# Weibull Analysis in Excel with QI Macros

## Use Weibull Analysis with Failure Rate Data

Not all data is normally distributed (i.e., bell-shaped). Weibull analysis is especially suited to failure rates (e.g., how long does a TV, PC, ball bearing or whatever operate before failing). Weibull analysis works well, even with small samples (less than 20).

Just select your failure data and choose **Histogram Weibull** from the QI Macros menu. The macro will prompt for spec limits, create a histogram and calculate Weibull and process capability metrics for you. Here's an example of Ball Bearing failure rates. Failure rates peak at 81.86:

### Weibull Distribution

The Weibull distribution can approximate many other distributions: normal, exponential and so on. The Weibull curve is called a "bathtub curve," because it descends in the beginning (infant mortality); flattens out in the middle and ascends toward the end of life.

**Shape**- The Shape parameter (slope = 2.10) describes the failure rate:

- Shape < 1 is a decreasing failure rate (infant mortality)
- Shape > 1 is an increasing failure rate (wear-out failures)
- Shape = 1 means random failure rate (independent of age)

- approximates the exponential distribution

- When Shape = 1, MTBF(Mean Time Between Failures) = Scale parameter - Shape = 3.6 approximates the normal distribution

**Scale**- The Scale parameter (characteristic life) is the age at which 63.2% of units will have failed.

There are several methods for estimating the scale and shape parameters:

- Maximum likelihood estimation (MLE) - QI Macros uses this method (July 2013).
- Least squares (rank regression).
- Probability Plotting - QI Macros creates a Probability Plot on the data worksheet to assist in determining when a certain percent of parts will have failed. In the example below, 10% of the parts will have failed by time 27.