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RELIABILITY MODELS. WHY? Modeling frameworks found in simulation studies: – Military combat hunter-prey, sensor or comm coverage, epidemiology, chaos.

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Presentation on theme: "RELIABILITY MODELS. WHY? Modeling frameworks found in simulation studies: – Military combat hunter-prey, sensor or comm coverage, epidemiology, chaos."— Presentation transcript:

1 RELIABILITY MODELS

2 WHY? Modeling frameworks found in simulation studies: – Military combat hunter-prey, sensor or comm coverage, epidemiology, chaos – Queuing networks Communications networks, factory operations, work processes, stages of life – Reliability models Actuarial, highway, computer networks, failure of interdependent components

3 BASICS Component starts new & functional Lifelength is random with known distr & param Failure to functional: repair (taking random time) COMPONENT

4 MEASURES F(t) = P[system fails before t] f(t) = d/dt F(t) = P[failure at “about” t] P[system functions at time t] = r(t) = 1-F(t) E[T] = expected life length h(t) = f(t)/(1-F(t)) = hazard function a 0 = availability (long run, filures & repairs) COMPONENT

5 SYSTEM RELIABILITY COMPONENT SERIES/PARALLEL CONSTRUCTION

6 PARALLEL F(t) = P[T 1 < t] * P[T 2 < t] = F 1 (t)F 2 (t) COMPONENT 1 COMPONENT 2

7 SERIES F(t) = P[T 1 > t] * P[T 2 > t] = (1-F 1 (t)) * (1-F 2 (t)) COMPONENT 2COMPONENT 1

8 SIMULATION ISSUES Input modeling – Data usually come as censored, results of testing – Maximum likelihood method Series/parallel reductions in Excel Repairs make this problem hard enough


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