These answer a different question from a plain distribution: not how long does this last? but what changes it? Temperature, load, supplier, operating mode — a covariate is anything you recorded alongside the failure time that might matter.
Every model here pairs a baseline distribution with an effect type, and it's the effect type that determines how you read the coefficients. Reliafy reports each coefficient with a 95% interval; an interval spanning zero means the data can't distinguish that covariate from no effect.
*_ph)Covariates multiply the hazard by a constant factor at every age.
h(t | z) = h₀(t) · exp(β·z)
exp(β) is the hazard ratio: 1.5 means 50% more failure rate per unit of
that covariate, at any age. The key assumption is proportionality — the ratio
doesn't change over time. If a covariate matters more to old units than new
ones, that assumption is violated and the fit will average the two.
*_aft)Covariates stretch or compress the time axis, as though the clock runs faster.
t(z) = t₀ · exp(−β·z)
exp(β) is a time ratio. This is the natural frame for stress: doubling the
load doesn't just raise the instantaneous risk, it makes everything happen
sooner. It's also the model underneath accelerated life testing and
load-sharing.
*_po)Covariates multiply the odds of failure rather than the hazard.
F(t|z)/R(t|z) = exp(β·z) · F₀(t)/R₀(t)
exp(β) is an odds ratio. Useful when effects appear to converge over time
— proportional odds allows hazard ratios that shrink toward 1 with age, which
proportional hazards cannot.
*_ah)Covariates add to the hazard instead of scaling it.
h(t | z) = h₀(t) + β·z
Coefficients are read on the hazard's own scale (excess failures per unit time), not as a ratio — which is often the more natural quantity for risk attribution. Watch out: nothing constrains the total hazard to stay positive, so a large negative coefficient can drive the cumulative hazard below zero and push reliability above 1. Reliafy warns you when that happens; the fix is to choose a different effect type rather than to trust the numbers.
Start with proportional hazards — it's the convention, and the hazard ratio is
the most widely understood output. Move to AFT when the covariate is a stress
and you think in terms of accelerated clocks, to proportional odds when effects
fade with age, and to additive hazards when you want excess risk rather than a
ratio. If you only care about whether a covariate matters and not about
absolute lives, cox_ph makes the fewest assumptions of all.
weibull_phA Weibull baseline — the usual choice, since its shape parameter already spans infant mortality, random and wear-out behaviour. Covariates act by multiplying the hazard — see proportional hazards above for how to read the coefficients (hazard ratio).
exponential_phA constant-hazard baseline. The simplest option: all age-dependence is assumed away, so the covariates carry the entire story. Covariates act by multiplying the hazard — see proportional hazards above for how to read the coefficients (hazard ratio).
lognormal_phA lognormal baseline — right-skewed, with a hazard that rises then falls. Suits fatigue and degradation-driven failure. Covariates act by multiplying the hazard — see proportional hazards above for how to read the coefficients (hazard ratio).
normal_phA Normal baseline — symmetric with a steadily rising hazard. Fits tight wear-out, but admits negative times. Covariates act by multiplying the hazard — see proportional hazards above for how to read the coefficients (hazard ratio).
gamma_phA Gamma baseline, appropriate when failure follows an accumulation of shocks or stages. Covariates act by multiplying the hazard — see proportional hazards above for how to read the coefficients (hazard ratio).
logistic_phA logistic baseline — symmetric like Normal but heavier in the tails. Covariates act by multiplying the hazard — see proportional hazards above for how to read the coefficients (hazard ratio).
gumbel_phA smallest-extreme-value baseline — the weakest-link case, and the log-scale relative of the Weibull. Covariates act by multiplying the hazard — see proportional hazards above for how to read the coefficients (hazard ratio).
cox_phSemi-parametric. Estimates covariate effects without assuming any baseline shape — the baseline hazard is left completely unspecified and only the ratios are estimated.
Use it when you care about how much a covariate matters rather than about absolute lives: it makes the weakest assumption of anything here. The cost is that it can't give you an absolute reliability curve or an MTTF, because there's no baseline to integrate. Reach for a parametric PH model when you need those.
weibull_aftA Weibull baseline — the usual choice, since its shape parameter already spans infant mortality, random and wear-out behaviour. Covariates act by scaling time to failure — see accelerated failure time above for how to read the coefficients (time ratio).
exponential_aftA constant-hazard baseline. The simplest option: all age-dependence is assumed away, so the covariates carry the entire story. Covariates act by scaling time to failure — see accelerated failure time above for how to read the coefficients (time ratio).
lognormal_aftA lognormal baseline — right-skewed, with a hazard that rises then falls. Suits fatigue and degradation-driven failure. Covariates act by scaling time to failure — see accelerated failure time above for how to read the coefficients (time ratio).
normal_aftA Normal baseline — symmetric with a steadily rising hazard. Fits tight wear-out, but admits negative times. Covariates act by scaling time to failure — see accelerated failure time above for how to read the coefficients (time ratio).
gamma_aftA Gamma baseline, appropriate when failure follows an accumulation of shocks or stages. Covariates act by scaling time to failure — see accelerated failure time above for how to read the coefficients (time ratio).
logistic_aftA logistic baseline — symmetric like Normal but heavier in the tails. Covariates act by scaling time to failure — see accelerated failure time above for how to read the coefficients (time ratio).
gumbel_aftA smallest-extreme-value baseline — the weakest-link case, and the log-scale relative of the Weibull. Covariates act by scaling time to failure — see accelerated failure time above for how to read the coefficients (time ratio).
weibull_poA Weibull baseline — the usual choice, since its shape parameter already spans infant mortality, random and wear-out behaviour. Covariates act by multiplying the odds of failure — see proportional odds above for how to read the coefficients (odds ratio).
exponential_poA constant-hazard baseline. The simplest option: all age-dependence is assumed away, so the covariates carry the entire story. Covariates act by multiplying the odds of failure — see proportional odds above for how to read the coefficients (odds ratio).
lognormal_poA lognormal baseline — right-skewed, with a hazard that rises then falls. Suits fatigue and degradation-driven failure. Covariates act by multiplying the odds of failure — see proportional odds above for how to read the coefficients (odds ratio).
normal_poA Normal baseline — symmetric with a steadily rising hazard. Fits tight wear-out, but admits negative times. Covariates act by multiplying the odds of failure — see proportional odds above for how to read the coefficients (odds ratio).
gamma_poA Gamma baseline, appropriate when failure follows an accumulation of shocks or stages. Covariates act by multiplying the odds of failure — see proportional odds above for how to read the coefficients (odds ratio).
logistic_poA logistic baseline — symmetric like Normal but heavier in the tails. Covariates act by multiplying the odds of failure — see proportional odds above for how to read the coefficients (odds ratio).
gumbel_poA smallest-extreme-value baseline — the weakest-link case, and the log-scale relative of the Weibull. Covariates act by multiplying the odds of failure — see proportional odds above for how to read the coefficients (odds ratio).
weibull_ahA Weibull baseline — the usual choice, since its shape parameter already spans infant mortality, random and wear-out behaviour. Covariates act by adding to the hazard — see additive hazards above for how to read the coefficients (additive effect).
exponential_ahA constant-hazard baseline. The simplest option: all age-dependence is assumed away, so the covariates carry the entire story. Covariates act by adding to the hazard — see additive hazards above for how to read the coefficients (additive effect).
lognormal_ahA lognormal baseline — right-skewed, with a hazard that rises then falls. Suits fatigue and degradation-driven failure. Covariates act by adding to the hazard — see additive hazards above for how to read the coefficients (additive effect).
normal_ahA Normal baseline — symmetric with a steadily rising hazard. Fits tight wear-out, but admits negative times. Covariates act by adding to the hazard — see additive hazards above for how to read the coefficients (additive effect).
gamma_ahA Gamma baseline, appropriate when failure follows an accumulation of shocks or stages. Covariates act by adding to the hazard — see additive hazards above for how to read the coefficients (additive effect).
logistic_ahA logistic baseline — symmetric like Normal but heavier in the tails. Covariates act by adding to the hazard — see additive hazards above for how to read the coefficients (additive effect).
gumbel_ahA smallest-extreme-value baseline — the weakest-link case, and the log-scale relative of the Weibull. Covariates act by adding to the hazard — see additive hazards above for how to read the coefficients (additive effect).