scholarly journals Multiple Dependent State Repetitive Sampling-Based Control Chart for Birnbaum–Saunders Distribution

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Muhammad Aslam ◽  
Ambreen Shafqat ◽  
G. Srinivasa Rao ◽  
Jean-Claude Malela-Majika ◽  
Sandile C. Shongwe
Keyword(s):  
Control Chart ◽  
Simulation Study ◽  
Control Charts ◽  
Average Run Length ◽  
Real Life ◽  
Detection Ability ◽  
Run Length ◽  
Comprehensive Comparison ◽  
Shift Detection ◽  
Dependent State

This paper proposes a new control chart for the Birnbaum–Saunders distribution based on multiple dependent state repetitive sampling (MDSRS). The proposed control chart is a generalization of the control charts based on single sampling, repetitive sampling, and multiple dependent state sampling. Its sensitivity is evaluated in terms of the average run length (ARL) using both exact formulae and simulations. A comprehensive comparison between the Birnbaum–Saunders distribution control chart based on the MDSRS method and other existing competing methods is provided using a simulation study as well as a real-life illustration. The results reveal that the proposed chart outperforms the existing charts considered in this study by having better shift detection ability.

scholarly journals Monitoring Mortality Caused by COVID-19 Using Gamma-Distributed Variables Based on Generalized Multiple Dependent State Sampling

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Muhammad Aslam ◽  
G. Srinivasa Rao ◽  
Muhammad Saleem ◽  
Rehan Ahmad Khan Sherwani ◽  
Chi-Hyuck Jun
Keyword(s):  
Control Chart ◽  
Control Charts ◽  
Average Run Length ◽  
Real Life ◽  
Quality Characteristics ◽  
Statistical Quality Control ◽  
Nonnormal Distributions ◽  
Run Lengths ◽  
Chart Design ◽  
Dependent State

More recently in statistical quality control studies, researchers are paying more attention to quality characteristics having nonnormal distributions. In the present article, a generalized multiple dependent state (GMDS) sampling control chart is proposed based on the transformation of gamma quality characteristics into a normal distribution. The parameters for the proposed control charts are obtained using in-control average run length (ARL) at specified shape parametric values for different specified average run lengths. The out-of-control ARL of the proposed gamma control chart using GMDS sampling is explored using simulation for various shift size changes in scale parameters to study the performance of the control chart. The proposed gamma control chart performs better than the existing multiple dependent state sampling (MDS) based on gamma distribution and traditional Shewhart control charts in terms of average run lengths. A case study with real-life data from ICU intake to death caused by COVID-19 has been incorporated for the realistic handling of the proposed control chart design.

scholarly journals A New Control Chart for Monitoring the Process Mean Using Successive Sampling and Multiple Dependent State Repetitive Sampling

Technologies ◽  
2018 ◽  
Vol 6 (3) ◽  
pp. 70
Author(s):  
Mansour Sattam Aldosari ◽  
Muhammad Aslam ◽  
Chi-Hyuck Jun ◽  
Khushnoor Khan
Keyword(s):  
Control Chart ◽  
Control Charts ◽  
Average Run Length ◽  
Artificial Data ◽  
Process Mean ◽  
Data Set ◽  
Successive Sampling ◽  
Shift Detection ◽  
Dependent State ◽  
Better Than

In this paper, a new control chart scheme has been developed for monitoring the production process mean using successive sampling over two occasions. The proposed chart reduces to three different existing control charts under different assumptions and is compared with these three existing control charts for monitoring the process average. It has been observed that the proposed control chart performs better than the other existing control charts in terms of average run length (ARL). A simulation study using an artificial data set was included for demonstrating the process shift detection power of the proposed control chart.

scholarly journals On Performance of Two-Parameter Gompertz-Based X¯ Control Charts

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Johnson A. Adewara ◽  
Kayode S. Adekeye ◽  
Olubisi L. Aako
Keyword(s):  
Control Chart ◽  
Coverage Probability ◽  
Control Charts ◽  
Average Run Length ◽  
Real Life ◽  
Correction Method ◽  
Gompertz Distribution ◽  
Real Life Data ◽  
Control Limits ◽  
Two Parameter

In this paper, two methods of control chart were proposed to monitor the process based on the two-parameter Gompertz distribution. The proposed methods are the Gompertz Shewhart approach and Gompertz skewness correction method. A simulation study was conducted to compare the performance of the proposed chart with that of the skewness correction approach for various sample sizes. Furthermore, real-life data on thickness of paint on refrigerators which are nonnormal data that have attributes of a Gompertz distribution were used to illustrate the proposed control chart. The coverage probability (CP), control limit interval (CLI), and average run length (ARL) were used to measure the performance of the two methods. It was found that the Gompertz exact method where the control limits are calculated through the percentiles of the underline distribution has the highest coverage probability, while the Gompertz Shewhart approach and Gompertz skewness correction method have the least CLI and ARL. Hence, the two-parameter Gompertz-based methods would detect out-of-control faster for Gompertz-based X¯ charts.

Design of EWMA Control Charts for Controlling Dependent Process Stages with Attribute Data

2013 ◽  
Vol 411-414 ◽  
pp. 1085-1088
Author(s):  
Chung Ming Yang ◽  
Su Fen Yang ◽  
Jin Tyan Yeh
Keyword(s):  
Control Chart ◽  
Simulation Study ◽  
Control Charts ◽  
Detection Ability ◽  
Numerical Example ◽  
Attribute Data ◽  
Dependent Process

In this study, we propose EWMA control charts to monitor two dependent process stages with attribute data. The detection ability of the EWMA control charts is compared to those of Shewhart attribute control charts and cause selecting control chart by different correlation. Numerical example and simulation study show that the EWMA control charts have better performance compared to Shewhart attribute control charts and cause selecting control charts.

scholarly journals Robust Multivariate Shewhart Control Chart Based on the Stahel-Donoho Robust Estimator and Mahalanobis Distance for Multivariate Outlier Detection

Mathematics ◽  
2021 ◽  
Vol 9 (21) ◽  
pp. 2772
Author(s):  
Ishaq Adeyanju Raji ◽  
Nasir Abbas ◽  
Mu’azu Ramat Abujiya ◽  
Muhammad Riaz
Keyword(s):  
Control Chart ◽  
Control Charts ◽  
Real Life ◽  
Robust Estimator ◽  
Estimation Of Parameters ◽  
Run Length ◽  
Control Charting ◽  
Shewhart Control ◽  
Multivariate Control Chart ◽  
Multivariate Control

While researchers and practitioners may seamlessly develop methods of detecting outliers in control charts under a univariate setup, detecting and screening outliers in multivariate control charts pose serious challenges. In this study, we propose a robust multivariate control chart based on the Stahel-Donoho robust estimator (SDRE), whilst the process parameters are estimated from phase-I. Through intensive Monte-Carlo simulation, the study presents how the estimation of parameters and presence of outliers affect the efficacy of the Hotelling T2 chart, and then how the proposed outlier detector brings the chart back to normalcy by restoring its efficacy and sensitivity. Run-length properties are used as the performance measures. The run length properties establish the superiority of the proposed scheme over the default multivariate Shewhart control charting scheme. The applicability of the study includes but is not limited to manufacturing and health industries. The study concludes with a real-life application of the proposed chart on a dataset extracted from the manufacturing process of carbon fiber tubes.

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.

scholarly journals Design of a Control Chart Based on COM-Poisson Distribution for the Uncertainty Environment

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-9
Author(s):  
Muhammad Aslam ◽  
Ali Hussein Al-Marshadi
Keyword(s):  
Poisson Distribution ◽  
Control Chart ◽  
Simulation Study ◽  
Average Run Length ◽  
Interval Method ◽  
Interval System ◽  
Run Length ◽  
Classical Statistics ◽  
Uncertainty Environment

This paper will introduce the neutrosophic COM-Poisson (NCOM-Poisson) distribution. Then, the design of the attribute control chart using the NCOM-Poisson distribution is given. The structure of the control chart under the neutrosophic statistical interval method will be given. The algorithm to determine the average run length under neutrosophic statistical interval system will be given. The performance of the proposed control chart is compared with the chart based on classical statistics in terms of neutrosophic average run length (NARL). A simulation study and a real example are also added. From the comparison of the proposed control chart with the existing chart, it is concluded that the proposed control chart is more efficient in detecting a shift in the process. Therefore, the proposed control chart will be helpful in minimizing the defective product. In addition, the proposed control chart is more adequate and effective to apply in uncertainty environment.

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.

Average Run Lengths in Shewhart Type Charts for 2-Order Autoregressive Process

2010 ◽  
Vol 139-141 ◽  
pp. 1860-1863
Author(s):  
Qiu Xia Sun ◽  
Jian Li Zhao ◽  
Qi Sheng Gao
Keyword(s):  
Control Chart ◽  
Control Charts ◽  
Average Run Length ◽  
Correlation Coefficients ◽  
Autoregressive Process ◽  
Run Length ◽  
Shewhart Control ◽  
Control Schemes ◽  
Run Lengths ◽  
Residual Control

In this paper the average run length is adopted as the tool to describe the performance of control charts. The respective methods for calculating the average run length of the modified Shewhart control chart and the Shewhart residual control chart for 2-order autoregressive process are derived and shown in detail. By the proposed approach some numerical results of average run lengths of both Shewhart type charts are formulated and discussed. We analyze and compare that the influence of the correlation coefficients of the 2-order autoregressive process on the performance of both charts based on the estimated data. Several clear and main points of the issue are summed up. Lastly, we give some recommendations for the choice of both Shewhart type control schemes.

Sign in / Sign up

Export Citation Format

Share Document