may be visible due to sample size restrictions or even short test times. An example of the S curve follows.
3. Varying Environmental Conditions
This possibility may occur when test units or field systems operate in different environmental conditions. This is normally inadvertent or accidental and is often not discovered until data is plotted upon the Weibull graph and questions asked. The situation leads typically to a bimodal or multimodal result on the Weibull graph.
4. Mixed-Age Parts
Since most parts and systems do not carry a time clock, we cannot easily tell how old or how aged a part or system may be just by looking at it or putting it on test. Imagine for a moment a collection of aged (already have operated about 500 hours) mixed with new parts and all placed on life test or in operation. The test results would probably look a lot like a mixed population Weibull graph. The difference here is that the age difference is the main reason for differing sub-populations.
5. Three Parameter Weibull
Some parts (or systems) seem to have a natural bias concerning time-to failure. Examples include many material strength situations, car tires, or telephone poles. This situation leads to non-straight lines because of the natural offset present. Once this offset is recognized and corrected by a software program, the curves often straighten out into one smooth line.
6. Odd Distributions
Some distributions do not appear as straight lines on a Weibull graph. The most prominent example is the LogNormal distribution, which often appears as two straight lines which join at or very near 50% cumulative failures. Test this possibility by plotting data on Lognormal plot or another distribution.
7. Mixed Failure Modes
Very different failure modes, if operational during a test time or study period, may lead to unusual lines on the Weibull graph. Each line is usually associated with dominant failure mode. When modes are separated, as is customarily done, each failure mode usually appears as a straight line.

Published in Practical Weibull Analysis Techniques – Fifth Edition by James A. McLinn Published by  The Reliability Division of ASQ – January 2010 ISBN 0277-9633 (available as free download for ASQ Reliability Division Members)

“The Eight Reasons for Non-Linear Weibull Behavior”


Picture © B. Poncelet

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