New Single Variables Control Charts Based On The Double Ewma Statistics

In Statistical Process Control (SPC) monitoring situations, there is a tendency for both the process mean and process variability to shift simultaneously. Traditionally, two separate control charts, each for the mean and variance are used concurrently to monitor the process mean and process variance. However, in many real life process monitoring situations, a simultaneous control of the process mean and process variance is necessary. This has motivated us to develop single DEWMA (called Double Exponentially Weighted Moving Average) charts which are capable of monitoring simultaneous shifts in both the process mean and process variance, when the underlying distribution of the process is normal. The DEWMA statistics are based on the approach of performing exponential smoothing twice on the original statistics of the underlying process. The objective of this study is to propose three single DEWMA charts, namely the DEWMA-Max (called the DEWMA maximum), Max-DEWMA (called the maximum DEWMA) and SS-DEWMA (called the sum of squares of DEWMA) charts

New Single Variables Control Charts Based On The Double Ewma Statistics

In Statistical Process Control (SPC) monitoring situations, there is a tendency for both the process mean and process variability to shift simultaneously. Traditionally, two separate control charts, each for the mean and variance are used concurrently to monitor the process mean and process variance. However, in many real life process monitoring situations, a simultaneous control of the process mean and process variance is necessary. This has motivated us to develop single DEWMA (called Double Exponentially Weighted Moving Average) charts which are capable of monitoring simultaneous shifts in both the process mean and process variance, when the underlying distribution of the process is normal. The DEWMA statistics are based on the approach of performing exponential smoothing twice on the original statistics of the underlying process. The objective of this study is to propose three single DEWMA charts, namely the DEWMA-Max (called the DEWMA maximum), Max-DEWMA (called the maximum DEWMA) and SS-DEWMA (called the sum of squares of DEWMA) charts

Data Mining For Robust Tests Of Spread [QA76.9.D343 T26 2008 f rb].

Data pelbagai dimensi (data simulasi) dalam kuantiti yang besar daripada halaman output SAS bagi enam ratus tiga puluh empat ujian teguh kehomogenan varians tersedia dihasilkan oleh Keselman, Wilcox, Algina, Othman, dan Fradette (dalam pencetakan). Large quantity of multidimensional data (simulation data sets) from SAS output listings of six hundred and thirty four robust tests of spread procedures conducted by Keselman, Wilcox, Algina, Othman, and Fradette (in press) was available

A Comparison on the MRL Performances of Optimal MEWMA and Optimal MCUSUM Control Charts

The MEWMA (called the multivariate exponentially weighted moving average) chart and the MCUSUM (called the multivariate cumulative sum) chart are used in process monitoring when a quick detection of small or moderate shifts in the mean vector is desired. The primary objective of this study is to compare the performances of the optimal MEWMA and optimal MCUSUM charts based on their median run length (MRL) profiles. The number of quality characteristics considered is p = 2. Two cases are studied, i.e., Case 1 (a shift in only one variable) and Case 2 (a shift in two variables). A Monte Carlo simulation is conducted using Statistical Analysis Software (SAS) to study and compare the MRL performances for various magnitudes of mean shifts when the process is normally distributed. Overall, the results show that the MRL performances of the MEWMA and MCUSUM charts are comparable

A new revised M-Of-K Run Rules Method in X-Bar control chart for estimated parameters.

Good knowledge and understanding of the behaviour of the control chart with estimated process parameters is very essential to engineers. Since the run length distribution is highly right-skewed and the skewness changes with designed parameters, average run length does not provide a complete understanding about the performance of the control chart with estimated process parameters

A robust test based on bootstrapping for the two-sample scale problem

For testing the homogeneity of variances, modifications of well-known tests are known which combine rigorous theory with resampling (bootstrap). We propose versions of these tests, which are computationally simpler (although asymptotically equivalent). The earlier procedures used the smooth bootstrap with two thousand bootstrap replications per sample whereas our proposals use only the classical bootstrap (or percentile method) with just one thousand bootstrap replications per sample, and also required much less computing time. Our proposals cover the Ansari-Bradley-, Mood- and Klotz-tests. We explain their superiority over the existing methodologies available in textbooks and package

Sensitivity of normality tests to non-normal data

In many statistical analyses, data need to be approximately normal or normally distributed. The Kolmogorov-Smirnov test, Anderson-Darling test, Cramer-von Mises test, and Shapiro-Wilk test are four statistical tests that are widely used for checking normality. One of the factors that influence these tests is the sample size. Given any test of normality mentioned, this study determined the sample sizes at which the tests would indicate that the data is not normal. The performance of the tests was evaluated under various spectrums of non-normal distributions and different sample sizes. The results showed that the Shapiro-Wilk test is the best normality test because this test rejects the null hypothesis of normality test at the smallest sample size compared to the other tests, for all levels of skewness and kurtosis of these distributions

A SAS program to assess the sensitivity of normality tests on non-normal data

In many statistical analyses, the data is usually assumed to be approximately normal or normally distributed. Unfortunately, not all data can be assumed normal in real life.To assess the normality of the data, there are four statistical tests, i.e. the Kolmogorov-Smirnov test, the Anderson-Darling test, the Cramer-von Mises test, and the Shapiro-Wilk test that are extensively used by practitioners.The general purpose of this article is to provide a demonstration of Base SAS programming codes of DATA STEP, PROC UNIVARIATE, PROC MEANS and SAS functions to evaluate the performance of the above mentioned tests, under various spectrums of non-normal distributions and different sample sizes.Another important goal is to help researchers adapt these codes to perform similar analyses for other non-normal distributions or other normality tests.This is to encourage the researchers to check the sensitivity of the normality tests before they implement any test that requires assumption of normality

A study on the S2-EWMA chart for monitoring the process variance based on the MRL performance

The existing optimal design of the fixed sampling interval S2-EWMA control chart to monitor the sample variance of a process is based on the average run length (ARL) criterion. Since the shape of the run length distribution changes with the magnitude of the shift in the variance, the median run length (MRL) gives a more meaningful explanation about the in-control and out-of-control performances of a control chart. This paper proposes the optimal design of the S2-EWMA chart, based on the MRL. The Markov chain technique is employed to compute the MRLs. The performances of the S2-EWMA chart, double sampling (DS) S2 chart and S chart are evaluated and compared. The MRL results indicated that the S2-EWMA chart gives better performance for detecting small and moderate variance shifts, while maintaining almost the same sensitivity as the DS S2 and S charts toward large variance shifts, especially when the sample size increases