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Monitoring the slopes of linear profiles

机译：监控线性轮廓的斜率

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It is discussed with an example that in case of vertical density profile (VDP) data, the density of the wood board (Y) is measured by a profilometer that uses laser devise to take measurements at a series of fixed depths (x) across the thickness' of the board. Due to the linear relationship between the density and thickness, it is observed that the slope, in fact, represents the speed of density increase when depth increases and hence and hence slope is an important characteristic to measure the quality of the wood board. It is argued that the classical control charting methods that consider both intercept and slope for the VDP data are misleading since monitoring the shift of slopes is the major concern. Therefore, it is attempted to propose a Shewhart-type control chart for monitoring slopes of linear profiles. The procedure of implementing the approach is presented in two phases. In the first phase, the control chart is developed and refined using the historical data, whereas in the second phase the chart is used to monitor on-line data. The comparison of the chart with the multivariate T2 chart is also performed using average run length. (9 refs.)
机译：举例说明，在垂直密度分布（VDP）数据的情况下，木板的密度（Y）由轮廓仪测量，轮廓仪使用激光装置在整个木板上的一系列固定深度（x）上进行测量。板的厚度”。由于密度和厚度之间的线性关系，可以观察到，实际上，斜率代表了深度增加时密度增加的速度，因此，斜率是衡量木板质量的重要特征。有人认为，同时考虑VDP数据的截距和斜率的经典控制制图方法具有误导性，因为监视斜率的变化是主要问题。因此，尝试提出一种Shewhart型控制图来监视线性轮廓的斜率。该方法的实现过程分为两个阶段。在第一阶段中，使用历史数据来开发和完善控制图，而在第二阶段中，该图将用于监视在线数据。使用平均游程长度也可以将图表与多元T2图表进行比较。 （9篇）

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