This chapter contains material which you certainly have learned some time ago and which is familiar to you. No doubt, you have met some elements of algebra of events, random variables, distribution function and have heard about binomial distribution. Among the material of this chapter is a fundamental Law of Total Probability which will be used further in our exposition. Maybe, the section of order statistics is new for you. This is not complex but very important material which will be used in introducing a cumulative destruction spectrum. Our advice–ignore the algebra and concentrate on the final results. The last section contains a few topics from statistics. They will be used to evaluate the relative error of Monte Carlo estimation procedures.
Random variables Binomial exponential distribution Order statistics Law of total probability
This is a preview of subscription content, log in to check access.
Samaniego, F. G. (2007). System signatures and their applications in engineering reliability. US: Springer.CrossRefGoogle Scholar
Elperin, T., Gertsbakh, I. B., & Lomonosov, M. (1991). Estimation of network reliability using graph evolution models. Transactions on Reliability, 40(5), 572–581.CrossRefGoogle Scholar
Bertsekas, D., & Tsitsliksis, J. (2008). Introduction to probability (2nd ed.). Belmont: Athena Scientific.Google Scholar
Ross S. M. (2019). Introduction to probability models (12th ed.). Cambridge: Academic Press.Google Scholar