Yupaporn Areepong

Bivariate copulas on the Hotelling's T2 control chart

ABSTRACT In this paper, we propose five types of copulas on the Hotellings T2 control chart when observations are from exponential distribution and use the Monte Carlo simulation to compare the performance of the control chart, which is based on the Average Run Length (ARL) for each copula. Five types of copulas function for specifying dependence between random variables are used and measured by Kendalls tau. The results show that the copula approach can be fitted the observation and we can use copula as an option for application on Hotellings T2 control chart.

Multivariate copulas on the MCUSUM control chart

Abstract The copula approach is a popular method for multivariate modeling applied in several fields; it defines non-parametric measures of dependence between random variables. In this paper, three families are proposed from elliptical and Archimedean copulas on the multivariate cumulative sum (MCUSUM) control chart when observations are draw from an exponential distribution. The performance of the control chart is based on the average run length (ARL)—via Monte Carlo simulations. A copula function for specifying the dependence between random variables is measured by Kendall’s tau. The numerical results indicate that the observations can be fitted and that the copula can be used on the MCUSUM for cases of small and large dependencies.

Explicit analytical solutions for ARL of CUSUM chart for a long-memory SARFIMA model

ABSTRACT This paper aims to derive explicit analytical solutions for Average Run Length (ARL) of CUSUM chart for the SARFIMA(P,D,Q)S process with exponential white noise. Measurement of performance was done with the ARL in terms of percentage error and CPU time. The results obtained from the explicit formulas were compared focusing on the performance using the numerical integral equation (NIE) method. Both methods had similarly excellent agreement with the percentage error at less than 0.25%. Meanwhile, the explicit formulas consumed less CPU time than the NIE method. It is clear that the explicit formulas are a good alternative in real applications.

Average run length of the long-memory autoregressive fractionally integrated moving average process of the exponential weighted moving average control chart

Abstract Measurement of control chart efficiency by comparison of average run length (ARL) is widely implemented in quality control. The aim of this study is to evaluate the ARL, which is a solution of the integral equation obtained from the Exponential Weighted Moving Average (EWMA) statistic with a long-memory Autoregressive Fractionally Integrated Moving Average (ARFIMA) process. The derivation of the analytical ARL of the EWMA control chart and proof of the existence and uniqueness of the analytical ARL by Fixed Point theory are shown. Moreover, the numerical ARL carried out by the Composite Midpoint Rule technique of the EWMA control chart is demonstrated. A comparison between the analytical and numerical ARL is also illustrated. The findings indicated that analytical ARL of the EWMA control chart is more quickly computational than the numerical ARL. Therefore, the analytical ARL is an alternative method for measuring the efficiency of the EWMA control chart with the long-memory ARFIMA process.

Odds Ratios Estimation of Rare Event in Binomial Distribution

We introduce the new estimator of odds ratios in rare events using Empirical Bayes method in two independent binomial distributions. We compare the proposed estimates of odds ratios with two estimators, modified maximum likelihood estimator (MMLE) and modified median unbiased estimator (MMUE), using the Estimated Relative Error (ERE) as a criterion of comparison. It is found that the new estimator is more efficient when compared to the other methods.

AN EXPLICIT EXPRESSION OF AVERAGE RUN LENGTH OF EXPONENTIALLY WEIGHTED MOVING AVERAGE CONTROL CHART WITH ARIMA(p, d, q)(P, D, Q)_L MODELS

In this paper we propose the explicit formulas of Average Run Length (ARL) of Exponentially Weighted Moving Average (EWMA) control chart for Autoregressive Integrated Moving Average: ARIMA (p,d,q) (P, D, Q)L process with exponential white noise. To check the accuracy, the ARL results were compared with numerical integral equations based on the Gauss-Legendre rule. There was an excellent agreement between the explicit formulas and the numerical solutions. Additionally, we compared the computational time between our explicit formulas for the ARL with the one obtained via Gauss-Legendre numerical scheme. The computational time for the explicit formulas was approximately one second that is much less than the numerical approximations. The explicit analytical formulas for evaluating ARL0 and ARL1 can produce a set of optimal parameters which depend on the smoothing parameter (λ) and the width of control limit (H), for designing an EWMA chart with a minimum ARL1.