Fuzzy confidence estimation of the parameter involving in the distribution of the total time on test for censored data

Abstract

Data mining has captured the interest of researchers from many different as well as diverse fields of study such as data base systems, machine learning, statistics, cluster analysis, knowledge based systems. One of the major issues in data mining is the analysis of attribute relevance. The basic idea is to come up with a measure that can be effectively used to quantify the relevance of an attribute in identifying a class or a concept. One possible application is the total failure time of censored data. That is, the total time on test for censored data of a system with several components often plays an important role in the reliability theory. In some cases, all components of a system with several identical components may be put on test until an r-th smallest failure time occurs and the total time on test is subsequently calculated. The total time on test for censored data from exponentially distributed censored data has been proved to be an adequate statistic by Nair and Cheng in light of the works by Skibinsky, Cheng and Mordeson, and others. The test may be repeated for many times. As a result, since the total time on test until the r-th ordered failure time is observed will be recorded for each test, several total time on test (for censored data) for the same system are available for use in analyzing the reliability of the system. Fuzzy set theory was formalized by Zadeh. Some fuzzy statistical techniques can be found in (J. J. Buckley 2004, H. J. Zimmerma 1990). In this proposal, we are investigating the fuzzy estimation of the parameter of underlying probability distribution for total failure time of censored data.