### Weibull Makes Data Useful

Klaus M. Blache | July 20, 2020

Among other things, a Weibull analysis can determine reliability trends by using a small sample size of data.

What does Weibull mean?

It refers to one of numerous probability distributions that are used to determine the amount of time that something can function. A unique feature of the technique is that it can determine reliability trends by using a small sample size of data about failures and time. It’s adaptable, relatively simple, and offers visual/easily understood graphics.

The Weibull distribution was invented by Waloddi Weibull in 1937 and presented in 1951, with poor acceptance. Eventually, it got traction, was used by the U.S. Air Force (1970s), and later by the automotive industry.

Today Weibull analysis is used in fields such as engineering sciences, biology, operations, fabrication, testing, economics, physics, dentistry, welding, hydrology, insurance, aerospace, safety, and reliability. Software has made once-tedious calculations relatively easy.

In simplest terms, performing a Weibull analysis entails compiling data that represent your life data, then determining which distribution best describes your data. Then add confidence intervals, if desired.

There are several types of plots that can be used to enhance the understanding of your data. A typical Weibull plot is executed on a log-log format on each axis. If the resulting plot is a straight line, then it’s aligned with a Weibull distribution (showing time to failure). The vertical axis generally depicts cumulative percentage failure and the horizontal axis shows life or aging data, i.e., cycles of use, bearing life, airplane landings, miles, parts produced, operational uptime. A line slope that is <1 indicates installation flaws, shipping damage, and other infant-mortality-related failures. A straight line also indicates a single failure mechanism.

A non-straight line is an indication of multiple failure causes. If the slope is >1, then it’s an indication of wear out failures. The slope of the Weibull plot is termed beta (β). If beta is equal to 1, then it depicts random failure. Weibull investigations also depict which type of failure your data represents.

A Weibull Analysis can be used to perform a variety of functions such as establish product warranty periods, flag improper maintenance, identify a poor production run, find component design flaws, pinpoint failure causes, develop maintenance strategies, and predict when spare parts will be needed. Trends from the analyzed data can help improve strategic planning. An analysis can also help you identify your failure types and better understand their frequency. EP

#### Get Started in Weibull Analysis

My colleague, Wes Fulton, is offering a free demo download file of SuperSMITH for Windows, including SuperSMITH Weibull, Visual, and YBath. These software versions have full functionality and can be used to teach Weibull to students, but the demo versions randomly change input data so real data cannot be analyzed. To perform analyses requires a licensed full version. Also available is a free tutorial booklet. Click here to obtain both.

Interested in more? There is a three-day virtual course (October 13 to 15, 2020) that provides a complete overview of Weibull analysis, starting with the basics of performing an analysis and interpreting results. Each attendee will receive the entire SuperSMITH package and a copy of The New Weibull Handbook (latest edition). You can find the course here.

Based in Knoxville, Klaus M. Blache is director of the Reliability & Maintainability Center at the Univ. of Tennessee, and a research professor in the College of Engineering. Contact him at

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