# Reliability: Probabilistic Models and Statistical Methods – Lawrence M. Leemis

Reliability theory is a branch of applied mathematics with so many clear applications in engineering, manufacturing, and business. Understanding structure functions, probabilistic ways to represent item lifetimes, accelerated life testing, and repairable systems aids in better system design, warranties, and decision making about maintenance and repair. I used this book during my first reliability class during my MS studies, and this is the book that kicked off my interest in reliability. It’s “mathematical”, as it were, but designed more for the engineer as a survey. Derivations exists, but the mathematics isn’t terribly heavy. It covers the notion of path and cut sets in a highly visual and intuitive way, discusses Poisson processes with accessible clarity, and utilizes good practical examples with tangible situations. I like that it brings up the topic of left and right censoring, as rarely do we see data that isn’t censored. The exercises are beneficial for building a theoretical understanding and applying this knowledge to practical problems. The entire book may be a bit harder for self-study if one doesn’t have some calculus background, and is comfortable with the notion of probability distributions. Certain chapters, especially in the beginning, are perfectly suited for almost anyone. It would make a great text for undergraduate or graduate engineers; one would simply change the pace of the course for each potential group. It is more of a survey book, so there isn’t tons of depth. Thus, it makes a good refresher reference for professionals in the field, but perhaps a more mathematical text would be best suited for those individuals. Those with a strong mathematical foundation in probability will enjoy seeing clear but rigorous applications of their favorite probabilistic concepts, sometimes lacking in the probability theory textbooks. Overall, I recommend for anyone wanting to survey the field. Engineers will regard it as a mathematical text; mathematicians will regard it as a survey and applied text. Regardless, the book’s writing style has a wide appeal.

– Rachel Traylor, Ph.D.

## Topics Covered

• System structure/reliability functions
• minimal path/cut sets
• system block diagrams
• Survival function
• hazard function
• cumulative hazard function
• mean residual life function
• Distribution classes
• increasing/decreasing failure rate
• Competing risks models
• accelerated life models
• proportional hazard models
• repairable systems
• data analysis
• point and interval estimation
• likelihood theory
• censoring
• parametric and nonparametric methods
• estimation from accelerated life methods
• proportional hazards
• non repairable systems