Bathtub hazard rate distributions and fuzzy life times. (English) Zbl 1398.62273
Summary: The development of life time analysis started back in the 20\(^{th}\) century and since then comprehensive developments have been made to model life time data efficiently. Recent development in measurements shows that all continuous measurements can not be measured as precise numbers but they are more or less fuzzy. Life time is also a continuous phenomenon, and has already been shown that life time observations are not precise measurements but fuzzy. Therefore, the corresponding analysis techniques employed on the data require to consider fuzziness of the observations to obtain appropriate estimates.
In this study generalized estimators for the parameters and hazard rates are proposed for bathtub failure rate distributions to model fuzzy life time data effectively.
In this study generalized estimators for the parameters and hazard rates are proposed for bathtub failure rate distributions to model fuzzy life time data effectively.
MSC:
| 62N05 | Reliability and life testing |
| 62N02 | Estimation in survival analysis and censored data |
| 62E10 | Characterization and structure theory of statistical distributions |
Software:
SPLIDAReferences:
| [1] | P. Abbas, P. G. Ali and S. Mansour, Reliability estimation in Rayleigh distribution based on fuzzy lifetime data, International Journal of System Assurance Engineering and Management, 5(5) (2013), 487{494.} |
| [2] | G. Barbato, A. Germak, G. Genta and A. Barbato, Measurements for Decision Making. Measurements and Basic Statistics, Esculapio, Bologna, 2013. |
| [3] | M. R. Casals, A. Colubi, N. Corral, M. A. Gil, M. Montenegro, M. A. Lubiano, A. B. Ramos- Guajardo, B. Sinova and others, Random fuzzy sets: a mathematical tool to develop statistical fuzzy data analysis, Iranian Journal of Fuzzy Systems, 10(2) (2013), 1{28.} · Zbl 1331.62055 |
| [4] | Z. Chen, A new two-parameter lifetime distribution with bathtub shape or increasing failure rate function, Statistics & Probability Letters, 49(2) (2000), 155{161.} · Zbl 0954.62117 |
| [5] | V. Couallier, L. Gerville-Reache, C. Huber-Carol, N. Limnios and M. Mesbah, Statistical Models and Methods for Reliability and Survival Analysis, Wiley, London, 2013. |
| [6] | M. S. Hamada, A. Wilson, C. S. Reese and H. Martz, Bayesian Reliability, Springer, New York, 2008. · Zbl 1165.62074 |
| [7] | E. Haupt and H. Schabe, A new model for a lifetime distribution with bathtub shaped failure rate, Microelectronics Reliability, 32(5) (1992), 633{639.} |
| [8] | D. W. Hosmer and S. Lemeshow, Applied Survival Analysis: Regression Modeling of Time to Event Data, Wiley, New York, 1999. · Zbl 0966.62071 |
| [9] | H. Huang, M. J. Zuo and Z. Sun, Bayesian reliability analysis for fuzzy lifetime data, Fuzzy Sets and Systems, 157(12) (2006), 1674{1686.} · Zbl 1090.62110 |
| [10] | N. Hung T and W. Berlin, Fundamentals of Statistics with Fuzzy Data, Springer, New York, 2006. · Zbl 1100.62002 |
| [11] | J. G. Ibrahim, M. H. Chen and D. Sinha, Bayesian Survival Analysis, Springer, New York, 2001. · Zbl 0978.62091 |
| [12] | D. G. Kleinbaum and M. Klein, Survival Analysis: A self-learning Text, Springer, New York, 2005. · Zbl 1093.62090 |
| [13] | G. J. Klir and Y. Bo, Fuzzy Sets and Fuzzy Logic: Theory and Applications, Prentice - Hal, New Jersey, 1995. · Zbl 0915.03001 |
| [14] | K. H. Lee, First Course on Fuzzy Theory and Applications, Springer, London, 2006. |
| [15] | E. T. Lee and J. W.Wang, Statistical Methods for Survival Data Analysis, Wiley, New Jersey, 2013. · Zbl 1274.62009 |
| [16] | W. Q. Meeker and L. A. Escobar, Statistical Methods for Reliability Data, Wiley, New York, 1998. · Zbl 0949.62086 |
| [17] | R. G. Miller, Survival Analysis, Wiley, New York, 2011. |
| [18] | W. B. Nelson, Applied Life Data Analysis, Wiley, New Jersey, 2005. · Zbl 0579.62089 |
| [19] | S. G. Tzafestas and A. N. Venetsanopoulos, Fuzzy Reasoning in Information, Decision, and Control Systems, Kluwer Academic Publishers, Norwell, MA, 1994. · Zbl 0864.00051 |
| [20] | R. Viertl, Beschreibung Und Analyse Unscharfer Information: Statistische Methoden Fur unscharfe Daten, Springer, Wien, 2006. · Zbl 1101.62003 |
| [21] | R. Viertl, On reliability estimation based on fuzzy lifetime data, Journal of Statistical Planning & Inference, 139(5) (2009), 1750{1755.} · Zbl 1156.62361 |
| [22] | R. Viertl, Statistical Methods for Fuzzy Data, Wiley, Chichester, 2011. · Zbl 1278.62014 |
| [23] | R. Viertl, Univariate statistical analysis with fuzzy data, Computational Statistics & Data Anaysis, 51(1) (2006), 133{147.} · Zbl 1157.62368 |
| [24] | H. C. Wu, Fuzzy bayesian estimation on lifetime data, Computational Statistics, 19(4) (2004), 613-633. · Zbl 1060.62037 |
| [25] | L. A. Zadeh, Fuzzy sets, Information and Control, 8(3) (1965), 338{353.} · Zbl 0139.24606 |
| [26] | H. J. Zimmermann, Fuzzy Set Theory - and Its Applications, Kluwer Academic Publishers, Massachusetts, 2001. |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
