Determine MTBF Given a Weibull Distribution
First off, not sure why anyone would want to do this, yet one of the issues I’ve heard concerning abandoning the use of MTBF is client ask for MTBF. If they will not accept reliability probabilities at specific durations, and insist on using MTBF, you probably should provide a value to them.
Let’s say you have a Weibull distribution model that described the time to failure distribution of your product. You’ve done the testing, modeling, and many field data analysis and know for the requestor’s application this is the best estimate of reliability performance. You can, quite easily calculate the MTBF value.
As you know, if theβ parameter is equal to one then the characteristic life, η, is equal to MTBF. If β is less than or greater than one, then use the following formula to determine the mean value, MTBF, for the distribution.
You’ll need the Gamma function and the Weibull parameters. The further β is from one, the bigger the difference between η and MTBF.
You can find a little more information and background at the article Calculate the Mean and Variance on the CREprep.wordpress.com site.