On Estimating the Reliability of a Component Subject to Several Different Stresses
SOUTHERN METHODIST UNIV DALLAS TX DEPT OF STATISTICAL SCIENCE
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A great deal has been written concerning the estimation of the probability and testing of whether one of two random variables is stochastically larger than the other and its relationship to the estimation of reliability for stress-strength relationships. A more general problem is the estimation and testing of whether one of N 1 random variables is simultaneously stochastically larger smaller than the others. An initial paper which deals with this problem for the special case N 2 is that of D. R. Whitney 1951, A Bivariate Extension of the U Statistic, where he provides a test function and discusses the asymptotic normality of the statistics proposed under the null hypothesis that all the random variables have the same distribution function. In the report, the problem of estimation of the probability of whether one of N 1 mutually independent random variables, each having a continuous cumulative distribution function, is simultaneously stochastically larger smaller than the others has been considered.
- Statistics and Probability
- Manufacturing and Industrial Engineering and Control of Production Systems