Statistical methods in process control and monitoring

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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.