|A publication of the National Electronics Manufacturing Center of Excellence||May 2004|
Michael D. Frederickson
One method of evaluating component reliability is called Weibull analysis. Weibull analysis is a method for modeling data sets and can be effectively used on failure data. Some common uses of Weibull analysis in electronics are with product life prediction, comparison of product design reliability and as a statistical basis for warranty policies and management of spare parts inventories.
Weibull analysis involves fitting a failure data set to the cumulative distribution function (cdf). The formula for reliability assuming a Weibull distribution is shown below.
The parameter x is the time (or the number of cycles) until failure. The Weibull shape parameter ß indicates whether the failure rate is increasing, constant or decreasing. This refers to the familiar "bathtub curve" scenario as shown below in Figure 3-1 .
A value of ß <1.0 indicates that the product has a decreasing failure rate. This is typical of “infant mortality” and indicates that the product is failing during its “burn-in” period. A value of ß =1.0 indicates a constant failure rate. Usually components that have survived “burn-in” will show a constant failure rate over most of their life. A ß >1.0 indicates an increasing failure rate. This is indicative of products that are in the “wear out” stage.
The Weibull characteristic of product life, called a, is a measure of the scale, or spread, in the distribution of data. Mathematically, a also equals the number of cycles at which 63.2% of the product has failed.
Automation of the data analysis using an Excel spread sheet or by using a reliability program offered by various vendors is the best way to visualize and compare the reliability of different designs or changes in component characteristics. The main advantage of Weibull mathematics is that a straight line can be fitted to a variety of different failure distributions.
An adaptation of the Weibull analysis can be used to look at step-stress testing of capacitors to failure in order to identify differences in design characteristics. Results of the following example can illustrate how the process is performed.
The basic procedure to prepare the data for Weibull analysis is: 
1) The failure voltages are ranked in order from lowest to highest.
2) The proportion of the population that will fail is calculated. This can be done by several methods, with "median rank" being the most popular.
3) Using regression analysis, a best-fitting straight line is drawn through the points as plotted for Lot A (Figure 3-2) and Lot B (Figure 3-3). The Beta and Alpha parameters were also calculated and are shown in Table 1-1.
Beta is a shape parameter, and since values for both lots are significantly over 1.0, this indicates that there is an increasing failure rate and that they are most likely "wear out" models. Neither lot showed a problem with infant mortality. The Alpha parameter indicated that there is approximately a 3.4 volt difference in the distribution of data between lot A and lot B, again showing that lot B has a more robust characteristic.
In conclusion, the Weibull analysis shows its main strength in its versatility. Depending on the parameters’ values, the Weibull distribution can approximate an exponential, normal or skewed distribution. Microsoft Excel, as well as other specialized software packages, can often be used to do the statistical and regression analysis needed to analyze Weibull data.
2) Marshall, Jim, "A Surge Step Stress Test for Tantalum Capacitors", KEMET Tech Topics, KEMET Electronics Corp., 1995.
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