Scale-Relative Reversed Hazard Aging in Reliability Analysis: Bias-Controlled Simultaneous Finite Sample Inference

In reliability analysis, scale-relative reversed hazard aging describes how retrospective failure risk in a lifetime distribution changes across proportional ages. Reversed hazard elasticity and log time curvature characterize its directions and connect them through reciprocal duality to failure rate ratio classes. On unbounded positive support, the inverse Weibull family forms the common global boundary, and the increasing class requires elasticity below −1. A geometric random maximum counterexample shows that preservation under fixed proportional parallel systems need not extend to random component counts. The principal inferential contribution connects the instantaneous reversed hazard ratio to observable log CDF increments. Under justified numerical bounds on the slope and curvature of the log reversed rate, deterministic window bias allowances combine with simultaneous conditional binomial confidence limits to yield finite sample confidence regions and directional tests for all declared instantaneous ratios and contrasts. Shared locations cancel before uncertainty propagation, and multiple declared widths combine on a common coverage event. With shrinking reporting resolution, region diameters contract at the second-order nonparametric rate, matching a local minimax estimation lower bound; fixed grouped reporting instead leaves irreducible identification uncertainty. Experiments on 28,000 simulated datasets assess estimation, joint coverage, bias envelope refinements, regularity sensitivity, and recorded window tests. The instantaneous regions exhibit conservative empirical joint coverage under valid analytic bounds and can have low directional power, whereas variance-only Gaussian intervals show severe coverage failure under rapid curvature. Published fatigue and device benchmarks illustrate retrospective comparisons, while turbine inspection counts demonstrate partial identification caused by missing proportional cutpoints. The framework separates structural aging, sampling uncertainty, approximation bias, and recording resolution, clarifying which reliability comparisons the data support and which additional inspections would resolve missing cutpoint uncertainty.