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This book is meant to serve as a textbook for students seeking careers in insurance, actuarial science, or finance. ... The author provides a variety of worked examples in each chapter to illustrate the main ideas, with an emphasis on those of more numerical and practical nature. Although good references for further reading are provided, basic knowledge in probability and statistics is required. This book will also serve as a nice reference for an insurance analyst.-Technometrics, February 2009, Vol. 51, No. 1 ... There are not many other books that cover actuarial topics based on statistical metho

AbstractA policy of periodic replacement with minimal repair at failure is considered for a complex system. Under such a policy the system is replaced at multiples of some period T while minimal repair is performed at any intervening system failures. The cost of a minimal repair to the system is assumed to be a nonde‐creasing function of its age. A simple expression is derived for the expected minimal repair cost in an interval in terms of the cost function and the failure rate of the system. Necessary and sufficient conditions for the existence of an optimal replacement interval are exhibited in the case where the system life distribution is strictly increasing failure rate (IFR).

AbstractTo location Li we are to allocate a "generator" and ni "machines" for i = 1, …,k, where n1 … n1 ≧ … ≧ nk. Although the generators and machines function independently of one another, a machine is operable only if it and the generator at its location are functioning. The problem we consider is that of finding the arrangement or allocation optimizing the number of operable machines. We show that if the objective is to maximize the expected number of operable machines at some future time, then it is best to allocate the best generator and the n1 best machines to location L1, the second‐best generator and the n2‐next‐best machines to location L2, etc. However, this arrangement is not always stochastically optimal. For the case of two generators we give a necessary and sufficient condition that this arrangement is stochastically best, and illustrate the result with several examples.