Functional Regression Control Chart

The modern development of data acquisition technologies in many industrial processes is facilitating the collection of quality characteristics that are apt to be modeled as functions, which are usually referred to as profiles. At the same time, measurements of concurrent variables, which are related to the quality characteristic profiles, are often available in a functional form as well, and usually referred to as covariates. To adjust the monitoring of the quality characteristic profiles by the effect of this additional information, a new functional control chart is elaborated on the residuals obtained from a function-on-function linear regression of the quality characteristic profile on the functional covariates. By means of a Monte Carlo simulation study, the proposed control chart is compared with other control charts already appeared in the literature and some remarks are given on its use in presence of covariate mean shifts. Furthermore, a real-case study in the shipping industry is presented with the purpose of monitoring ship fuel consumption and thus, CO2 emissions from a Ro-Pax ship, with particular regard to detecting their reduction after a specific energy efficiency initiative.当前诸多工业流程中的数据采集技术持续升级，正推动各类可建模为函数形式的质量特性的采集工作，这类质量特性通常被称为轮廓（profiles）。与此同时，与该质量特性轮廓相关的同步变量测量值，往往也以函数形式给出，一般被称为协变量（covariates）。为借助该额外信息对质量特性轮廓的监控流程进行校正，研究人员基于将质量特性轮廓对功能协变量进行函数对函数线性回归所得到的残差，构建了一种新型功能控制图。通过蒙特卡洛（Monte Carlo）模拟实验，本文将所提出的控制图与现有文献中已公开的各类控制图进行对比，并针对协变量均值漂移场景下该控制图的应用给出若干评述。此外，本文还提供了一项航运业的实际案例研究：针对一艘滚装客船（Ro-Pax）的船舶燃油消耗及伴随产生的二氧化碳排放量开展监控，重点关注在实施特定能效举措后，相关能耗与排放量的降低情况。