📉 Customer Churn Predictor — Survival Curve Live

Survival analysis is a family of statistical methods for modeling the time until an event happens — originally time until death in medical studies, but the same machinery applies to time until a customer cancels a subscription. Unlike a simple yes/no classifier, survival models handle censoring gracefully: customers who are still active at the end of the observation window have not churned yet, but they might in the future, and a survival model treats that uncertainty correctly instead of discarding those customers or mislabeling them as loyal. This simulation builds a synthetic cohort, assigns each customer a hazard function driven by real features, and estimates the cohort survival curve with the Kaplan-Meier estimator, exactly as a churn analytics team would on real subscription data.

The hazard function h(t) is the instantaneous risk that a customer churns at time t, given that they have survived up to t. This simulation uses a Cox-proportional-hazards-style model: h_i(t) = h0(t) × exp(β1·usage_decline_i(t) + β2·support_tickets_i(t) − β3·tenure_i(t) − β4·discount_applied_i), where h0(t) is a Weibull baseline hazard shared by every customer and the exponential term is a per-customer risk multiplier built from that customer's actual accumulated usage decline, support-ticket load, tenure and whether a retention discount has been applied. Every month the simulation draws a Bernoulli churn event for each active customer with probability 1 − e^(−h_i(t)), so the hazard genuinely drives who leaves and when.

At every monthly time step the simulation records n_t, the number of customers still at risk (not yet churned) at the start of the month, and d_t, the number of churn events that occur during that month. The Kaplan-Meier estimator then updates the cohort survival probability as S(t) = S(t−1) × (1 − d_t/n_t), a running product of one-minus-the-hazard-rate at every step where an event was observed. This is the same non-parametric estimator used in real churn and clinical survival studies — it is derived directly from the simulated event history rather than being a pre-drawn decorative curve, so tightening or loosening the hazard genuinely reshapes it.

Proactive Discount Rate sets the probability that a customer whose risk score crosses the Intervention Threshold receives a targeted retention discount, which multiplies their hazard by e^(−β4) from that month onward — a real, persistent reduction in churn risk. Support Responsiveness scales down how fast unresolved support tickets accumulate for every customer, which lowers the β2·support_tickets_i(t) term in every hazard calculation. Because both levers feed directly into the same Cox-style hazard equation used to draw churn events, moving a slider recomputes the entire cohort's event history against the same underlying random draws and immediately reshapes the Kaplan-Meier curve — it is not a cosmetic overlay.

Each customer's baseline usage-decline trajectory, support-ticket noise and monthly churn-draw sequence are generated once per cohort and stored. When a lever changes, the simulation reruns the exact same monthly loop with the new hazard coefficients against those same stored random numbers, rather than resampling fresh randomness. That isolates the causal effect of the lever: any difference you see in the survival curve after moving a slider comes from the change in hazard, not from a new roll of the dice, which is exactly the counterfactual comparison a real retention team wants when asking "what would happen if we discounted more aggressively?"

Production churn systems typically fit a Cox proportional hazards model or a discrete-time hazard model (logistic regression per period) on real historical usage, billing and support data with dozens of engineered features, then validate the fitted hazard ratios and Kaplan-Meier curves against held-out cohorts. This simulation implements the same mathematical objects — a genuine per-customer hazard function, real Bernoulli churn draws, and a real Kaplan-Meier estimator over the resulting event history — but the feature weights are hand-tuned rather than fit by maximum partial likelihood on real data, so it should be read as a faithful mechanism demonstration of survival-based churn modeling rather than a calibrated production model.