Statistical analysis of interval and imprecise data : applications in the analysis of reliability field data

• Autorzy: Hryniewicz O.
• Języki publikacji: EN

Abstrakty

EN

The analysis of field lifetime data is much more complicated than the analysis of the results of reliability laboratory tests. In the paper we present an overview of the most important problems of the statistical analysis of field lifetime data, and present their solutions known from literature. When the input information is partial or imprecise, we propose to use interval arithmetics for the calculation of bounds on reliability characteristics of interest. When this information can be described in a more informative fuzzy form, we can generalize our interval-valued results to their fuzzy equivalents.

Słowa kluczowe

EN

reliability; statistical analysis; field data; interval data; fuzzy data

• Wydawca: Polskie Towarzystwo Bezpieczeństwa i Niezawodności
• Czasopismo: Journal of Polish Safety and Reliability Association
• Rocznik: 2007
• Tom: Vol. 1
• Strony: 181--192
• Opis fizyczny: Bibliogr. 27 poz.

Twórcy

autor

Hryniewicz O.

• Systems Research Institute, Warszawa, Poland

Bibliografia

• [1] Cohen, C. A. (1959). Simplified estimators for the normal distribution when samples are singly censored or truncated. Technometrics, 1, 217-237.
• [2] Cohen, C. A. (1991). Truncated and censored samples: theory and applications. Marcel Dekker, New York.
• [3] Coit, D. W. & Dey, K. A. (1999). Analysis of grouped data from field-failure reporting systems. Reliability Engineering and System Safety, 65, 95-101.
• [4] Coit, D. W. & Jin, T. (2000). Gamma distribution parameter estimation for field reliability data with missing failure times. IEE Transactions, 32, 1161-1166.
• [5] Cox, D. R. (1972). Regression models and life tables (with discussion). Journal of the Royal Statistical Society, ser.B, 34, 187-202.
• [6] Dubois, D. & Prade, H. (1980). Fuzzy Sets and Systems. Theory and Applications. Academic Press, New York.
• [7] Duchesne, T. & Lawless, J. F. (2000). Alternative time scales and failure time models. Lifetime Data Analysis, 6, 157-179.
• [8] Hryniewicz, O. (2007). Fuzzy sets in the evaluation of reliability. In: Computational Intelligence in Reliability Engineering. New Metaheuristcs, Neural and Fuzzy Techniques in Reliability, Levitin, G. (Ed.), Springer, Berlin., 363-386.
• [9] Hu, J. X. & Lawless, J. F. (1996a). Estimation from truncated lifetime data with supplementary information on covariates and censoring times. Biometrika, 83(4), 747-761.
• [10] Hu, J. X. & Lawless, J. F. (1996b). Estimation of rate and mean functions from truncated recurrent event data. Journal of the American Statistical Association, 91, 300-310.
• [11] Hu, J. X., Lawless, J. F. & Suzuki, K. (1998). Nonparametric estimation of a lifetime distribution when censoring times are missing. Technometrics, 40, 3-13.
• [12] Jung, M. & Bai, D. S. (2007). Analysis of field data under two-dimensional warranty. Reliability Engineering and System Safety, 92, 135-143.
• [13] Kalbfleisch, J. D. & Lawless, J. F. (1988). Estimation of reliability in field-performance studies. Technometrics. 30, 365-388.
• [14] Kalbfleisch, J. D., Lawless, J. F. & Robinson, J.A. (1991). Methods for the analysis and prediction of warranty claims. Technometrics, 33, 273-285.
• [15] Kaplan, E. L. & Meier, P. (1958). Nonparametric estimation from incomplete observations. Journal of the American Statistical Association, 53, 457-481.
• [16] Lawless, J. F. (1982). Statistical Models and Methods for Lifetime Data. John Wiley and Sons, New York.
• [17] Lawless, J. F. (1998). Statistical analysis of product warranty data. International Statistical Review, 66, 41-60.
• [18] Lawless, J. F., Hu, J. & Cao, J. (1995). Methods for the estimation of a lifetime distributions and rates from automotive warranty data. Lifetime Data Analysis, 1, 227-240.
• [19] Lin, D. K. J., Usher, J. S. & Guess, F.M (1996). Bayes estimation of component-reliability from masked system-life data. IEEE Transactions on Reliability, 45, 233-237.
• [20] Oh, Y. S. & Bai, D. S. (2001). Field data analyses with after-warranty failure data. Reliability Engineering and System Safety, 72, 1-8.
• [21] Rai, B. & Singh, N. (2003). Hazard rate estimation from incomplete and unclean warranty data. Reliability Engineering and System Safety, 81, 79-82.
• [22] Suzuki, K. (1985). Estimation of lifetime parameters from incomplete field data. Technometrics, 27, 263-272.
• [23] Suzuki, K. (1985). Nonparametric estimation of lifetime distributions from a record of failures and follow-ups. Journal of the American Statistical Association, 80, 68-72.
• [24] Usher, J. S. (1996). Weibull component reliability-prediction in the presence of masked data. IEEE Transactions on Reliability, 45, 229-232.
• [25] Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8, 338-353.
• [26] Zadeh, L.A. (1978). Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems, 1, 3-28.
• [27] Zimmermann, H. J. (1996). Fuzzy Set Theory and its Applications (Third Edition), Kluwer, Boston.