Imprecise reliability: An introductory overview

Studies in Computational Intelligence

Volumn 40, Issue , 2007, Pages 261-306

  Utkin, Lev V ^a   Coolen, Frank P A ^b  

^a SAINT PETERSBURG STATE FOREST TECHNICAL UNIVERSITY   (Russian Federation)

^b DURHAM UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33846175368     PISSN: 1860949X     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-3-540-37372-8_10     Document Type: Review

References (151)

1. Arts GRJ, Coolen FPA, van der Laan P (2004) Nonparametric predictive inference in statistical process control. Quality Technology and Quantitative Management 1, 201-216.
2. Augustin T (2001) On decision making under ambiguous prior and sampling information. In: De Cooman G, Fine T, Seidenfeld T (eds.): Imprecise Probabilities and Their Applications. Proc. of the 2nd Int. Symposium ISIPTA'01. Ithaca, USA, pp. 9-16.
3. Augustin T (2002) Expected utility within a generalized concept of probability- a comprehensive framework for decision making under ambiguity. Statistical Papers 43, 5-22.
4. Augustin T, Coolen FPA (2004). Nonparametric predictive inference and interval probability. Journal of Statistical Planning and Inference 124, 251-272.
5. Aven T, Korte J (2003) On the use of risk and decision analysis to support decision-making. Reliability Engineering and System Safety 79, 289-299.
6. Bae H-R, R. Grandhi, Canfield R (2004) Epistemic uncertainty quantification techniques including evidence theory. Computers and Structures 82(13-14), 1101-1112.
7. Bardossy A, Bogardi I (1989) Fuzzy fatigue life prediction. Structural Safety 6, 25-38.
8. Barlow R, Proschan F (1975), Statistical Theory of Reliability and Life Testing: Probability Models. New York: Holt, Rinehart and Winston.
9. Barlow R, Wu A (1978) Coherent systems with multistate components. Math. Ops. Res. 3, 275-281.
10. Barzilovich E, Kashtanov V (1971) Some Mathematical Problems of the Complex System Maintenance Theory. Moscow: Sovetskoe Radio. (in Russian).
11. Bedford T, Cooke RM (2001) Probabilistic Risk Analysis: Foundations and Methods. Cambridge University Press.
12. Ben-Haim Y (1996) Robust Reliability in the Mechanical Sciences. Berlin: Springer-Verlag.
13. Ben-Haim Y (2004) Uncertainty, probability and information-gaps. Reliability Engineering and System Safety 85, 249-266.
14. Berger JO (1990) Robust Bayesian analysis: Sensitivity to the prior. J of Statistical Planning and Inference 25, 303-328.
15. Brocklehurst S, Littlewood B, Olovsson T, Jonsson E (1994) On measurement of operational security. Technical Report PDCS TR 160, City University, London and Chalmers University of Technology, Goteborg.
16. Cai K-Y (1993) Parameter estimations of normal fuzzy variables. Fuzzy Sets and Systems 55, 179-185.
17. Cai K-Y (1996) Introduction to Fuzzy Reliability. Boston: Kluwer Academic Publishers.
18. Cai K-Y (1996) System failure engineering and fuzzy methodology. An introductory overview. Fuzzy Sets and Systems 83, 113-133.
19. Cai K-Y (1998), Software Defect and Operational Profile Modeling. Dordrecht/Boston: Kluwer Academic Publishers.
20. Cai K-Y, Wen C, Zhang M (1991) A critical review on software reliability modeling. Reliability Engineering and System Safety 32, 357-371.
21. Cai K-Y, Wen C, Zhang M (1993) A novel approach to software reliability modeling. Microelectronics and Reliability 33, 2265-2267.
22. Cano, A, S. Moral (2002) Using probability trees to compute marginals with imprecise probability. Int J of Approximate Reasoning 29, 1-46.
23. Cooke RM (1991) Experts in Uncertainty. Opinion and Subjective Probability in Science. New York: Oxford University Press.
24. Coolen FPA (1994) On Bernoulli experiments with imprecise prior probabilities. The Statistician 43, 155-167.
25. Coolen FPA (1994). Bounds for expected loss in Bayesian decision theory with imprecise prior probabilities. The Statistician 43, 371-379.
26. Coolen FPA (1996) On Bayesian reliability analysis with informative priors and censoring. Reliability Engineering and System Safety 53, 91-98.
27. Coolen FPA (1997) An imprecise Dirichlet model for Bayesian analysis of failure data including right-censored observations. Reliability Engineering and System Safety 56, 61-68.
28. Coolen FPA (2004) On the use of imprecise probabilities in reliability. Quality and Reliability Engineering International 20(3), 193-202.
29. Coolen FPA (2006). On nonparametric predictive inference and objective Bayesianism. J of Logic, Language and Information, to appear.
30. Coolen FPA (2006) On probabilistic safety assessment in case of zero failures. J of Risk and Reliability, to appear.
31. Coolen FPA, Augustin T (2005) Learning from multinomial data: A nonparametric predictive alternative to the Imprecise Dirichlet Model. In: Cozman FG, Nau R, Seidenfeld T (eds.): Proc. of the 4th Int. Symposium on Imprecise Probabilities and their Applications, ISIPTA'05. Pittsburgh, USA, pp. 125-134.
32. Coolen FPA, Coolen-Schrijner P (2000) Condition monitoring: A new perspective. J of the Operational Research Society 51, 311-319.
33. Coolen FPA, Coolen-Schrijner P (2005) Nonparametric predictive reliability demonstration for failure-free periods. IMA J of Management Mathematics 16, 1-11.
34. Coolen FPA, Coolen-Schrijner P, Yan KJ (2002) Nonparametric predictive inference in reliability. Reliability Engineering and System Safety 78, 185-193.
35. Coolen FPA, Goldstein M, Munro M (2001) Generalized partition testing via Bayes linear methods. Information and Software Technology 43, 783-793.
36. Coolen FPA, Goldstein M, Wooff DA (2005) Using Bayesian statistics to support testing of software systems. In: Proc. 16th Advances in Reliability Technology Symposium, Loughborough, UK, 109-121.
37. Coolen FPA, Newby M (1994) Bayesian reliability analysis with imprecise prior probabilities. Reliability Engineering and System Safety 43, 75-85.
38. Coolen FPA, Newby MJ (1997) Guidelines for corrective replacement based on low stochastic structure assumptions. Quality and Reliability Engineering International 13, 177-182.
39. Coolen FPA, Yan KJ (2003) Nonparametric predictive inference for grouped lifetime data. Reliability Engineering and System Safety 80, 243-252.
40. Coolen FPA, Yan KJ (2003) Nonparametric predictive comparison of two groups of lifetime data. In: De Cooman G, Fine T, Seidenfeld T (eds.): Proc. of the 3rd International Symposium on Imprecise Probabilities and Their Applications, ISIPTA'03. Lugano, Switzerland, 148-161.
41. Coolen FPA, Yan KJ (2004) Nonparametric predictive inference with right-censored data. J of Statistical Planning and Inference 126, 25-54.
42. Coolen-Schrijner P, Coolen FPA (2004) Nonparametric predictive inference for age replacement with a renewal argument. Quality and Reliability Engineering International 20, 203-215.
43. Coolen-Schrijner P, Coolen FPA (2004) Adaptive age replacement based on nonparametric predictive inference. J of the Operational Research Society 55, 1281-1297.
44. Coolen-Schrijner P, Coolen FPA (2006) Nonparametric adaptive age replacement with a one-cycle criterion. Reliability Engineering and System Safety, to appear.
45. Coolen-Schrijner P, Coolen FPA, Shaw SC (2006) Nonparametric adaptive opportunity-based age replacement strategies. J of the Operational Research Society, to appear.
46. Couso I, Moral S, Walley P (1999) Examples of independence for imprecise probabilities. In: De Cooman G, Cozman F, Moral S, Walley P (eds.): ISIPTA '99- Proc. of the First Int. Symposium on Imprecise Probabilities and Their Applications. Zwijnaarde, Belgium, pp. 121-130.
47. Cyert RM, DeGroot MH (1987). Bayesian Analysis and Uncertainty in Economic Theory. Chapter 9: Adaptive Utility. Chapman and Hall, pp. 127-143.
48. de Cooman G (1996) On modeling possibilistic uncertainty in two-state reliability theory. Fuzzy Sets and Systems 83, 215-238.
49. de Cooman G (2002) Precision-imprecision equivalence in a broad class of imprecise hierarchical uncertainty models. J of Statistical Planning and Inference 105(1), 175-198.
50. Dubois D, Kalfsbeek H (1990) Elicitation, assessment and pooling of expert judgement using possibility theory. In: Manikopoulos C (ed.): Proc. of the 8th Int. Congress of Cybernetics and Systems. Newark, NJ, pp. 360-367.
51. Dubois D, Prade H (1988), Possibility Theory: An Approach to Computerized Processing of Uncertainty. Plenum Press, New York.
52. Dubois D, Prade H (1992) When upper probabilities are possibility measures. Fuzzy Sets and Systems 49, 65-74.
53. Ekenberg L, Boman M, Linnerooth-Bayer J (1997) Catastrophic risk evaluation. Interim report IR-97-045, IIASA, Austria.
54. Ferson S, Ginzburg L, Kreinovich V, Nguyen H, Starks S (2002) Uncertainty in risk analysis: Towards a general second-order approach combining interval, probabilistic, and fuzzy techniques. In: Proc. of FUZZ-IEEE'2002, Vol. 2. Honolulu, Hawaii, pp. 1342-1347.
55. Frechet M (1935) Generalizations du theoreme des probabilities totales. Fundamenta Mathematica 25, 379-387.
56. Freudenthal A (1956) Safety and the probability of structural failure. Transactions ASCE 121, 1337-1397.
57. Genest C, Zidek J (1986) Combining probability distributions: A critique and an annotated bibliography. Statistical Science 1, 114-148.
58. Gilbert L, de Cooman G, Kerre E (2000) Practical implementation of possibilistic probability mass functions. In: Proc. of Fifth Workshop on Uncertainty Processing (WUPES 2000). Jindvrichouv Hradec, Czech Republic, pp. 90-101.
59. Goldstein M (1999) Bayes linear analysis. In: Kotz S, Read CB, Banks DL (eds.): Encyclopaedia of Statistical Sciences, update vol. 3. New York: Wiley, pp. 29-34.
60. Goldstein M, Shaw SC (2004) Bayes linear kinematics and Bayes linear graphical models. Biometrika 91, 425-446.
61. Good I (1980) Some history of the hierarchical Bayesian methodology. In: Bernardo J, DeGroot M, Lindley D, Smith A (eds.): Bayesian Statistics. Valencia: Valencia University Press, pp. 489-519.
62. Goodman IR, Nguyen HT (1999) Probability updating using second order probabilities and conditional event algebra. Information Sciences 121(3-4), 295-347.
63. Gurov SV, Utkin LV (1999) Reliability of Systems under Incomplete Information. Saint Petersburg: Lubavich Publ. (in Russian).
64. Gurov SV, Utkin LV, Habarov SP (2000) Interval probability assessments for new lifetime distribution classes. In: Proceedings of the 2nd Int. Conf. on Mathematical Methods in Reliability, Vol. 1. Bordeaux, France, pp. 483-486.
65. Hall J, Lawry J (2001) Imprecise probabilities of engineering system failure from random and fuzzy set reliability analysis. In: De Cooman G, Fine T, Seidenfeld T (eds.): Imprecise Probabilities and Their Applications. Proc. of the 1st Int. Symposium ISIPTA'01. Ithaca, USA, pp. 195-204.
66. Hollnagel E (1993) Human reliability analysis. Context and control. London: Academic Press.
67. Holmberg, J, Hukki K, Norros L, Pulkkinen U, Pyy P (1999) An integrated approach to human reliability analysis- decision analytic dynamic reliability model. Reliability Engineering and System Safety 65, 239-250.
68. Hsiao D, Kerr S, Madnick S (1979) Computer Security. New York: Academic Press.
69. Khintchine A (1938) On unimodal distributions. Izv. Nauchno-Isled. Inst. Mat. Mech. 2, 1-7.
70. Kozine I (1999) Imprecise probabilities relating to prior reliability assessments. In: De Cooman G, Cozman F, Moral S, Walley P (eds.): ISIPTA'99 - Proc of the First International Symposium on Imprecise Probabilities and Their Applications. Zwijnaarde, Belgium, pp. 241-248.
71. Kozine I, Filimonov Y (2000) Imprecise reliabilities: Experiences and advances. Reliability Engineering and System Safety 67, 75-83.
72. Kozine I, Utkin LV (2000) Generalizing Markov chains to imprecise previsions. In: Proc. of the 5th Int Conference on Probabilistic Safety Assessment and Management. Osaka, Japan, pp. 383-388.
73. Kozine I, Utkin LV (2001) Constructing coherent interval statistical models from unreliable judgements. In: Zio E, Demichela M, Piccini N (eds.): Proc. of the European Conference on Safety and Reliability ESREL2001, Vol. 1. Torino, Italy, pp. 173-180.
74. Kozine I, Utkin LV (2002) Interval-valued finite Markov chains. Reliable Computing 8(2), 97-113.
75. Kozine I, Utkin LV (2002) Processing unreliable judgements with an imprecise hierarchical model. Risk Decision and Policy 7(3), 325-339.
76. Kozine I, Utkin LV (2003) Variety of judgements admitted in imprecise statistical reasoning. In: Proc. of the 3-rd Safety and Reliability Int. Conf. Vol. 2. Gdynia, Poland, pp. 139-146.
77. Kuznetsov VP (1991) Interval Statistical Models. Moscow: Radio and Communication. (in Russian).
78. Levitin G, Lisnianski A (2003) Multi-state system reliability. Assessment, optimization and applications. Singapore, New Jersey: World Scientific.
79. Lindqvist B, Langseth H (1998) Uncertainty bounds for a monotone multistate system. Probability in the Engineering and Informational Sciences 12, 239-260.
80. Mosleh A, Apostolakis G (1984) Models for the use of expert opinions. In: Waller R, Covello V (eds.): Low Probability / High Consequence Risk Analysis. New York: Plenum Press.
81. Nau RF (1992) Indeterminate probabilities on finite sets. The Annals of Statistics 20, 1737-1767.
82. Nguyen H, Kreinovich V, Longpre L (2001) Second-order uncertainty as a bridge between probabilistic and fuzzy approaches. In: Proceedings of the 2nd Conf. of the European Society for Fuzzy Logic and Technology EUSFLAT'01. England, pp. 410-413.
83. Onisawa T (1988) An approach to human reliability in man-machine system using error possibility. Fuzzy Sets and Systems 27, 87-103.
84. Penmetsa R, Grandhi R (2002) Efficient estimation of structural reliability for problems with uncertain intervals. Int J of Computers and Structures 80, 1103-1112.
85. Penmetsa R, Grandhi R (2003) Uncertainty propagation using possibility theory and function approximation. Int J of Mechanics of Structures and Machines 31(2), 257-279.
86. Rees K, Coolen FPA, Goldstein M, Wooff DA (2001) Managing the uncertainties of software testing: A Bayesian approach. Quality and Reliability Engineering International 17, 191-203.
87. Quaeghebeur E, de Cooman G (2003) Game-theoretic learning using the imprecise Dirichlet model. In: Bernard J-M, Seidenfeld T, Zaffalon M (eds.): Proc. of the 3rd Int. Symposium on Imprecise Probabilities and Their Applications, ISIPTA'03. Lugano, Switzerland, pp. 450-464.
88. Quaeghebeur E, de Cooman G (2005) Imprecise probability models for inference in exponential families. In: Cozman FG, Nau R, Seidenfeld T (eds.): Proc. of the 4th Int. Symposium on Imprecise Probabilities and Their Applications, ISIPTA'04. Pittsburgh, USA, pp. 287-296.
89. Shafer G (1976) A Mathematical Theory of Evidence. Princeton University Press.
90. Singpurwalla ND, Wilson SP (1999) Statistical Methods in Software Engineering: Reliability and Risk. New York: Springer.
91. Tanaka K, Klir G (1999) A design condition for incorporating human judgement into monitoring systems. Reliability Engineering and System Safety 65, 251-258.
92. Tonon F, Bernardini A (1998) A random set approach to optimisation of uncertain structures. Computers and Structures 68, 583-600.
93. Tonon F, Bernardini A, Elishakoff I (1999) Concept of random sets as applied to the design of structures and analysis of expert opinions for aircraft crash. Chaos, Solutions and Fractals 10(11), 1855-1868.
94. Tonon F, Bernardini A, Mammino A (2000) Determination of parameters range in rock engineering by means of Random Set Theory. Reliability Engineering and System Safety 70, 241-261.
95. Tonon F, Bernardini A, Mammino A (2000) Reliability analysis of rock mass response by means of Random Set Theory. Reliability Engineering and System Safety 70, 263-282.
96. Troffaes M, de Cooman G (2002) Extension of coherent lower previsions to unbounded random variables. In: Proc. of the Ninth International Conference IPMU 2002 (Information Processing and Management). Annecy, France, pp. 735-742.
97. Troffaes M, de Cooman G (2003) Uncertainty and conflict: A behavioural approach to the aggregation of expert opinions. In: Vejnarova J (ed.): Proc. of the 6th Workshop on Uncertainty Processing (WUPES '03). pp. 263-277.
98. Utkin LV (1998) General reliability theory on the basis of upper and lower previsions. In: Ruan D, Abderrahim H, D'hondt P, Kerre E (eds.): Fuzzy Logic and Intelligent Technologies for Nuclear Science and Industry. Proc. of the 3rd Int. FLINS Workshop. Antwerp, Belgium, pp. 36-43.
99. Utkin LV (2000) Imprecise reliability analysis by comparative judgements. In: Proc. of the 2nd Int. Conf. on Mathematical Methods in Reliability, Vol. 2. Bordeaux, France, pp. 1005-1008.
100. Utkin LV (2000) Security analysis on the basis of the imprecise probability theory. In: Cottam M, Harvey DW, Pape R, Tait J (eds.): Foresight and Precaution. Proc. of ESREL 2000, Vol. 2. Rotterdam, pp. 1109-1114.
101. Utkin LV (2001) Assessment of risk under incomplete information. In: Proc. of Int. Scientific School "Modelling and Analysis of Safety, Risk and Quality in Complex Systems". Saint Petersburg, Russia, pp. 319-322.
102. Utkin LV (2002) Avoiding the conflicting risk assessments. In: Proc. of Int. Scientific School "Modelling and Analysis of Safety, Risk and Quality in Complex Systems". Saint Petersburg, Russia, pp. 58-62.
103. Utkin LV (2002) A hierarchical uncertainty model under essentially incomplete information. In: Grzegorzewski P, Hryniewicz O, Gil M (eds.): Soft Methods in Probability, Statistics and Data Analysis. Heidelberg, New York: Phisica-Verlag, pp. 156-163.
104. Utkin LV (2002) Imprecise calculation with the qualitative information about probability distributions. In: Grzegorzewski P, Hryniewicz O, Gil M (eds.): Soft Methods in Probability, Statistics and Data Analysis. Heidelberg, New York: Phisica-Verlag, pp. 164-169.
105. Utkin LV (2002) Interval software reliability models as generalization of probabilistic and fuzzy models. In: German Open Conf. on Probability and Statistics. Magdeburg, Germany, pp. 55-56.
106. Utkin LV (2002) Involving the unimodality condition of discrete probability distributions into imprecise calculations. In: Proc. of the Int. Conf. on Soft Computing and Measurements (SCM'2002), Vol. 1. St. Petersburg, Russia, pp. 53-56.
107. Utkin LV (2002) Some structural properties of fuzzy reliability models. In: Proc. of the Int. Conf. on Soft Computing and Measurements (SCM'2002), Vol. 1. St. Petersburg, Russia, pp. 197-200.
108. Utkin LV (2003) Imprecise reliability of cold standby systems. Int. J of Quality and Reliability Management 20(6), 722-739.
109. Utkin LV (2003) Imprecise second-order hierarchical uncertainty model. Int. J of Uncertainty, Fuzziness and Knowledge-Based Systems 11(3), 301-317.
110. Utkin LV (2003) Reliability of monotone systems by partially defined interval probabilities. In: Proc. of the 3-rd Safety and Reliability Int. Conf., Vol. 2. Gdynia, Poland, pp. 187-194.
111. Utkin LV (2003) A second-order uncertainty model for the calculation of the interval system reliability. Reliability Engineering and System Safety 79(3), 341-351.
112. Utkin LV (2003) A second-order uncertainty model of independent random variables: An example of the stress-strength reliability. In: Bernard J-M, Seidenfeld T, Zaffalon M (eds.): Proc. of the 3rd Int. Symposium on Imprecise Probabilities and Their Applications, ISIPTA'03. Lugano, Switzerland, pp. 530-544.
113. Utkin LV (2004) Belief functions and the imprecise Dirichlet model. In: Batyrshin I, Kacprzyk J, Sheremetov L (eds.): Proc. of the Int. Conf. on Fuzzy Sets and Soft Computing in Economics and Finance, Vol. 1. St.Petersburg, Russia, pp. 178-185.
114. Utkin LV (2004) Interval reliability of typical systems with partially known probabilities. European J of Operational Research 153(3), 790-802.
115. Utkin LV (2004) A new efficient algorithm for computing the imprecise reliability of monotone systems. Reliability Engineering and System Safety 86(3), 179-190.
116. Utkin LV (2004) Probabilities of judgements provided by unknown experts by using the imprecise Dirichlet model. Risk, Decision and Policy 9(4), 391-400.
117. Utkin LV (2004) Reliability models of m-out-of-n systems under incomplete information. Computers and Operations Research 31(10), 1681-1702.
118. Utkin LV (2004) An uncertainty model of the stress-strength reliability with imprecise parameters of probability distributions. Zeitschrift für Angewandte Mathematik und Mechanik (Applied Mathematics and Mechanics) 84(10-11), 688-699.
119. Utkin LV (2005) Extensions of belief functions and possibility distributions by using the imprecise Dirichlet model. Fuzzy Sets and Systems 154(3), 413-431.
120. Utkin LV (2005) A hierarchical model of reliability by imprecise parameters of lifetime distributions. Int J of Reliability, Quality and Safety Engineering 12(2), 167-187.
121. Utkin LV (2005) Imprecise second-order uncertainty model for a system of independent random variables. Int J of Uncertainty, Fuzziness and Knowledge-Based Systems 13(2), 177-194.
122. Utkin LV, Augustin T (2003) Decision making with imprecise second-order probabilities. In: Bernard J-M, Seidenfeld T, Zaffalon M (eds.): Proc. of the 3rd Int. Symposium on Imprecise Probabilities and Their Applications, ISIPTA'03. Lugano, Switzerland, pp. 545-559.
123. Utkin LV, Augustin T (2003) Risk analysis on the basis of partial information about quantiles. In: Modelling and Analysis of Safety and Risk in Complex Systems. Proc. of the Third Int. Scientific School MA SR-2003. IPME RAS, St. Petersburg, Russia, pp. 172-178.
124. Utkin LV, Augustin T (2004) Fuzzy decision making using the imprecise Dirichlet model. In: Batyrshin I, Kacprzyk J, Sheremetov L (eds.): Proc. of the Int. Conf. on Fuzzy Sets and Soft Computing in Economics and Finance, Vol. 1. St.Petersburg, Russia, pp. 186-193.
125. Utkin LV, Augustin T (2005) Decision making under imperfect measurement using the imprecise Dirichlet model. In: Cozman FG, Nau R, Seidenfeld T (eds.): Proc. of the 4th Int. Symposium on Imprecise Probabilities and Their Applications, ISIPTA'05. Pittsburgh, USA, pp. 359-368
126. Utkin LV, Augustin T (2005) Efficient algorithms for decision making under partial prior information and general ambiguity attitudes. In: Cozman FG, Nau R, Seidenfeld T (eds.): Proc. of the 4th Int. Symposium on Imprecise Probabilities and Their Applications, ISIPTA'05. Pittsburgh, USA, pp. 349-358.
127. Utkin LV, Gurov SV (1996) A general formal approach for fuzzy reliability analysis in the possibility context. Fuzzy Sets and Systems 83, 203-213.
128. Utkin LV, Gurov SV (1998) New reliability models on the basis of the theory of imprecise probabilities. In: The 5th Int. Conf. on Soft Computing and Information/Intelligent Systems IIZUKA'98, Vol. 2. Iizuka, Japan, pp. 656-659.
129. Utkin LV, Gurov SV (1998) Steady-state reliability of repairable systems by combined probability and possibility assumptions. Fuzzy Sets and Systems 97(2), 193-202.
130. Utkin LV, Gurov SV (1999) Imprecise reliability models for the general lifetime distribution classes. In: De Cooman G, Cozman F, Moral S, Walley P (eds.): Proc. of the First Int. Symposium on Imprecise Probabilities and Their Applications. Zwijnaarde, Belgium, pp. 333-342.
131. Utkin LV, Gurov SV (1999) Imprecise reliability of general structures. Knowledge and Information Systems 1(4), 459-480.
132. Utkin LV, Gurov SV (2000) Generalized ageing lifetime distribution classes. In: Cottam M, Harvey DW, Pape R, Tait J (eds.): Foresight and Precaution. Proc. of ESREL 2000, Vol. 2. Rotterdam, pp. 1539-1545.
133. Utkin LV, Gurov SV (2001) New reliability models based on imprecise probabilities. In: Hsu C (ed.): Advanced Signal Processing Technology. World Scientific, Chapt. 6, pp. 110-139.
134. Utkin LV, Gurov SV (2002) Imprecise reliability for the new lifetime distribution classes. J of Statistical Planning and Inference 105(1), 215-232.
135. Utkin LV, Gurov SV, Shubinsky M (2002) A fuzzy software reliability model with multiple-error introduction and removal. Int J of Reliability, Quality and Safety Engineering 9(3), 215-228.
136. Utkin LV, Kozine I (2000) Conditional previsions in imprecise reliability. In: Ruan D, Abderrahim H, D'Hondt P (eds.): Intelligent Techniques and Soft Computing in Nuclear Science and Engineering. Bruges, Belgium, pp. 72-79.
137. Utkin LV, Kozine I (2001) Computing the reliability of complex systems. In: De Cooman G, Fine T, Seidenfeld T (eds.): Imprecise Probabilities and Their Applications. Proc. of the 2st Int. Symposium ISIPTA'01. Ithaca, USA, pp. 324-331.
138. Utkin LV, Kozine I (2001) Different faces of the natural extension. In: de Cooman G, Fine T, Seidenfeld T (eds.): Imprecise Probabilities and Their Applications. Proc. of the 2nd Int. Symposium ISIPTA'01. Ithaca, USA, pp. 316-323.
139. Utkin LV, Kozine I (2002) A reliability model of multi-state units under partial information. In: (eds.): Proc. of the Third Int. Conf. on Mathematical Methods in Reliability (Methodology and Practice). Trondheim, Norway, pp. 643-646.
140. Utkin LV, Kozine I (2002) Stress-strength reliability models under incomplete information. Int J of General Systems 31(6), 549-568.
141. Utkin LV, Kozine I (2002) Structural reliability modelling under partial source information. In: Langseth H, Lindqvist B (eds.): Proc. of the Third Int. Conf. on Mathematical Methods in Reliability (Methodology and Practice). Trondheim, Norway, pp. 647-650.
142. Utkin LV, Shubinsky IB (2000) Unconventional Methods of the Information System Reliability Assessment. St. Petersburg: Lubavich Publ. (in Russian).
143. Viertl R (1996) Statistical Methods for Non-Precise Data. Boca Raton, Florida: CRC Press.
144. Walley P (1991) Statistical Reasoning with Imprecise Probabilities. London: Chapman and Hall.
145. Walley P (1996) Inferences from multinomial data: Learning about a bag of marbles. J of the Royal Statistical Society, Series B58, 3-57.
146. Walley P (1997) A bounded derivative model for prior ignorance about a real-valued parameter. Scandinavian J of Statistics 24(4), 463-483.
147. Walley P (1997) Statistical inferences based on a second-order possibility distribution. Int J of General Systems 9, 337-383.
148. Weichselberger K (2000) The theory of interval-probability as a unifying concept for uncertainty. Int J of Approximate Reasoning 24, 149-170.
149. Weichselberger K (2001) Elementare Grundbegriffe einer allgemeineren Wahrscheinlichkeitsrechnung, Vol. I Intervallwahrscheinlichkeit als umfassendes Konzept. Heidelberg: Physika.
150. Wooff DA, Goldstein M, Coolen FPA (2002). Bayesian graphical models for software testing. IEEE Transactions on Software Engineering 28, 510-525.
151. Xie M (1991) Software Reliability Modeling. Singapore: World Scientific.