This simulator builds a bathtub-shaped hazard curve from three additive parts: early-life defects that fade, a flat background hazard and a wear-out term that grows with age. You move an inspection cursor along the life span, or let it sweep, and read the hazard and survival at each age.
• A 3D early-life inspection oven, useful-life endurance rack, wear-out shaft and bearing and a hazard curve with an age cursor. • Sliders for displayed life span (2000-20000 h), initial early-failure hazard (1-10 per 1000 h), early-defect decay time (100-1000 h), background hazard (0.02-0.3 per 1000 h), hazard contribution at the end of the span (1-5 per 1000 h) and inspection age, plus an automatic age sweep. • Six live readouts: current age, total conditional hazard, survival to that age, early contribution, wear contribution and expected survivors from 1000 units. • Two presets: Remove early emphasis (the early contribution decays sooner) and Inspect old equipment (the wear hazard reaches its entered end-of-span value).
The illustrative hazard is lambda(t) = a exp(-t/tau) + b + c (t/L)^3, the sum of an early decaying term, a constant background and a wear term that reaches c at the end of the span L. Its integral is H(t) = a tau (1 - exp(-t/tau)) + b t + c t^4 / (4 L^3), and the survival is R(t) = exp(-H(t)). Hazard is an instantaneous conditional rate, not the fraction already failed; survival depends on the accumulated hazard over the whole age.
This is an illustrative additive hazard model, not a fitted product-life distribution. The early, background and wear terms are nonnegative and integrated analytically. The equipment motion is explanatory only and does not calculate material damage, and one automatic sweep takes 40 animation seconds. Shorten the early decay time to see the left wall of the bathtub collapse and increase the wear contribution to steepen the right wall.
No. Hazard is the conditional instantaneous failure rate for units that are still working. The fraction failed comes from the survival function, which depends on the accumulated hazard.
The integrated hazard over age: R(t) = exp(-H(t)), where H(t) is the area under the hazard curve from zero to t.
Early life with a decaying defect hazard, useful life with an approximately constant background hazard, and wear-out with a hazard that rises as the equipment ages.
It is an illustrative additive hazard, not a fitted life distribution, and the animated parts do not compute material damage.