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# Reliability, maintainability, and safety mathematics

DOI link for Reliability, maintainability, and safety mathematics

Reliability, maintainability, and safety mathematics book

# Reliability, maintainability, and safety mathematics

DOI link for Reliability, maintainability, and safety mathematics

Reliability, maintainability, and safety mathematics book

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## ABSTRACT

This chapter presents basic mathematical concepts considered useful to understand the subsequent chapters of this book. It covers arithmetic mean and mean deviation, Boolean algebra laws, probability definition and properties, probability definition and properties, mathematical definitions, probability distributions, solving first-order differential equations using Laplace transforms, problems, and references.

The mathematical definitions are the cumulative distribution function definition, the probability density function definition, the expected value definition, the Laplace transform definition, and the final value theorem Laplace transform definition. Similarly, the probability distributions are the exponential distribution, the Rayleigh distribution, the Weibull distribution, and the bathtub hazard rate curve distribution.

At appropriate places, the chapter contains examples along with their solutions, and there are ten problems at the end of the chapter to test the reader's comprehension in the area.