Musa–Okumoto Logarithmic ModeL
The Musa–Okumoto Logarithmic Poisson Execution Time Model is a software reliability growth model designed to predict and analyze software failure behavior over execution time. Like Musa’s basic execution time model, it uses failure data measured in execution time to model reliability improvements as faults are detected and removed.
Functional Form
The Musa–Okumoto model belongs to the mean value function family of reliability growth models. Its failure intensity decreases logarithmically with respect to execution time, making it suitable for systems where fault detection slows down over time.
Key Assumptions
No initial failures
At execution time Ï„ = 0, no failures have been observed:
P(M (0)=0)=1
Exponential decay of failure intensity
The failure intensity decreases exponentially with the cumulative number of observed failures:
- β₀ = initial failure intensity
- β₁ = failure intensity decay parameter (β₀⁻¹ sometimes referred to as the decay rate)
Poisson process
The total number of failures observed by time Ï„, denoted M(Ï„), follows a nonhomogeneous Poisson process (NHPP).
Fault exposure ratio
- The model’s derivation via the fault exposure ratio shows that this exponential decrease implies a per-fault hazard rate with a bathtub-shaped curve — initially high, then decreasing, and finally flattening as faults become harder to find.
