Quantum-Tech Startup Survival Analysis

Startup Cohort

Funding environment 1.0×

Clock speed 1.0×

Live Statistics

Months elapsed

0 / 60

At risk

Failed

Censored

Ŝ(t) now

1.000

Median survival

—

Ŝ(t) — Kaplan–Meier estimate
Failed (death, red endpoint)
Alive / censored (gray tick)

How it works

Every startup in the 60-company cohort is assigned a true survival time by sampling from a real hazard function before the clock starts — not by scripting outcomes. The hazard is a Weibull hazard h(t) = h₀·k·tᵏ⁻¹ with k < 1, so failure risk is highest in the early "valley of death" and falls as a company matures, scaled by the funding-environment multiplier m you control:

h(t) = h₀ · m · k · t^(k-1)
H(t) = h₀ · m · tᵏ          (cumulative hazard)
T = H⁻¹(−ln U) = (−ln(U) / (h₀·m))^(1/k),  U ~ Uniform(0,1)

That inverse-transform draw gives each startup an exact failure month T. If T falls beyond the 60-month observation horizon (or you end the study early), that startup is right-censored: it is known to have survived at least to the cutoff, but its true failure time is unobserved — exactly the censoring real venture-survival studies deal with, since most tracked companies are still operating when the study ends.

As the clock advances, the Kaplan–Meier product-limit estimator is recomputed from the event times that have actually occurred so far:

Ŝ(t) = Π_{t_i ≤ t} (1 − d_i/n_i)

t_i = a distinct failure month observed so far
d_i = number of startups that failed exactly at t_i
n_i = number still at risk (not yet failed or censored) just before t_i

This is the actual product-limit formula (Kaplan & Meier, 1958) applied to the realized failure and censoring times — no smoothing, no faking. Every drop in the curve corresponds to a real death (or several, if d_i > 1) in the lifeline strip below the chart; the curve only ever steps down, and stays flat between events by construction.

Ŝ(t) = 1.000 · t = 0 mo