# How the Weibull Distribution is Used in Reliability Engineering

This article discusses the Weibull distribution and how it is used in the field of reliability engineering.

Reliability engineering uses statistics to plan maintenance, determine life cycle cost, predict failures, and determine warranty periods for products.

This is a common topic that is discussed in all fields of engineering and is seen often in power electronics, in particular. If you have to design a product for space, drugs, or other specialized fields, where subsystem failures can cause mission failure or loss of life, you should study the New Weibull Handbook, on which this article is based.

If you spend some time on reliability engineering, you are sure to come across the Weibull distribution. The Swedish engineer Waloddi Weibull introduced this probability distribution to the world in 1951 and it is still widely used today.

Before you start, you can read my first article introducing the concept of reliability engineering to get some basic information.

### Route failures: the road to Weibull

Product families used in a similar way will fail on predictable timelines. This excludes failures due to external factors (electrostatic discharge, improper handling, intentional abuse, etc.).

Weibull charts record the percentage of products that have failed over an arbitrary period of time which can be measured in startup cycles, hours of run time, driven in miles, and others. The timescale should be based on logical conditions for the product. For example, an oscilloscope could be “run time hours”, while a vehicle instrument cluster could be measured in “highway miles” and a spring programmer in “number of times used”.

Data is recorded on a log-log graph.

##### Figure 1. This time to failure graph shows the percentage of a widget that has failed over time.

The slope of the graph is not linear, but a straight, best-fit line provides a decent approximation.

The slope of this line of best fit, β, describes the Weibull fault distribution.

• β <1.0 indicates infant mortality
• B = 1 means random failure
• β> 1 indicates a wear fault.

(See Chapter 2 of the New Weibull Handbook for more details.)

##### Figure 2

The time to failure of a particular percentage of a product is historically described as the B1, B10, B20 time, etc., where the number describes the percentage of products that have failed. For example, B10 is when 10% of the products have failed.

Some manufacturers use L-times (L1, L10, L20, etc.), where L stands for “service life”. Weibull distributions describe a wide range of products; B is believed to possibly represent “Bearing life”.