Uniqueness and convergence of solutions to average run length integral equations for cumulative sum and other control charts

2001 ◽  
Vol 33 (6) ◽  
pp. 463-469 ◽  
Author(s):  
B. VENKATESHWARA RAO ◽  
RALPH L. DISNEY ◽  
JOSEPH J. PIGNATIELLO
Keyword(s):  
Integral Equations ◽  
Control Charts ◽  
Average Run Length ◽  
Cumulative Sum ◽  
Run Length ◽  
Convergence Of Solutions

scholarly journals Multivariate Statistical Quality Control Based on Ranked Set Sampling

2017 ◽  
Vol 14 (1) ◽  
pp. 1
Author(s):  
Hakan Eygü ◽  
M. Suphi Özçomak
Keyword(s):  
Control Charts ◽  
Sampling Methods ◽  
Average Run Length ◽  
Ranked Set Sampling ◽  
Multivariate Statistical ◽  
Run Length ◽  
Hotelling's T2 ◽  
Median Ranked Set Sampling ◽  
Hotelling’S T2 ◽  
T2 Control Chart

The sample of the study was formed using simple random sampling, ranked set sampling, extreme ranked set sampling and median ranked set sampling. At the end of this process, the researcher created Hotelling’s T2 control charts, a multivariate statistical process control method. The performances of SRS, RSS, ERSS and MRSS sampling methods were compared to one another using these control charts. A simulation was performed to see the average run-length values for Hotelling’s T2 control charts, and these findings were also used for the comparison of the sampling performances.At the end of the study, the researcher formed a sample using median ranked set sampling and created the Hotelling’s T2 control chart. As a result of this operation, the researcher found that there was an out-of-control signal in the process, while there was no such signal in other sampling methods. When the average run-length values obtained from Hotelling’s T2 control charts were compared, it was seen that a shift in the process was detected by the ranked set sampling earlier, when compared to other sampling methods. This paper it can be said that the methods used are unique to the literature because they are applied to multivariate data.

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 GRAFIK PENGENDALI MIXED EXPONENTIALLY WEIGHTED MOVING AVERAGE – CUMULATIVE SUM (MEC) DALAM ANALISIS PENGAWASAN PROSES PRODUKSI (Studi Kasus : Wingko Babat Cap “Moel”)

2021 ◽  
Vol 10 (1) ◽  
pp. 114-124
Author(s):  
Aulia Resti ◽  
Tatik Widiharih ◽  
Rukun Santoso
Keyword(s):  
Control Chart ◽  
Control Charts ◽  
Average Run Length ◽  
Moving Average ◽  
Exponentially Weighted Moving Average ◽  
Cumulative Sum ◽  
Statistical Process ◽  
Cusum Charts ◽  
Weighted Moving Average ◽  
Exponentially Weighted

Quality control is an important role in industry for maintain quality stability.  Statistical process control can quickly investigate the occurrence of unforeseen causes or process shifts using control charts. Mixed Exponentially Weighted Moving Average - Cumulative Sum (MEC) control chart is a tool used to monitor and evaluate whether the production process is in control or not. The MEC control chart method is a combination of the Exponentially Weighted Moving Average (EWMA) and Cumulative Sum (CUSUM) charts. Combining the two charts aims to increase the sensitivity of the control chart in detecting out of control. To compare the sensitivity level of the EWMA, CUSUM, and MEC methods, the Average Run Length (ARL) was used. From the comparison of ARL values, the MEC chart is the most sensitive control chart in detecting out of control compared to EWMA and CUSUM charts for small shifts. Keywords: Grafik Pengendali, Exponentially Weighted Moving Average, Cumulative Sum, Mixed EWMA-CUSUM, Average Run Lenght, EWMA, CUSUM, MEC, ARL

In-control robustness comparison of different control charts

2017 ◽  
Vol 40 (13) ◽  
pp. 3860-3871 ◽  
Author(s):  
Muhammad Abid ◽  
Hafiz Zafar Nazir ◽  
Muhammad Riaz ◽  
Zhengyan Lin
Keyword(s):  
Standard Deviation ◽  
Control Chart ◽  
Control Charts ◽  
Average Run Length ◽  
Location Parameter ◽  
Normal Distributions ◽  
Run Length ◽  
Design Structure ◽  
Control Robustness ◽  
Proper Design

Control charts are widely used to monitor the process parameters. Proper design structure and implementation of a control chart requires its in-control robustness, otherwise, its performance cannot be fairly observed. It is important to know whether a chart is sensitive to disturbances to the model (e.g. normality under which it is developed) or not. This study, explores the robustness of Mixed EWMA-CUSUM (MEC) control chart for location parameter under different non-normal and contaminated environments and compares it with its counterparts. The robustness of the MEC scheme and counterparts is evaluated by using the run length distributions, and for better assessment not only is in-control average run length (ARL) used, but also standard deviation of run length (SDRL) and different percentiles – that is, 5th, 50th and 95th– are considered. A careful insight is necessary in selection and application of control charts in non-normal and contaminated environments. It is observed that the in-control robustness performance of the MEC scheme is quite good in the case of normal, non-normal and contaminated normal distributions as compared with its competitor’s schemes.

ARL1 of the Attribute c Control Chart with Estimated Parameter

2015 ◽  
Vol 22 (02) ◽  
pp. 1550009 ◽  
Author(s):  
Teodor Tiplica
Keyword(s):  
Control Chart ◽  
Control Charts ◽  
Average Run Length ◽  
Computational Results ◽  
Run Length ◽  
Estimated Parameters ◽  
Starting Point ◽  
Polynomial Expression ◽  
Discrete Nature ◽  
Good Starting Point

In this paper, the out of control average run length (ARL1) of the c control chart with estimated parameter is computed for various shifts in the average number of nonconformities. In spite of the discrete nature of this chart, it is proved that a target in-control average run length (ARL0) can be obtained when the average number of nonconformities is estimated. This is a good starting point for comparing the performances of the c control chart with those of other attribute control charts with estimated parameters. Based on the computational results obtained, it is showed that the ARL1 of the c control chart with estimated parameter can be approximated by using a polynomial expression.

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