In some statistical process control applications, quality of a process or product can be characterized by a relationship between a response and one or more independent variables, which is typically referred to a profile. In this paper, polynomial profiles are considered to monitor processes in which there is a first order autoregressive relation between the error terms in each profile. A remedi...

In these notes we describe how to measure the confidence we have in our Monte-Carlo estimates. In particular, we use he Central Limit Theorem to construct confidence intervals for the quantity we are truing to estimate. We also describe methods to estimate the number of samples that are required to achieve a given confidence level.

With the dramatic increase of 3D imaging techniques, there is a great demand for new approaches in texture analysis of volumetric data. In this paper, we present a new approach for volumetric texture analysis using a runlength encoding matrix and its texture descriptors. We experiment with our approach on the volumetric data generated from two normal Computed Tomography (CT) studies of the ches...

In this paper, first the available single charting methods, which have been proposed to detect simultaneous shifts in a single process mean and variance, are reviewed. Then, by designing proper simulation studies these methods are evaluated in terms of in-control and out-ofcontrol average run length criteria (ARL). The results of these simulation experiments show that the EWMA and EWMS methods ...

I N recent years, statistical process control (SPC) for autocorrelated processes has received a great deal of attention, due in part to the increasing prevalence of autocorrelation in process inspection data. With improvements in measurement and data collection technology, processes can be sampled at higher rates, which often leads to data autocorrelation. It is well known that the run length p...

This paper presents a pattern run-length compression method. Compression is conducted by encoding 2 runs of compatible or inversely compatible patterns into codewords in both views either inside a single segment or across multiple segments. With the provision of high compression flexibility, this method can achieve significant compression. Experimental results for the large ISCAS’89 benchmark c...

Due to slow time variation, variable run length and nonlinearity of sequencing batch reactor (SBR) wastewater treatment batch process, a multivariate statistical MPCA model based on double moving window along the time×variable axis and batch-axis is used for online monitoring the progress of sequencing batch reactor. Moving window MPCA along the time×variable axis can copy seamlessly with varia...

We give an efficient algorithm to randomly generate finitely generated subgroups of a given size, in a finite rank free group. Here, the size of a subgroup is the number of vertices of its representation by a reduced graph such as can be obtained by the method of Stallings foldings. Our algorithm randomly generates a subgroup of a given size n, according to the uniform distribution over size n ...