Statistical methods in process control and monitoring

统计过程控制在工业、服务业、行政管理等领域有着广泛的应用。所需的统计方法取决于所提出的问题和过程质量数据的特征。总体目标是提高工艺性能。控制图是统计过程控制的核心方法。它们的发展主要集中在故障特征，其特征在于在产品制造或服务提供中的质量特性的平均值中向上或向下跳跃。过程控制变量中的单步滑动通常是这些故障特征的原因。然而，在实践中，更常见的是，利息质量特征的平均值慢慢地漂移，随着时间的推移不断变化。线性、二次、指数和正弦曲线趋势在工艺操作中并不少见。自然地，这些故障特征被隐藏在噪声中，因此直接不可观察。我们建议的主要目标是开发控制图方法来检测各种故障特征。具体来说，其目的是开发故障敏感控制图，即，图表是非常有效的检测故障签名担心提前。最近的控制图文献集中在这类问题。另一个重要的目标是为利益质量不一定遵循正态分布的情况开发图表。这些情况在可靠性研究中非常常见，其中产品或部件的失效时间往往是（正）偏斜的，或者在环境研究中，污染物的浓度在许多情况下是对数正态分布的。我们将应用基于似然函数和得分统计的合理统计方法来解决这些问题。

Statistical process  control has a wide range of applications in industry, services, administration and other areas. The statistical methods required depend on both the questions being asked and the features of the process quality data. The overall objective is to improve process performance. Control charts are the core methods used in statistical process control. Their development has largely focused on fault signatures characterized by a jump, up- or down-wards, in the mean of a quality characteristic in the manufacturing of a product or the offering of a service. Single-step slippages in the process controling variables are often responsible for these fault signatures. In practice, however, more often the mean of the quality characteristic of interest drifts away slowly, constantly changing over time. Linear, quadratic, exponential and sinusoidal trends are not uncommonly observed in process operation. Naturally these fault signatures are buried in noise, thus directly unobservable. Our proposal's main objective is to develop control chart methods to detect this variety of fault signatures. Specifically, the aim is to develop fault-sensitized control charts, that is, charts that are highly efficient in detecting a fault signature feared in advance. The recent control chart literature has focused on this type of problems. Another important objective is to develop charts for situations where the quality of interest does not necessarily follow a normal distribution. These situations are very common in reliability studies where the failure times of products or parts tend to be (positively) skewed, or in environmental studies where the concentrations of contaminants are in many cases log-normally distributed. We will apply sound statistical methods based on likelihood functions and score statistics to tackle these problems.