The setting of the control limits to utilize on a control chart supposes the assumption of the normality. However, in many situations, this condition does not hold. There are numerous studies on the control charts when the underlying distribution is non-normal. This paper examines the effects of non-normality as measured by skewness and provides an alternative method of designing individuals co...

Ordinal systems are structures for describing ordinal notation systems, which extend the more predicative approaches to ordinal notation systems, like the Can-tor normal form, the Veblen function and the Sch utte Klammer symbols, up to the Bachmann-Howard ordinal.-ordinal systems, which are natural extensions of this approach, reach without the use of cardinals the strength of the theories for ...

The method of change (or anomaly) detection in high-dimensional discrete-time processes using a multivariate Hotelling chart is presented. We use normal random projections as a method of dimensionality reduction. We indicate diagnostic properties of the Hotelling control chart applied to data projected onto a random subspace of R. We examine the random projection method using artificial noisy i...

The method of change (or anomaly) detection in high-dimensional discrete-time processes using a multivariate Hotelling chart is presented. We use normal random projections as a method of dimensionality reduction. We indicate diagnostic properties of the Hotelling control chart applied to data projected onto a random subspace of R. We examine the random projection method using artificial noisy i...

Nonparametric control chart is useful when the underlying distribution is unknown, or is not likely to be normal. In this paper, we provide a sequential rank-based nonparametric adaptive EWMA (NAE) control chart for detecting the persistent shift in the location parameter. This NAE chart is a self-starting scheme and thus can be used to monitor processes at the start-up stages rather than waiti...

Control charts, known for more than 80 years, have been important tools for business and industrial manufactures. Among many different types of control charts, the attribute control chart (np-chart or p-chart) is one of the most popular methods to monitor the number of observed defects in products, such as semiconductor chips, automobile engines, and loan applications. The attribute control cha...

Control charts are the most popular Statistical Process Control (SPC) tools used to monitor process changes. When a control chart indicates an out of control signal it means that the process has changed. However control chart signals do not indicate the real time of process changes, which is essential for identifying and removing assignable causes and ultimately improving the process. Identifyi...

Not all data in practice came from a process with normal distribution. When the process distribution is non-normal or unknown, the commonly used Shewhart control charts are not suitable. In this paper, a new non-parametric CUSUM Mean Chart is proposed to monitor the possible small mean shifts in the process. The sampling properties of the new monitoring statistics are examined and the average r...

Because of the importance of damage detection in manufacturing systems and other areas, many fault detection methods have been developed that are based on a vibration signal. Little work, however, has been reported in the literature on using a recurrence plot method to analyze the vibration signal for damage detection. In this paper, we develop a recurrence plot based fault detection method by ...