Nonparametric Estimation of a Distribution Subject to a Stochastic Precedence Constraint

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On comparing coherent systems with heterogeneous components (2016, background): “In the first case, it may be natural to compare the systems’ reliability by explicitly considering the probability that one system survives the other (that is, using the metric of ‘stochastic precedence’ as employed in [2], [9], and [15]).”
Mixture Representations for the Joint Distribution of Lifetimes of two Coherent Systems with Shared Components (2013, background): “P(X > t) ≤ P(Y > t) for all t), then X is smaller than Y in the SP sense (see [1]).”
Comparisons of coherent systems using stochastic precedence (2010, background): “Arcones et al. (2002) introduced the concept of stochastic precedence (SP) as an alternative approach to the notion that one random variable is smaller than another.”
The stochastic precedence ordering with applications in sampling and testing (2004, methodology): “[1], and two random variables which are equivalent in their sense may be different in ours.”
Inferences Under a Stochastic Ordering Constraint (2005, background): “These include likelihood ratio ordering, uniform stochastic ordering or hazard rate ordering, and stochastic ordering, of which stochastic ordering is the weakest; however, recently, Arcones, Kvam, and Samaniego (2002) have considered an even weaker ordering that they call stochastic precedence.”