Abstract
This chapter consists in a short review of survival probabilities based on failure rate and reliability functions, in connection with Poisson processes having a time-dependent intensity.
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Exercise
Exercise
Exercise 12.1
Assume that the random time \(\tau \) has the Weibull distribution with probability density
where \(\beta > 0\) is a called the shape parameter.
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(a)
Compute the distribution function \(F_\beta \) of the Weibull distribution.
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(b)
Compute the reliability function \(R(t) = \mathbb {P}( \tau > t )\).
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(c)
Compute the failure rate function \(\lambda (t)\).
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(d)
Compute the mean time to failure.
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Privault, N. (2018). Reliability Theory. In: Understanding Markov Chains. Springer Undergraduate Mathematics Series. Springer, Singapore. https://doi.org/10.1007/978-981-13-0659-4_12
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DOI: https://doi.org/10.1007/978-981-13-0659-4_12
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Publisher Name: Springer, Singapore
Print ISBN: 978-981-13-0658-7
Online ISBN: 978-981-13-0659-4
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