An Asymptotic Theory for Empirical Reliability and Concentration Processes l. Introduction 2. The basic setting for the approximations and variance preliminaries 3. Auxiliary processes: Integrals of empirical processes 4. Mean residual life processes 5. Auxiliary processes: Empirical increments of Brownian bridge integrals 6. Total time on test processes 7. Scaled total time on test processes 8. Discussion of results on total time on test processes 9. Total time on test from the first failure 10. Unscaled empirical Lorenz processes 11. Empirical Lorenz processes 12. Discussion of results on empirical Lorenz processes 13. The empirical concentration process of Goldie 14. Discussion of results on the Goldie concentration process 15. Further diversity and concentration processes 16. Indices of inequality diversity and concentration 17. Bootstrapping empirical functionals 18. References. Mik16s Cs6rgO and David M. Mason initiated their collaboration on the topics of this book while attending the CBMS NSF Regional Confer­ ence at Texas A & M University in 1981. Independently of them Sandor Cs6rgO and Lajos Horv~th have begun their work on this subject at Szeged University. The idea of writing a monograph together was born when the four of us met in the Conference on Limit Theorems in Probability and Statistics Veszpr~m 1982. This collaboration resulted in No. 2 of Technical Report Series of the Laboratory for Research in Statistics and Probability of Carleton University and University of Ottawa 1983. Afterwards David M. Mason has decided to withdraw from this project. The authors wish to thank him for his contributions. In particular he has called our attention to the reverse martingale property of the empirical process together with the associated Birnbaum Marshall inequality (cf. the proofs of Lemmas 2.4 and 3.2) and to the Hardy inequality (cf. the proof of part (iv) of Theorem 4.1). These and several other related remarks helped us push down the 2 moment condition to EX < 00 in all our weak approximation theorems.