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.

A MAGNITUDE-ROBUST CONTROL CHART FOR MONITORING AND ESTIMATING STEP CHANGES IN A POISSON RATE PARAMETER

2007 ◽  
Vol 14 (01) ◽  
pp. 1-19 ◽  
Author(s):  
MARCUS B. PERRY ◽  
JOSEPH J. PIGNATIELLO ◽  
JAMES R. SIMPSON
Keyword(s):  
Control Chart ◽  
Control Charts ◽  
Average Run Length ◽  
Maximum Likelihood Estimates ◽  
Cusum Chart ◽  
Rate Parameter ◽  
Statistical Process ◽  
Wide Range ◽  
Statistical Process Control Charts ◽  
Performance Results

Statistical process control charts are intended to assist operators in detecting process changes. If a process change does occur, the control chart should detect the change quickly. If the operator is provided with an estimate as to when the process changed, the search to find the special cause can be more easily facilitated. We investigate a process-monitoring tool for Poisson count data that quickly responds to process mean count rate changes regardless of the magnitude of the change, while supplying useful diagnostic information. A likelihood ratio approach was used to develop a control chart for a permanent step change in a Poisson process rate parameter. The average run length (ARL) performance of this chart is compared to that of several Poisson cumulative sum (CUSUM) control charts. Our performance results show that the proposed chart performs better than any one CUSUM chart over a wide range of potential shift magnitudes. The proposed chart also provides maximum likelihood estimates of the time and the magnitude of the process shift. These crucial change point diagnostics can greatly enhance the special cause investigation.

scholarly journals An EWMA-DiD Control Chart to Capture Small Shifts in the Process Average Using Auxiliary Information

Technologies ◽  
2018 ◽  
Vol 6 (3) ◽  
pp. 69
Author(s):  
Muhammad Mughal ◽  
Muhammad Azam ◽  
Muhammad Aslam
Keyword(s):  
Control Chart ◽  
Control Charts ◽  
Average Run Length ◽  
Auxiliary Information ◽  
Process Variations ◽  
Specific Situation ◽  
Practical Application ◽  
Statistical Process ◽  
Real Scenario ◽  
Better Than

Among the Statistical Process Control (SPC) techniques, control charts are considered to be high weight-age due to their effectiveness in process variation. As the Shewhart’s charts are not that active in monitoring small and moderate process variations, the statisticians have been making efforts to improve the performance of the control chart by introducing several techniques within the tool. These techniques consist of experimenting with different estimators, different sampling selection techniques, and mixed methodologies. The proposed chart is one of the examples of a mixed chart technique that has shown its efficiency in monitoring small variations better than any of the existing techniques in the specific situation of auxiliary information. To show and compare its performance, average run length (ARL) tables and ARL curves have been presented in the article. An industrial example has also been included to show the practical application of the proposed chart in a real scenario.

Statistical Process Control on Time Delay Feedback Adjustment Process

2011 ◽  
Vol 211-212 ◽  
pp. 305-309
Author(s):  
Hai Yu Wang
Keyword(s):  
Time Delay ◽  
Control Chart ◽  
Control Charts ◽  
Average Run Length ◽  
Adjustment Process ◽  
Statistical Process ◽  
Controlled Processes ◽  
Monitoring Process ◽  
Set Up ◽  
And Control

Control chart can be designed to quickly detect small shifts in the mean of a sequence of independent normal observations. But this chart cannot perform well for autocorrelated process. The main goal of this article is to suggest a control chart method using to monitoring process with different time delay feedback controlled processes. A quality control model based on delay feedback controlled processes is set up. And the calculating method of average run length of control charts based on process output and control action of multiple steps delay MMSE feedback controlled processes is provided to evaluate control charts performance. A simple example is used to illustrate the procedure of this approach.

scholarly journals An Improved Dual-Kurtogram-Based T 2 Control Chart for Condition Monitoring and Compound Fault Diagnosis of Rolling Bearings

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Zhiyuan Jiao ◽  
Wei Fan ◽  
Zhenying Xu
Keyword(s):  
Fault Diagnosis ◽  
Control Chart ◽  
Condition Monitoring ◽  
Control Limit ◽  
Normal Operation ◽  
Multivariate Statistical ◽  
Statistical Process ◽  
Envelope Analysis ◽  
Spectral Kurtosis ◽  
Vibration Data

Condition monitoring and compound fault diagnosis are crucial key points for ensuring the normal operation of rotating machinery. A novel method for condition monitoring and compound fault diagnosis based on the dual-kurtogram algorithm and multivariate statistical process control is established in this study. The core idea of this method is the capability of the dual-kurtogram in extracting subbands. Vibration data under normal conditions are decomposed by the dual-kurtogram into two subbands. Then, the spectral kurtosis (SK) of Subband I and the envelope spectral kurtosis (ESK) of Subband II are formulated to construct a control limit based on kernel density estimation. Similarly, vibration data that need to be monitored are constructed into two subbands by the dual-kurtogram. The SK of Subband I and the ESK of Subband II are calculated to derive T 2 statistics based on the covariance determinant. An alarm will be triggered when the T 2 statistics exceed the control limit and suitable subbands for square envelope analysis are adopted to obtain the characteristic frequency. Simulation and experimental data are used to verify the feasibility of the proposed method. Results confirm that the proposed method can effectively perform condition monitoring and fault diagnosis. Furthermore, comparison studies show that the proposed method outperforms the traditional T 2 control chart, envelope analysis, and empirical mode decomposition.

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

scholarly journals PENERAPAN METODE PENGENDALIAN KUALITAS MEWMA BERDASARKAN ARL DENGAN PENDEKATAN RANTAI MARKOV (Studi Kasus: Batik Semarang 16, Meteseh)

2021 ◽  
Vol 10 (1) ◽  
pp. 125-135
Author(s):  
Enggartya Andini ◽  
Sudarno Sudarno ◽  
Rita Rahmawati
Keyword(s):  
Markov Chain ◽  
Production Process ◽  
Control Chart ◽  
Average Run Length ◽  
Moving Average ◽  
Control Limit ◽  
Quality Characteristic ◽  
Markov Chain Approach ◽  
Mewma Control Chart ◽  
Weighted Moving Average

An industrial company requires quality control to maintain quality consistency from the production results so that it is able to compete with other companies in the world market. In the industrial sector, most processes are influenced by more than one quality characteristic. One tool that can be used to control more than one quality characteristic is the Multivariate Exponentially Weighted Moving Average (MEWMA) control chart. The graph is used to determine whether the process has been controlled or not, if the process is not yet controlled, the next analysis that can be used is to use the Average Run Length (ARL) with the Markov Chain approach. The markov chain is the chance of today's event is only influenced by yesterday's incident, in this case the chance of the incident in question is the incident in getting a sampel of data on the production process of batik cloth to get a product that is in accordance with the company standards. ARL is the average number of sample points drawn before a point indicates an uncontrollable state. In this study, 60 sample data were used which consisted of three quality characteristics, namely the length of the cloth, the width of the cloth, and the time of the fabric for the production of written batik in Batik Semarang 16 Meteseh. Based on the results and discussion that has been done, the MEWMA controller chart uses the λ weighting which is determined using trial and error. MEWMA control chart can not be said to be stable and controlled with λ = 0.6, after calculating, the value is obtained Upper Control Limit (BKA) of 11.3864 and Lower Control Limit (BKB) of 0. It is known that from 60 data samples there is a Tj2 value that comes out from the upper control limit (BKA) where the amount of 15.70871, which indicates the production process is not controlled statistically. Improvements to the MEWMA controller chart can be done based on the ARL with the Markov Chain approach. In this final project, the ARL value used is 200, the magnitude of the process shift is 1.7 and the r value is 0.28, where the value of r is a constant obtained on the r parameter graph. The optimal MEWMA control chart based on ARL with the Markov Chain approach can be said to be stable and controlled if there is no Tj2 value that is outside the upper control limit (BKA). The results of the MEWMA control chart based on the ARL with the Markov Chain approach show that the process is not statistically capable because the MCpm value is 0.516797 and the MCpmk value is 0.437807, the value indicates a process capability index value of less than 1. Keywords: Handmade batik, Multivariate Exponentially Weighted Moving Average (MEWMA), Average Run Length (ARL), Capability process.

DOUBLE BOOTSTRAP CONTROL CHART FOR MONITORING SUKUK VOLATILITY AT BURSA MALAYSIA

2017 ◽  
Vol 79 (6) ◽  
Author(s):  
Muhamad Safiih Lola ◽  
Nurul Hila Zainuddin ◽  
Mohd Noor Afiq Ramlee ◽  
Hizir Sofyan
Keyword(s):  
Control Chart ◽  
Average Run Length ◽  
Control Limit ◽  
Medium Size ◽  
Large Magnitude ◽  
Proposed Model ◽  
Bootstrap Approach ◽  
Sample Data ◽  
Double Bootstrap ◽  
Type Ii Error Rate

The bootstrap approach on control limit has provided a solution in solving uncertainty estimation problem in control chart performance. However, the limitation of this standard chart has shown to be less efficient and invalidation at certain magnitude shift, especially the monitored sample data is assumed from skewed family distribution. Thus, in this study, a double bootstrap base-model and its control limit is developed in order to improve the efficiency and decrease the invalidation chart performance. In order to test the performance of proposed model, a simulation study using Average Run Length (ARL) and Type II Error rate were implemented. The result has shown that the proposed chart is sensitive and effective in detecting the shift process for small and medium size of skewed sample data. Also, it has found that the proposed chart shown to has better performance on large magnitude shift. The performance of the proposed model was investigated further using sukuk volatility data at Bursa Malaysia. The result revealed that the double bootstrap control chart is sensitive to small shifts process when it can detect changes in the volatility faster. In other words, it is efficient in monitoring the shifts process. Thus, the proposed model could help the traders in making a new decision, for example, either save/hold for a certain period, sell or buy the sukuk certificate.  

scholarly journals Impact of Different Repetitive Sampling Schemes on the Performance of X-bar Control Chart

2020 ◽  
pp. 191-201
Author(s):  
Muhammad Anwar Mughal ◽  
Muhammad Azam ◽  
Muhammad Aslam
Keyword(s):  
Control Chart ◽  
Control Charts ◽  
Selection Process ◽  
Average Run Length ◽  
Control Limit ◽  
Sample Sizes ◽  
Sampling Schemes ◽  
Additional Control ◽  
And Performance ◽  
Control Limits

Repetitive sampling has been found very popular in improving the control chart techniques for last couple of years. In repetitive sampling based control charts, there are two additional control limits inside the usual upper control limit (UCL) and lower control limit (LCL). If any subgroup crosses these limits but remain inside outer limits, it is deferred and replaced with another selection. Process is said to be out of control if any subgroup falls outside UCL/LCL. In this article, the technique has been modified by introducing a relation between outer and inner control limits in terms of a ratio and need of this modification has also been justified by highlighting a gap in the existing technique. By using Monte Carlo simulation, several results have been generated relevant to different sample sizes and introduced ratios. The results have been described with the help of average run length (ARL) tables that how the efficiency of control chart is effected by using different ratios. The modification in the technique also provides variety of alternatives within the scope of repetitive based control charts. All the discussed options have summarized to one table to see that how the control limits under this technique behave and impact on detecting shifts in the process average. The schemes have been interpreted in the light of above ratio and their comparison has been described under different sample sizes that facilitate the user to select most appropriate scheme for a desired process control. An example has been included by choosing one of the proposed schemes to show the application and performance of the proposed control chart in a manufacturing process. 

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