EXPLICIT FORMULAS OF AVERAGE RUN LENGTH OF CUMULATIVE SUM CONTROL CHART FOR AUTOREGRESSIVE INTEGRATED MOVING AVERAGE WITH EXOGENOUS VARIABLE MODEL

2017 ◽  
Vol 50 (1) ◽  
pp. 21-36
Author(s):  
Yupaporn Areepong ◽  
Saowanit Sukparungsee
Keyword(s):  
Control Chart ◽  
Average Run Length ◽  
Moving Average ◽  
Exogenous Variable ◽  
Cumulative Sum ◽  
Explicit Formulas ◽  
Variable Model ◽  
Autoregressive Integrated Moving Average ◽  
Run Length ◽  
Cumulative Sum Control

The Performance of CUSUM Control Chart for Monitoring Process Mean for Autoregressive Moving Average with Exogenous Variable Model

2020 ◽  
Author(s):  
Wilasinee Peerajit ◽  
Yupaporn Areepong
Keyword(s):  
Control Chart ◽  
Average Run Length ◽  
Moving Average ◽  
Exogenous Variable ◽  
Percentage Error ◽  
Autoregressive Moving Average ◽  
Explicit Formulas ◽  
Variable Model ◽  
Cusum Control Chart ◽  
R Process

The objective of this study was to derive explicit formulas for the average run length (ARL) of an autoregressive moving average with an exogenous variable (ARMAX(p,q,r)) process with exponential white noise on a cumulative sum (CUSUM) control chart. To check the accuracy of the ARL derivations, the efficiency of the proposed explicit formulas was compared with a numerical integral equation (NIE) method in terms of the absolute percentage error. There was excellent agreement between the two methods, but when comparing their computational times, the explicit formulas only required 1 second whereas the NIE method required 599.499–835.891 s. In addition, real-world application of the derived explicit formulas was illustrated using Hong Kong dollar exchange rates data with an exogenous variable (the US dollar) to evaluate the ARL of an ARMAX (p,q,r) process on a CUSUM control chart.

scholarly journals Explicit Formula for Average Run Length of Double Moving Control Chart for INAR(1) Processes

2016 ◽  
Author(s):  
Sukanya Phant ◽  
Saowanit Sukparungsee ◽  
Yupaporn Areepong
Keyword(s):  
Control Chart ◽  
Count Data ◽  
Average Run Length ◽  
Moving Average ◽  
Serial Dependence ◽  
Explicit Formulas ◽  
Run Length ◽  
Marginal Process ◽  
Average Control ◽  
Better Than

Count data are used in many fields of practice, especially Poisson distribution as a popular choice for the marginal process distribution. If these counts exhibit serial dependence, a popular approach is to use a Poisson INAR(1) model to describe the autocorrelation structure of process. In this paper, the explicit formulas are proposed to evaluate performance characteristics of Double Moving Average control chart (DMA) for Integer valued autoregressive of serial dependence Poisson process. The characteristics of the control chart are frequently measured as Average Run Length (ARL) which means that the average of observations are taken before a system is signaled to be out-of-control. These proposed explicit formulas of ARL are simple and easy to implement for practitioner. The numerical results show that the DMA chart performs better than others when the magnitudes of shift are moderate and large.

Explicit Formulas of ARL on Double Moving Average Control Chart for Monitoring Process Mean of ZIPINAR(1) Model with an Excessive Number of Zeros

2021 ◽  
Author(s):  
Kobkun Raweesawat ◽  
Saowanit Sukparungsee
Keyword(s):  
Control Chart ◽  
Control Charts ◽  
Average Run Length ◽  
Moving Average ◽  
Mean Shift ◽  
Process Mean ◽  
Explicit Formulas ◽  
Run Length ◽  
Number Of Zeros ◽  
Excessive Number

Usually, the performance of control charts are widely measured by average run length (ARL). In this paper, the derivative explicit formulas of the ARL for double moving average (DMA) control chart are proposed for monitoring the process mean of zero-inflated Poisson integer-valued autoregressive first-order (ZIPINAR(1)) model. This model is fit when there are an excessive number of zeros in the count data. The performance of the DMA control chart is compared with the results of moving average and Shewhart control charts by considering from out of control average run length (ARL1). The numerical results found that the DMA control chart performed better than other control charts in order to detect mean shift in the process. In addition, the real-world application of the DMA control chart for ZIPINAR(1) process is addressed.

scholarly journals Average Run Length on CUSUM Control Chart for Seasonal and Non-Seasonal Moving Average Processes with Exogenous Variables

Symmetry ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 173
Author(s):  
Rapin Sunthornwat ◽  
Yupaporn Areepong
Keyword(s):  
Control Chart ◽  
Average Run Length ◽  
Moving Average ◽  
Optimal Parameters ◽  
Exogenous Variables ◽  
Explicit Formulas ◽  
Run Length ◽  
Ewma Control Chart ◽  
Cusum Control Chart ◽  
Moving Average Processes

The aim of this study was to derive explicit formulas of the average run length (ARL) of a cumulative sum (CUSUM) control chart for seasonal and non-seasonal moving average processes with exogenous variables, and then evaluate it against the numerical integral equation (NIE) method. Both methods had similarly excellent agreement, with an absolute percentage error of less than 0.50%. When compared to other methods, the explicit formula method is extremely useful for finding optimal parameters when other methods cannot. In this work, the procedure for obtaining optimal parameters—which are the reference value ( a ) and control limit ( h )—for designing a CUSUM chart with a minimum out-of-control ARL is presented. In addition, the explicit formulas for the CUSUM control chart were applied with the practical data of a stock price from the stock exchange of Thailand, and the resulting performance efficiency is compared with an exponentially weighted moving average (EWMA) control chart. This comparison showed that the CUSUM control chart efficiently detected a small shift size in the process, whereas the EWMA control chart was more efficient for moderate to large shift sizes.

scholarly journals An Explicit Expression of Average Run Length of Exponentially Weighted Moving Average Control Chart with ARIMA (p,d,q)(P, D, Q)L Models

2016 ◽  
Author(s):  
Yupaporn Areepong ◽  
Saowanit Sukparungsee
Keyword(s):  
Control Chart ◽  
Numerical Solutions ◽  
Average Run Length ◽  
Moving Average ◽  
Computational Time ◽  
Exponentially Weighted Moving Average ◽  
Explicit Formulas ◽  
Run Length ◽  
Weighted Moving Average ◽  
Exponentially Weighted

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.

scholarly journals PERBANDINGAN KINERJA PETA KENDALI CUMULATIVE SUM DAN PETA KENDALI EXPONENTIALLY WEIGHTED MOVING AVERAGE

2020 ◽  
Vol 9 (4) ◽  
Author(s):  
Dhea Trinandya Wijayanti, Helmi, Nurfitri Imro’ah
Keyword(s):  
Average Run Length ◽  
Moving Average ◽  
Exponentially Weighted Moving Average ◽  
Cumulative Sum ◽  
Run Length ◽  
Weighted Moving Average ◽  
Exponentially Weighted

 Pada umumnya peta kendali yang sering digunakan dalam pengendalian kualitas statistik adalah peta kendali Shewhart. Peta kendali ini bekerja hanya dengan menggunakan informasi yang terkandung dalam titik sampel terakhir dan mengabaikan informasi dari seluruh barisan titik sampel sebelumnya. Hal ini membuat peta kendali Shewhart kurang efektif dalam mendeteksi pergeseran rata-rata yang relatif kecil pada proses produksi. Sebagai alternatif, dikembangkan peta kendali Cumulative Sum (Cusum) dan peta kendali Exponentially Weighted Moving Average (EWMA). Penelitian ini menerapkan peta kendali Cusum dan peta kendali EWMA serta membandingkan kinerjanya dalam mendeteksi pergeseran rata-rata yang relatif kecil pada data produksi. Tahapan pengerjaan dimulai dari melakukan analisis peta kendali Cusum dan peta kendali EWMA dengan menghitung nilai statistik, batas kendali, dan membentuk grafik setiap peta kendali. Selanjutnya, dihitung nilai Average Run Length (ARL) sebagai acuan untuk membandingkan kinerja kedua peta kendali. Berdasarkan hasil penerapannya pada produksi wajan nomor 18 di CV. XYZ, pada peta kendali Cusum tidak terdapat titik-titik yang berada di luar batas kendali. Namun, pada peta kendali EWMA mampu mendeteksi adanya 9 titik yang berada di luar batas kendali sehingga proses produksi tidak terkendali secara statistik. Selain itu berdasarkan perolehan nilai ARL, diketahui nilai ARL peta kendali EWMA menunjukkan hasil yang lebih kecil yaitu sebesar 45,832 dibandingkan dengan nilai ARL peta kendali Cusum yang sebesar 69,108. Dari hasil analisis didapat kesimpulan bahwa peta kendali EWMA lebih efektif daripada peta kendali Cusum dalam mendeteksi adanya pergeseran rata-rata yang relatif kecil pada produksi wajan nomor 18 di CV. XYZ. Kata Kunci: Cusum, EWMA, ARL                                       

An EWMA control chart based on the Wilcoxon rank-sum statistic using repetitive sampling

2018 ◽  
Vol 35 (3) ◽  
pp. 711-728 ◽  
Author(s):  
Jean-Claude Malela-Majika ◽  
Olatunde Adebayo Adeoti ◽  
Eeva Rapoo
Keyword(s):  
Control Chart ◽  
Average Run Length ◽  
Moving Average ◽  
Location Parameter ◽  
Process Mean ◽  
Content Type ◽  
Underlying Process ◽  
Run Length ◽  
Design And Implementation ◽  
Ewma Control Chart

Purpose The purpose of this paper is to develop an exponentially weighted moving average (EWMA) control chart based on the Wilcoxon rank-sum (WRS) statistic using repetitive sampling to improve the sensitivity of the EWMA control chart to process mean shifts regardless of the prior knowledge of the underlying process distribution. Design/methodology/approach The proposed chart is developed without any distributional assumption of the underlying quality process for monitoring the location parameter. The authors developed formulae as well as algorithms to facilitate the design and implementation of the proposed chart. The performance of the proposed chart is investigated in terms of the average run-length, standard deviation of the run-length (RL), average sample size and percentiles of the RL distribution. Numerical examples are given as illustration of the design and implementation of the proposed chart. Findings The proposed control chart presents very attractive RL properties and outperforms the existing nonparametric EWMA control chart based on the WRS in the detection of the mean process shifts in many situations. However, the performance of the proposed chart relatively deteriorates for small phase I sample sizes. Originality/value This study develops a new control chart for monitoring the process mean using a two-sample test regardless of the nature of the underlying process distribution. The proposed control chart does not require any assumption on the type (or nature) of the process distribution. It requires a small number of subgroups in order to reach stability in the phase II performance.

Sign in / Sign up

Export Citation Format

Share Document