I am looking for an equation to establish a confidence level of MTBF in a test environment.
For the exponential distribution:

Two situations must to be considered for estimating confidence intervals:
  • The test is run until a pre assigned number of failures ( r* ) occurs
  • The test is stopped after a pre assigned number of test hours ( t* ) is accumulated 
     

The formula for the confidence intervals is based in the chi - square distribution.
The equations for confidence limits (Exponential distribution) are showing above.