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Musa-Okumoto Logarithmic Model

The failure intensity is:

Musa-Okumoto Logarithmic Model

Belongs to the mean value function

Musa-Okumoto Logarithmic Model

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

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.


  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., Musa-Okumoto Logarithmic Model, 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.

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