Abstract
We address the problem of robust inference about the stress–strength reliability parameter R = P(X < Y), where X and Y are taken to be independent random variables. Indeed, although classical likelihood based procedures for inference on R are available, it is well-known that they can be badly affected by mild departures from model assumptions, regarding both stress and strength data. The proposed robust method relies on the theory of bounded influence M-estimators. We obtain large-sample test statistics with the standard asymptotic distribution by means of delta-method asymptotics. The finite sample behavior of these tests is investigated by some numerical studies, when both X and Y are independent exponential or normal random variables. An illustrative application in a regression setting is also discussed.
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Greco, L., Ventura, L. Robust inference for the stress–strength reliability. Stat Papers 52, 773–788 (2011). https://doi.org/10.1007/s00362-009-0286-9
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DOI: https://doi.org/10.1007/s00362-009-0286-9