The expected number of failures in a Weibull reliability model can be estimated from the Weibull cumulative hazard, with the basic two-parameter form commonly written as \(H(t)=(t/\eta)^\beta\), where \(\beta\) is the shape parameter and \(\eta\) is the scale parameter. For \(N\) independent units, the expected number of units that have failed by time \(t\) is instead \(N[1-e^{-(t/\eta)^\beta}]\). The correct formula depends on whether you mean expected cumulative failures in a population or the expected number of recurrent failures from a repairable system.
What Is the Weibull Distribution?
The Weibull distribution is widely used in reliability engineering to model time-to-failure, life data, and component reliability. It can represent decreasing, approximately constant, or increasing failure behavior depending on its shape parameter.
