Probability Applications

Contents
xiii
13.4.5 Summary 338
13.5 Part B: General methodology extended with fuzzy logic 341
13.5.1 Membership functions 341
13.5.2 Dependence 341
13.5.3 Summary 344
13.6 Conclusions 345
References 345
14 Uncertainty Distributions Using Fuzzy Logic 347
Ronald E. Smith, W. Jerry Parkinson, and Thomas R. Bement
14.1 Introduction 347
14.2 Example 1: The use of fuzzy expertise to develop uncertainty
distributions for cutting tool wear 349
14.2.1 Demonstration of the technique 350
14.3 Example 2: Development of uncertainty distributions using fuzzy and
probabilistic techniques 352
14.3.1 Description and illustration of the fuzzy setup of
the method 353
14.3.2 Fuzzy development of uncertainty distributions 356
14.3.3 Probabilistic characterization of the development of
uncertainty distributions 359
14.3.4 Extended example 361
14.3.5 Concluding remarks 362
14.4 Summary 363
References 364
15 Signal Validation Using Bayesian Belief Networks and Fuzzy Logic 365
Hrishikesh Aradhye and A. Sharif Heger
15.1 Introduction 365
15.2 Bayesian belief networks 367
15.2.1 BBNsforSFDIA 373
15.2.2 Construction of nodes, links, and associated functions . . 373
15.2.3 A single-variable, single-sensor system 374
15.2.4 Incorporation of redundancies in the network structure . . 375
15.3 Fuzzy logic 381
15.3.1 Using fuzzy logic for fault detection 382
15.4 Summary 389
References 390
Index 393