Question 5. Consider n components of a system having independently exponentially distributed lifetimes so that Xn...

Question 5. Consider n components of a system having independently exponentially distributed lifetimes so that Xn ~ exp(θ)

a) For a single component, find the reliability to time t1 + t2 given that the component has already lived past time t1. Why is the constant failure rate referred to as the “memory-less” property?

b) For the series of n components, find an expression for Rs(t). What is the mean lifetime of the system?

Expert Solution

orchestra answered 1 year ago

Consider n components of a system having independently exponentially distributed lifetimes so that Xn ~ exp(θ)...

Consider n components of a system having independently exponentially distributed lifetimes so that Xn ~ exp(θ) a) For a single component, find the reliability to time t1 + t2 given that the component has already lived past time t1. Why is the constant failure rate referred to as the “memory-less” property? b) For the series of n components, find an expression for Rs(t). What is the mean lifetime of the system?

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