Calculations for Exponential Distribution

Failure Rate

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CDF

Reliability

Note: In GE Digital APM, there is only one MTBF parameter (η)for exponential distribution.

MLE

Where, is the failure time of component i, i=1,..., r or the censoring time of component i, i=r+1,..., n. If there is no censoring (complete data), r = n and the last term in the Likelihood function disappears.

Least Square

Suppose, and

Using these transformed data, we can obtain the parameter estimate using the following equation: