Musa-Okumoto Logarithmic Model

The failure intensity is:

Belongs to the mean value function

This is the functional form of the Musa-Okumoto logarithmic model:

Like Musa's basic execution time model, the "Logarithmic Poisson Execution Time Model" by Musa and Okumoto is based on failure data measured in execution time.

Assumptions

1. At time τ = 0 no failures have been observed, i.e., P(M(0) = 0) = 1.
2. The failure intensity reduce exponentially with the expected number of failures observed, i.e., , where β₀ β₁is the initial failure intensity and β₀^-1 is dubbed failure intensity decay parameter.
3. The number of failures observed by time τ,M(τ), follows a Poisson Process.

As the derivation of the Musa-Okumoto logarithmic model by the fault exposure ratio has shown, the exponentially decreasing failure intensity implies that the per-fault hazard rate has the shape of a bathtub curve.