Diagnose a metric drop in search time

Over the last 3 calendar months, the metric 'searching time per user per session' dropped by 35%. A teammate proposes modeling two distributions: T1 = time before first successful result and T2 = time before giving up. Critique this and design a robust analysis to find root cause. - Precisely define the metric and population; handle multi‑tab sessions, background inactivity, and timeouts. Specify inclusion/exclusion rules. - Explain biases from splitting into T1 and T2: selection bias (excluding no‑success sessions), right‑censoring, competing risks (success vs abandonment), and left‑truncation. How would you detect and correct them? - Choose methods (e.g., survival/hazard models with censoring; mixture models) and show how to estimate and compare hazards across cohorts (device, locale, query type). - Rule out non‑product causes: instrumentation changes, seasonality, traffic mix shifts, bot filtering, release flags. List concrete checks and guardrail metrics. - Build a time‑series decomposition and change‑point analysis; specify covariates and counterfactual baselines. - Propose a minimal experiment or holdout (e.g., rollback of ranking feature) with success criteria and expected directional outcomes.