Average run length function of CUSUM test with independent but non-stationary log-likelihood ratios

2013 ◽  
Author(s):  
Yu Liu ◽  
X. Rong Li
Keyword(s):  
Average Run Length ◽  
Length Function ◽  
Cusum Test ◽  
Likelihood Ratios ◽  
Run Length ◽  
Log Likelihood

scholarly journals ARL Estimation of the Control Chart of Log Likelihood Ratios’ Sum for Markov Sequence

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Yi Guo ◽  
Lei Gao ◽  
Yan Zhu
Keyword(s):  
Control Chart ◽  
Average Run Length ◽  
Positive Control ◽  
Negative Control ◽  
Control Limit ◽  
Likelihood Ratios ◽  
Statistical Process ◽  
Markov Sequence ◽  
Log Likelihood ◽  
Proof Procedure

To evaluate the surveillance performance of a control chart with the charting statistic of the sum of log likelihood ratios in the statistical process control (SPC), in this paper, we give the proof procedure based on Markov chains for the asymptotic estimation of the average run length (ARL) for this kind of chart. The out-of-control ARL 1 is approximately equal to 1 for any fixed in-control ARL 0 with a negative control limit. By the equivalence between limit distribution of a sum and that of a suprema sum of Markov chain, we derive the estimation of ARL 1 with a large enough positive control limit. Numerical experiments are conducted to confirm our results.

scholarly journals Water Particles Monitoring in the Atacama Desert: SPC Approach Based on Proportional Data

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 154
Author(s):  
Anderson Fonseca ◽  
Paulo Henrique Ferreira ◽  
Diego Carvalho do Nascimento ◽  
Rosemeire Fiaccone ◽  
Christopher Ulloa-Correa ◽  
...  
Keyword(s):  
Control Chart ◽  
Average Run Length ◽  
Atacama Desert ◽  
Real Data ◽  
Interval Data ◽  
Total Quality ◽  
Statistical Process ◽  
Monte Carlo Simulation Study ◽  
Run Length ◽  
Study Results

Statistical monitoring tools are well established in the literature, creating organizational cultures such as Six Sigma or Total Quality Management. Nevertheless, most of this literature is based on the normality assumption, e.g., based on the law of large numbers, and brings limitations towards truncated processes as open questions in this field. This work was motivated by the register of elements related to the water particles monitoring (relative humidity), an important source of moisture for the Copiapó watershed, and the Atacama region of Chile (the Atacama Desert), and presenting high asymmetry for rates and proportions data. This paper proposes a new control chart for interval data about rates and proportions (symbolic interval data) when they are not results of a Bernoulli process. The unit-Lindley distribution has many interesting properties, such as having only one parameter, from which we develop the unit-Lindley chart for both classical and symbolic data. The performance of the proposed control chart is analyzed using the average run length (ARL), median run length (MRL), and standard deviation of the run length (SDRL) metrics calculated through an extensive Monte Carlo simulation study. Results from the real data applications reveal the tool’s potential to be adopted to estimate the control limits in a Statistical Process Control (SPC) framework.

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 Monitoring multinomial processes based on a weighted chi-square control chart

2021 ◽  
Vol 28 (3) ◽  
Author(s):  
Achouri Ali ◽  
Emira Khedhiri ◽  
Ramzi Talmoudi ◽  
Hassen Taleb
Keyword(s):  
Quality Improvement ◽  
Control Chart ◽  
Process Improvement ◽  
Average Run Length ◽  
The Other ◽  
Statistical Control ◽  
Chi Square ◽  
Crucial Step ◽  
Run Length ◽  
Control Situation

Abstract: Interpreting an out-of-control signal is a crucial step in monitoring categorical processes. For the Chi-Square Control Chart (CSCC), an out-of control situation does not specify if it was a process deterioration or a process improvement. For this reason, a weighted chi-square statistical control chart WSCC is proposed with different weighting categories in order to enable an accelerated disclosure of a control situation after a shift due to a deterioration of quality and on the other hand, decelerate an out of control situation after a shift due to a quality improvement. Furthermore, in comparison with Marcucci’s method, the new procedure provides an accurate and easier way to interpret several signals. In other words, the WSCC allows a faster detection of an out-of control situation in the case of a quality deterioration, however, an out-of control situation is not quickly detected in the case of a quality improvement. Indeed, comparative studies have been performed to find the best control chart for each combination. Concluding remarks with comments and recommendations are given based on Average Run Length (ARL) and standard deviation run length (SDRL).

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                                       

Monitoring Parkinson's Disease from phonation improvement by Log Likelihood Ratios

2015 ◽  
Author(s):  
Pedro Gomez-Vilda ◽  
Agustin Alvarez-Marquina ◽  
Victoria Rodellar-Biarge ◽  
Victor Nieto-Lluis ◽  
Rafael Martinez-Olalla ◽  
...  
Keyword(s):  
Parkinson’S Disease ◽  
Parkinson's Disease ◽  
Likelihood Ratios ◽  
Log Likelihood
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