구독경제 환경에서의 수익 최적화를 위한 신뢰성 모델 기반의 서비스 주기 결정 모형

With the rapid expansion of the subscription economy, service providers face the critical challenge of maximizing customer lifetime value while balancing the trade-off between customer churn risk and operational costs. While previous research has focused on dynamic pricing and demand forecasting, this study introduces a novel mathematical framework based on reliability engineering principles—specifically, the age replacement model—to optimize delivery intervals and service termination policies. We propose and analyze two optimization models: (1) Model 1, a baseline model with a single fixed interval and an optimal stopping point (  ), and (2) Model 2, an adaptive model that allows a one-time interval change to transition from an intensive onboarding phase to a maintenance phase. Incorporating the selection effect and population heterogeneity, we mathematically demonstrate the existence of a unique optimal policy under the assumption of a non-increasing hazard rate. Numerical analysis reveals that when initial conversion rates are low, the optimal strategy involves minimizing the first stage and extending a cost-effective second stage to maximize long-term profitability. This research provides service providers with a data-driven methodology to scientifically determine “how often” and “how long” to engage with subscribers, offering a practical tool for maximizing the profit rate in diverse subscription business environments.