An Equipment Failure Probability Density Function May Not Excite You, But Its Great Insights Into Your Equipment Failures Will

Equipment failures can appear to be random events. When historic failure events are charted on a graph they show you the Failure Probability Density Function curve for those events.

You see the spread of frequency over which the events occurred. These distribution curves contain a lot of useful intelligence about what happened to the equipment from the operating and maintenance strategies and practices used in an organisation.


Slide 13 – Plot Historic Failures During an Equipment’s Operating Service Life and Get Its Greatly Insightful Failure Probability Density Function Curve

Such a plot is called a Failure Probability Density Function, or a Failure Density Distribution Curve

Historic failures of an asset when charted against a critical variable create distribution curves of the event frequency. An example is in the slide above. It shows the number of failures of a paperclip against the number of cycles to break the clip. The technical name for these curves is a Failure Probability Density Function, also called a Failure Density Distribution Curve.

During the Plant Wellness Way EAM training course we get the participants to break a paperclip in any way they wish. This creates a situation where many random stress events occur because each person is allowed to fail their paperclip in any way they want—be it by bending, by twisting, or some combination of those two actions. The participants count the cycles to failure and we plot those on the graph. The graph shows 26 historic failure points. The spread of points forms a Failure Probability Density Function curve. It extends from the first break at four cycles to the break that occurred at 41 cycles.

There is important intelligence to be extracted from the Failure Probability Density Function in the graph. We know that the material-of-construction and the design of the paperclip are the same for everyone. The paperclip design and construction are not variables, they are given quantities that never change. The only variable in the activity is the way people broke their paperclip. One person used an aggressive approach that broke their clip in four cycles. Most folk’s paperclip-breaking-procedure led to a spread between 10 cycles and 20 cycles to failure. The person that achieved 41 cycles to failure must have induced much less stress into the paperclip than anyone.

The individual procedures used by the 26 participants produced the failure outcomes in the Failure Probability Density Function graph. The person who got 41 cycles to failure used a very different procedure than the person who got just four cycles to failure, or to the people who got between 10 to 20 cycles to failure. The real variable that caused the failures were not the people, it was the procedure that each person used.

This is a hugely important understanding in equipment reliability improvement: the procedure used is a variable. That is a foundational insight in the Plant Wellness Way EAM methodology.


This slide is a companion to the new Industrial and Manufacturing Wellness book. The book has extensive information, all the necessary templates, and useful examples of how to design and build your own Plant Wellness Way enterprise asset life cycle management system-of-reliability. Get the book from its publisher, Industrial Press, and Amazon Books.

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