# Estimating MTBF Based on L10 Life

The Reliability Analytics Toolkit L10 to MTBF Conversion tool provides a quick and easy way to convert a quoted L10% life to an average failure rate (or MTBF), provided that an educated guess can be made regarding a Weibull shape parameter (β). For example, an L10% life of 15,500 hours is shown in the Weibull probability plot  below (green line). For a population of these devices, what average failure rate should be used?  The average failure depends on the underlying failure distribution and any renewal that may take place over time. With an L10% life and an estimate for the Weibull shape parameter, β, the underlying failure distribution is completely defined.  For example, if the L10% life is quoted as 15,500 hours and β is estimated to be 2.15, the Weibull characteristic life (η) has to be approximately 44,000 hours (red dot). This is because defining β defines the slope of the line in the Weibull plot below.  So, if know one point (L10 life) and the slope, you can determine any other point.  Of special interest is the Weibull characteristic life.  The characteristic life is the point where 63.2% percent of the population will fail, regardless of the Weibull shape parameter β. Therefore, defining L10% life and β defines η, and thus the underlying Weibull failure distribution.

In the L10 to MTBF Conversion tool, enter the estimated β value of 2.15, the given L10% life of 15,500 hours, and any maintenance interval for item renewal. The renewal time is that time when the item is renewed to “as good as new.”

The resulting average failure rate is then output, as shown in the picture below. For these inputs, the hazard varies between 0 at “time zero” to approximately 45 at the five year point, with average failure rate of 18.77 FPMH. The item is renewed at five years and the process starts over again.

Thus, a 15,500 hour L10% life translates into approximately a 50,000 hour MTBF, assuming a  five year renewal process.

References:

1. Bazovsky, Igor, Reliability Theory and Practice
2. http://www.barringer1.com/wdbase.htm, database of typical Weibull shape and characteristic life parameters.
3. 3. O’Connor, Patrick, D. T., Practical Reliability Engineering