## In Weibull++’s usage format warranty folio, how do I choose an interval width for the usage distribution?

The usage format of the Weibull++ warranty analysis folio allows you to use a statistical distribution to describe the amount of usage a product accumulated, instead of the amount of time the product spent in the field (e.g., a warranty based on the number of miles a vehicle accumulated). The interval width of the usage distribution is an estimate for the size of the usage rate intervals. For example, if the usage distribution represents the amount of miles accumulated by a vehicle, and the interval width is 500, then the usage rate intervals are 0 to 500 miles per year, 500 to 1,000 miles per year, 1,000 to 1,500 miles per year, and so on.

The appropriate value for the interval width will depend upon your knowledge of typical product usage levels and your assumptions about the shape of the usage distribution. In general, the interval width should be selected such that when the warranty data are converted into failure/suspension times, sampling errors are minimized. In other words, you want the frequency distribution of the suspensions in the data set to follow the general shape of the assumed usage distribution.

Weibull++ 8 includes a new Interval Width Estimator utility, which shows you a histogram of the frequency distribution of the suspensions in the data set superimposed over the pdf of the usage distribution. The following examples show how the width of the intervals affects the shape of the histogram.

Interval Width = 3,750

Interval Width = 1,000

You can adjust the number of intervals to obtain a shape for the histogram that tracks the pdf well. The utility approximates the value of the interval width based on your input. If you select a width that is too narrow (i.e., many intervals with few suspended units in each interval), the accuracy of the usage values estimated for the suspensions may be insufficient and random variations in the amount of usage may become prominent. On the other hand, if the width is too wide (i.e., few intervals with a high number of suspended units in each interval), there may be insufficient granularity of the suspensions and the data set may not represent the underlying usage distribution. You can view the number of suspensions in each interval by pointing to the interval in the histogram.

Note that the Interval Width Estimator serves only as a guide. To learn more about the usage format of the warranty folio, consult the online user documentation at http://help.synthesis8.com/weibull_alta8/index.htm#estimating_usage.htm or the ReliaWiki portal at http://www.ReliaWiki.org/index.php/Warranty_Data_Analysis#Usage_Format.