Public procurement is vulnerable to error, fraud, and corruption, particularly as high transaction volumes overwhelm oversight. While research often focuses on tender-stage anomalies, post-award payment monitoring remains underexplored. Since labelled datasets are rare and methods like Benford's Law face restrictive assumptions, there is a need for interpretable, unsupervised frameworks for high-volume procurement oversight and decision support. This paper introduces the Structural Heterogeneity Index (SHI), a composite statistic for one-dimensional samples, and its payment-specific instantiation, the Payment Heterogeneity Index (PHI), characterising payment structure and latent regimes. It incorporates Gaussian Mixture Model (GMM) parameters alongside non-parametric statistics, integrating four interpretable components: modality, asymmetry, tail behaviour, and structural dispersion. Uniquely, the tail-behaviour component captures both distributional heaviness and extreme-value concentration, while structural-dispersion combines the variability, prevalence, and separation of latent payment regimes. Applied to UK municipal procurement data, PHI identifies a financially significant cohort (0.6\% of suppliers; 10.1\% of high-volume vendors) with structurally distinct payment patterns. Statistical testing further supports these differences, and targeted human verification confirms the plausibility of prioritised cases. Comparative analysis shows PHI reveals regime separation obscured by the Coefficient of Variation ($ρ= 0.310$). PHI provides a transparent, decomposable, and computationally lightweight framework for procurement integrity oversight and targeted audit prioritisation.

翻译：公共采购易受错误、欺诈和腐败的影响，尤其是在高交易量导致监督资源不堪重负的情况下。现有研究多聚焦于招标阶段的异常检测，而合同授予后的支付监控仍鲜有探索。由于标注数据集稀缺，且本福德定律等方法受制于严格假设，亟需开发可解释、无监督的高量采购监督与决策支持框架。本文提出结构异质性指数（Structural Heterogeneity Index, SHI）——一种面向一维样本的复合统计量，并进一步引入其支付场景的特定实例——支付异质性指数（Payment Heterogeneity Index, PHI），用于刻画支付结构与潜在行为模式。该指数融合高斯混合模型（Gaussian Mixture Model, GMM）参数与非参数统计量，包含四个可解释分量：模态性、不对称性、尾部行为及结构离散度。其中，尾部行为分量独特地捕获了分布的厚重性与极值集中度，而结构离散度则综合了潜在支付模式的变异性、普遍性与分离程度。应用于英国市政采购数据的分析表明，PHI能够识别出支付模式存在结构性差异的财务显著性群体（占供应商总数的0.6%，占高量供应商总数的10.1%）。统计检验进一步验证了这些差异的显著性，针对性的人工核查也证实了优先关注案例的合理性。对比分析显示，PHI能够揭示变系数（$ρ= 0.310$）所遮蔽的模式分离特征。PHI为采购完整性监督与定向审计优先级排序提供了透明、可分解且计算轻量化的框架。