We study statistical process control (SPC) through charting of $p$-values. When in control (IC), any valid sequence $(P_{t})_{t}$ is super-uniform, a requirement that can hold in nonparametric and two-phase designs without parametric modelling of the monitored process. Within this framework, we analyse the Shewhart rule that signals when $P_{t}\leα$. Under super-uniformity alone, and with no assumptions on temporal dependence, we derive universal IC lower bounds for the average run length (ARL) and for the expected time to the $k$th false alarm ($k$-ARL). When conditional super-uniformity holds, these bounds sharpen to the familiar $α^{-1}$ and $kα^{-1}$ rates, giving simple, distribution-free calibration for $p$-value charts. Beyond thresholding, we use merging functions for dependent $p$-values to build EWMA-like schemes that output, at each time $t$, a valid $p$-value for the hypothesis that the process has remained IC up to $t$, enabling smoothing without ad hoc control limits. We also study uniform EWMA processes, giving explicit distribution formulas and left-tail guarantees. Finally, we propose a modular approach to directional and coordinate localisation in multivariate SPC via closed testing, controlling the family-wise error rate at the time of alarm. Numerical examples illustrate the utility and variety of our approach.

翻译：本研究通过$p$值控制图探讨统计过程控制方法。当过程处于受控状态时，任何有效的$p$值序列$(P_{t})_{t}$均满足超均匀性要求，该性质可在非参数化设计与两阶段设计中成立，无需对监测过程进行参数化建模。在此框架下，我们分析了当$P_{t}\leα$时发出信号的Shewhart规则。在仅满足超均匀性且无时间依赖性假设的条件下，我们推导出平均运行长度的通用受控状态下界及第$k$次误报期望时间的通用下界。当条件超均匀性成立时，这些下界可锐化为常见的$α^{-1}$与$kα^{-1}$收敛速率，从而为$p$值控制图提供简洁的无分布校准方案。除阈值方法外，我们利用相依$p$值的合并函数构建类EWMA方案，该方案在每个时刻$t$输出关于过程在$t$前保持受控状态假设的有效$p$值，实现无需特设控制限的平滑监测。我们还研究了均匀EWMA过程，给出显式分布公式与左尾保证。最后，我们通过闭检验提出模块化方法，实现多元统计过程中方向性与坐标定位的局部化，并在警报时刻控制族错误率。数值算例展示了本方法的多功能性与多样性。