Dear All, we are happy to release our 76th video on Crow AMSAA Model for Reliability Growth. We recommend viewers to watch the following videos before watching this video for better experience:
(1) Homogeneous Poisson Process (HPP) and Nonhomogeneous Poisson Process (NHPP)
(2) Reliability Growth Concepts and Duane Model with Illustration
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Understanding the AMSAA Model
The AMSAA model is used to track reliability within a series of growth testing cycles. Unlike the Duane model, which applies across multiple test phases, the AMSAA model is typically applied to a single test phase.
The core idea is that as design changes are implemented (e.g., at test times S1, S2, etc.), the failure rate (Lambda), which is assumed constant within each stage, reduces between stages. Even though this reduction happens in steps, the model approximates it with a continuous curve.
Mathematical Functions
The AMSAA model is a Non-Homogeneous Poisson Process (NHPP) that uses a power law to model reliability growth:
- Cumulative Number of Failures (M(T)): This is given by the formula M(T)=a⋅Tb, where ‘a’ and ‘b’ are constants, and ‘T’ is the accumulated test time. For positive reliability growth, ‘b’ must be less than 1.
- Instantaneous Failure Intensity Function (ρ(T)): This represents the failure rate at any given moment and is found by differentiating M(T) with respect to T. So, ρ(T)=dM(T) / dT = a⋅b⋅Tb−1.
- Instantaneous MTBF (Mean Time Between Failures): This is the reciprocal of the instantaneous failure intensity function: θI=1 / ρ(T)= 1 / (a⋅b⋅Tb−1).
The constants ‘a’ and ‘b’ are estimated from test data using the Maximum Likelihood Estimate (MLE) method. The specific formulas for ‘a’ and ‘b’ vary depending on whether it’s a time-terminated test (test runs until a target time is reached) or a failure-terminated test (test runs until a target number of failures occur).
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