TEXT exercises on Monte Carlo Method AY 2023 2024

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EXERCISE 2 Consider a continuously monitored component with constant failure (𝜆) and repair (𝜇) rates in the table. Assuming a mission time 𝑇 = 1000 ℎ𝑜𝑢𝑟𝑠, write the MC code for the estimation of: 1. The instantaneous availability 2. The time dependent reliability 𝜆=3*10^(-3) h-1 𝜇 =25*10^(-3) h-1 EXERCISE 4 Consider the system in figure composed of three components(A, B, C). Each component can be in two different health states (1-nominal, 2-failed) with exponentially distributed transition times (table) between them. Assuming a mission time 𝑇 = 500 ℎ𝑜𝑢𝑟𝑠, write the MC code for the estimation of: ▪ The time dependent reliability ▪ The instantaneous availability. ▪ The estimators uncertainty 1 2 3 λ 1*10^-3 2*10^-2 5*10^-2 m 3*10^-2 5*10^-2 5*10^-3 EXERCISE 1 Consider the Weibull distribution with 𝛽 = 1,5 and 𝜏 = 1,0 1. Sample N=400 values from 𝑓𝑇 𝑡 2. Verify whether the obtained distribution provides a good approximation of the Weibull distribution. To this aim, you are required to: A. find the empirical probability density function (pdf) of the sampled values in 1 B. compare the empirical pdf found in 2A. with the analytical Weibull distribution 3. Provide an estimate 𝐺𝑁 of 4. Estimate the variance of 𝐺𝑁