Safety Factor in Light of the Bienaymé-Markov and Chebychev Inequalities

We have amply seen in previous chapters that in order to relate the reliability and the safety factor, one needs the knowledge of the probability densities of the involved random variables. Often, such information is missing. It is shown in this chapter that the celebrated inequalities by Irenée-Jules Bienaymé (1796–1878), Andrei Andreevich Markov (1856–1922) and Pafnutii Lvovich Chebychev (1821–1894) may come to help in finding bounds on the desired probabilities and safety factors. Short biographical notes about Bienayme and Chebychev are given in the Appendix B.