scholarly journals The Expected Average Run Length of the EWMA Median Chart with Estimated Process Parameters

2020 ◽  
Vol 49 (3) ◽  
pp. 19-24
Author(s):  
Huay Woon You ◽  
Michael Khoo Boon Chong ◽  
Chong Zhi Lin ◽  
Teoh Wei Lin
Keyword(s):  
Phase I ◽  
Control Chart ◽  
Process Parameters ◽  
Average Run Length ◽  
Moving Average ◽  
Background Knowledge ◽  
Exponentially Weighted Moving Average ◽  
Control Phase ◽  
Run Length ◽  
Weighted Moving Average

The performance of a control chart is commonly investigated based on the assumption of known process parameters. Nevertheless, in most manufacturing and service applications, the process parameters are usually unknown to practitioners. Hence, they are estimated from an in-control Phase-I samples. As such, the performance of the control chart with estimated process parameters will behave differently from the corresponding chart with known process parameters. To study this issue, the exponentially weighted moving average (EWMA) median chart is examined in this article. The EWMA median chart is traditionally investigated based on the average run length (ARL). The limitation of the ARL is that it requires practitioners to specify the shift size in advance. This phenomenon is not ideal for practitioners who do not have background knowledge of the process. In view of this, the EWMA median chart with known and estimated process parameters is studied based on the ARL and expected average run length (EARL). The results indicate that as long as the particular shift size is within the range of shifts, the performance of the chart is almost the same, for the EWMA median chart with known and estimated process parameters.

scholarly journals A New Generalized Range Control Chart for the Weibull Distribution

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
Osama H. Arif ◽  
Muhammad Aslam
Keyword(s):  
Weibull Distribution ◽  
Control Chart ◽  
Control Charts ◽  
Average Run Length ◽  
Moving Average ◽  
Comparison Study ◽  
Exponentially Weighted Moving Average ◽  
Run Length ◽  
Weighted Moving Average ◽  
Exponentially Weighted

In this study, a generalized range control chart is designed for the Weibull distribution using generally weighted moving average statistics. The proposed chart is based on minimum generally weighted moving average statistic and maximum generally weighted moving average statistics. We utilize the inverse erf function to transform the Weibull data to normal data. The necessary measures are given to assess the performance of the proposed control chart. The comparison study shows that the proposed control chart outperforms the existing control charts based on exponentially weighted moving average statistic in terms of the average run length. A real example is given for applying the proposed chart in the industry.

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                                       

scholarly journals A synthetic exponentially weighted moving average control chart to monitor process median based on ranked set sampling

2021 ◽  
Vol 36 ◽  
pp. 01002
Author(s):  
Jing Wen Ng ◽  
Voon Hee Wong ◽  
Sook Theng Pang
Keyword(s):  
Control Chart ◽  
Moving Average ◽  
Length Distribution ◽  
Ranked Set Sampling ◽  
Exponentially Weighted Moving Average ◽  
Process Mean ◽  
Run Length ◽  
Ewma Chart ◽  
Run Length Distribution ◽  
Weighted Moving Average

Exponentially Weighted Moving Average (EWMA) control charts yield insights into data in a way more comprehensible to the practitioners and researchers because of its capability in discovering small to moderate process mean shifts. EWMA control chart is incorporated with conforming run length (CRL) chart, named synthetic EWMA chart, to enhance the performance of the chart in detecting the out-of-control signal. Synthetic EWMA chart based on ranked set sampling (RSS) for monitoring process mean has been proposed as it advanced the detection of chart over a series of mean shifts. With the situation that normality assumption is scarcely attain in practice, we proposed synthetic EWMA median chart based on RSS. Rather than select average run length (ARL) as sole performance evaluating tool, the median and percentiles of run-length distribution are used to examine the performance of the proposed chart as it provides more information on the entire run-length distribution. Near-optimal parameters of the proposed chart will be acquired by setting the incontrol ARL at a designated value. The run length performances of the proposed chart are then compared with the existing charts such as EWMA median chart based on RSS.

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