Reliability, Life Testing and the Prediction of Service Lives: For Engineers and Scientists
The prerequisite for reading this text is a calculus based course in Probability and Mathematical Statistics, along with the usual curricularmathematical requi- ments for every science major. For graduate students from disciplines other than mathematical sciences much advantage, viz., both insight and mathematical - turity, is gained by having had experience quantifying the assurance for safety of structures, operability of systems or health of persons. It is presumed that each student will have some familiarity with Mathematica or Maple or better yet also have available some survival analysis software such as S Plus or R, to handle the computations with the data sets. This material has been selected under the conviction that the most practical aid any investigator can have is a good theory. The course is intended for p- sons who will, during their professional life, be concerned with the 'theoretical' aspects of applied science. This implies consulting with industrial mathema- cians/statisticians' lead engineers in various fields, physcists, chemists, material scientists and other technical specialists who are collaborating to solve some d- ficult technological/scientific problem. Accordingly, there are sections devoted to the deportment of applied mathematicians during consulting. This corresponds to the 'bedside manner' of physicians and is a important aspect of professionalism.
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CHAPTER 2 Elements of Reliability
CHAPTER 3 Partitions and Selection
CHAPTER 4 Coherent Systems
CHAPTER 5 Applicable Life Distributions
CHAPTER 6 Philosophy Science and Sense
CHAPTER 7 Nonparametric Life Estimators
CHAPTER 8 Weibull Analysis
CHAPTER 9 Examine Data Diagnose and Consult
CHAPTER 10 Cumulative Damage Distributions
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analysis application asas assume assumption asymptotic calculate censoring coefficient of variation coherent system component compute consider Corollary crack cumulative damage Dataset defined in eqn definition denote determine duty cycle engineering Ep(X Epstein equation estimate Euler–Mascheroni constant event Exercise Set expected fatigue FL-distribution follows Fy(y Gaussian given in eqn harmonic means hazard function hazard rate IHRA iid sample incremental damage independent integral interval inverse-Gaussian Lemma life-length likelihood load log-normal distribution mathematical maximum mean and variance Miner's rule mles normal notation observations obtain occurs operation Pr[T probability problem PROOF random variable reliability renewal function replacement result sample space scale parameter service-life statistical stochastic stress structure survival distribution Theorem theory transform Tweedie utilized vector Wald Wald distribution Weibull distribution