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During the startup phase of a production process while statistics on the product quality are being collected it is useful to establish that the process is under control. Small samples ni qi=1 are taken periodically for q periods. We shall assume each measurement is multivariate. A process is under control or on-target if all the observations are deemed to be independent and identically distributed. Let Fi represent the empirical distribution function of the ith sample. Let F¯ represent the empirical distribution function of all observations. Following Lehmann (1951) we propose statistics of the form i=1q -infinityinfinityFi s-F- s2d Fs. The asymptotics of nonparametric q-sample Cramer-Von Mises statistics were studied in Kiefer (1959). The emphasis there, however, is on the case where n(i) → infinity while q stayed fixed. Here we study the asymptotics of a family of randomness statistics, that includes the above. These asymptotics are in the quality control situation (i.e q → infinity while n( i) stay fixed). Such statistics can be used in many situations; in fact one can use randomness statistics in any situation where the problem amounts to a test of homoscedasticity or homogeneity of a collection of observations. We give two such applications. First we show how such statistics can be used in nonparametric regression. Second we illustrate the application to retrospective quality control.

The widespread use of the Internet signals the need for a better understanding of trust as a basis for secure on-line interaction. In the face of increasing uncertainty and risk, users and machines must be allowed to reason effectively about the trustworthiness of other entities. In this thesis, we propose a trust model that assists users and machines with decision-making in online interactions by using past behavior as a predictor of likely future behavior. We develop a general method to automatically compute trust based on self-experience and the recommendations of others. Our trust model solves the problem of recommendation combination and detection of unfair recommendations. Our approach involves data analysis methods (Bayesian estimation, Dirichlet distribution), and machine learning methods (Weighted Majority Algorithm). Furthermore, we apply our trust model to several utility models to increase the accuracy of decision-making in different contexts of Web Services. We describe simulation experiments to illustrate its effectiveness, robustness and the evolution of trust.