The literature on nonparametric or distribution-free control charts for univariate variables data is examined. The advantages of these charts have over more traditional distribution-based control charts are demonstrated. Constructive criticism of the li..

Nonparametric Control Charts: An Overview and Some Results

Rational subgroups of size n = 1 are frequently encountered in process monitoring and control. The Shewhart control chart for individuals is often used in these situations. It is well-known that the in-control average run length (ARL) of this chart is 3..

Robustness of the EWMA Control Chart to Non-Normality

This paper considers Statistical Process Control (SPC) when the process measurement is multivariate. In the literature, most existing multivariate SPC procedures assume that the in-control distribution of the multivariate process measurement is known and it is a Gaussian distribution. In applications, however, the measurement distribution is usually unknown and it needs to be estimated from data. Furthermore, multivariate measurements often do not follow a Gaussian distribution (e.g., cases when some measurement components are discrete). We demonstrate that results from conventional multivariate SPC procedures are usually unreliable when the data are non-Gaussian. Existing statistical tools for describing multivariate non-Gaussian data, or transforming the multivariate non-Gaussian data to multivariate Gaussian data, are limited, making appropriate multivariate SPC difficult in such cases. In this paper, we suggest a methodology for estimating the in-control multivariate measurement distribution when a se...

Distribution-free multivariate process control based on log-linear modeling

Since their inception by Walter Shewhart in the late 1920s, most control chart developments have been distribution-based procedures in the sense that the process output is assumed to follow a specified probability distribution (normal for continuous measurements and binomial or Poisson for attribute data). Due to Deming's influence and their widespread adoption as one of the seven basic tools of total quality management (TQM), control charts have been applied to processes where data may be markedly nonnormal. In this article, we propose a distribution-free (or nonparametric) statistical quality control chart for monitoring a process center. The proposed chart is of the Shewhart type and is based on the signed-ranks of grouped observations. The exact false alarm rate and the in-control average run length of the proposed chart are computed by using the null distribution of the well-known Wilcoxon signed-rank statistic. The out-of-control run lengths are computed exactly for normal underlying distri...

A Distribution-Free Shewhart Quality Control Chart Based on Signed-Ranks

Data that represent complex and multivariate processes are well known to be multiscale due to the variety of changes that could occur in a process with different localizations in time and frequency. Examples of changes may include mean shift, spikes, drifts and variance shifts all of which could occur in a process at different times and at different frequencies. Acoustic emission signals arising from machining, images representing MRI scans and musical audio signals are some examples that contain these changes and are not suited for single scale analysis. The recent literature contains several wavelet-decomposition-based multiscale process monitoring approaches including many real life process monitoring applications. These approaches are shown to be effective in handling different data types and, in concept, are likely to perform better than existing single scale approaches. There also exists a vast literature on the theory of wavelet decomposition and other statistical elements of multiscale monitoring ...

Wavelet-based multiscale statistical process monitoring: A literature review

Nonparametric control chart are presented for the problem of detecting changes in the process median (or mean), or changes in the process variability when samples are taken at regular time intervals. The proposed procedures are based on sign-test statistics computed for each sample, and are used in Shewhart and cumulative sum control charts. When the process is in control the run length distributions for the proposed nonparametric control charts do not depend on the distribution of the observations. An additional advantage of the non-parametric control charts is that the variance of the process does not need to be established in order to set up a control chart for the mean. Comparisons with the corresponding parametric control charts are presented. It is also shown that curtailed sampling plans can considerably reduce the expected number of observations used in the Shewhart control schemes based on the sign statistic.

Bakir Saad

Papers

Nonparametric quality control charts based on the sign statistic