Process capability indices such as $C_{pk}$ are widely used in manufacturing to support supplier qualification, pilot-build release, and production approval. In practice, approval decisions are often based on deterministic threshold rules of the form $\widehat{C}_{pk} \ge C_0$. Because $\widehat{C}_{pk}$ is estimated from finite samples, however, such decisions are inherently stochastic, especially when the true capability lies near the approval threshold. This paper develops a risk-calibrated decision framework for process capability approval that explicitly accounts for estimation uncertainty and asymmetric operational loss. Capability approval is formulated as a binary statistical decision problem, leading to a rule of the form $\widehat{C}_{pk} \ge C_0 + k\,SE(\widehat{C}_{pk})$, where the calibration constant $k$ is determined either by a tolerable failure probability or by a false-accept/false-reject cost ratio. The resulting formulation unifies several commonly used procedures, including deterministic thresholding, lower confidence bound rules, and probability-based approval rules, and naturally extends them to cost-sensitive decision rules derived from asymmetric operational loss. Simulation experiments and an industrial case study show that risk calibration primarily affects near-threshold decisions, improves approval stability, and can substantially reduce expected operational loss when false acceptance is more costly than false rejection.

翻译：过程能力指标（如$C_{pk}$）广泛应用于制造业，用于支持供应商资质认定、试生产放行及量产批准。实践中，批准决策常基于确定性阈值规则，即$\widehat{C}_{pk} \ge C_0$。然而，由于$\widehat{C}_{pk}$通过有限样本估计得出，此类决策本质上具有随机性，尤其当真实能力接近批准阈值时更为显著。本文提出一种风险校准的决策框架用于过程能力批准，该框架明确将估计不确定性和非对称运营损失纳入考量。我们将能力批准建模为二元统计决策问题，推导出规则形式为$\widehat{C}_{pk} \ge C_0 + k\,SE(\widehat{C}_{pk})$，其中校准常数$k$由可容忍失效概率或误接收/误拒绝成本比共同决定。该公式统一了若干常用方法，包括确定性阈值规则、置信下限规则及基于概率的批准规则，并将其自然扩展为源自非对称运营损失的成本敏感决策规则。仿真实验与工业案例研究表明：风险校准主要影响近阈值决策，提升批准稳定性，并在误接收代价高于误拒绝代价时显著降低期望运营损失。