scholarly journals Shewhart-Type Charts for Masked Data: A Strategy for Handling the Privacy Issue

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Said Farooq Shah ◽  
Zawar Hussain ◽  
Muhammad Riaz ◽  
Salman Arif Cheema
Keyword(s):  
Control Chart ◽  
Control Charts ◽  
Data Privacy ◽  
Average Run Length ◽  
Real Life ◽  
Performance Measure ◽  
Privacy Issue ◽  
Control Charting ◽  
Data Masking ◽  
Randomized Response Techniques

Data privacy is a serious issue and therefore needs our attention. In this study, we propose masking through randomized response techniques (RRTs) to ensure the privacy and thus to avoid falsification. We assume that the process characteristic is of sensitive nature, and due to privacy issue, the actual measurements cannot be shared with the monitoring team. In such situations, the producer is very likely to falsify the measurements. Consequently, the usual control charting techniques will mislead about the process status. We discuss different data masking strategies to be used with Shewhart-type control charts. The usual Shewhart-type control chart appears to be a subchart of the proposed charts. Average run length (ARL) is used as a performance measure of the study proposals. We have evaluated the performance of the proposed charts for different shift sizes and under different intensities of masking. We have also carried out a comparative analysis for various models under varying sensitivity parameters. We have also compared the performance of the proposals with the traditional Shewhart chart. It is observed that the B-L control chart under the RRT model performs better for smaller shifts and for larger shift sizes, the G-B chart under an unrelated question model tperforms better. A real-life application of the study proposal is also considered where monitoring of thickness of paint on refrigerators is of interest.

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.

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 Fuzzy EWMA Attribute Control Chart to Monitor Process Mean

Information ◽  
2018 ◽  
Vol 9 (12) ◽  
pp. 312 ◽  
Author(s):  
Muhammad Zahir Khan ◽  
Muhammad Farid Khan ◽  
Muhammad Aslam ◽  
Seyed Taghi Akhavan Niaki ◽  
Abdur Razzaque Mughal
Keyword(s):  
Fuzzy Control ◽  
Control Chart ◽  
Control Charts ◽  
Moving Average ◽  
Real Life ◽  
Fuzzy Data ◽  
Process Mean ◽  
Statistical Process ◽  
Control Charting ◽  
Real Life Data

Conventional control charts are one of the most important techniques in statistical process control which are used to assess the performance of processes to see whether they are in- or out-of-control. As traditional control charts deal with crisp data, they are not suitable to study unclear, vague, and fuzzy data. In many real-world applications, however, the data to be used in a control charting method are not crisp since they are approximated due to environmental uncertainties and systematic ambiguities involved in the systems under investigation. In these situations, fuzzy numbers and linguistic variables are used to grab such uncertainties. That is why the use of a fuzzy control chart, in which fuzzy data are used, is justified. As an exponentially weighted moving average (EWMA) scheme is usually used to detect small shifts, in this paper a fuzzy EWMA (F-EWMA) control chart is proposed to detect small shifts in the process mean when fuzzy data are available. The application of the newly developed fuzzy control chart is illustrated using real-life data.

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.

scholarly journals Statistical Development of the V S Q -Control Chart for Extreme Data with an Application to the Carbon Fiber Industry

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Faisal Shah ◽  
Zahid Khan ◽  
Muhammad Aslam ◽  
Seifedine Kadry
Keyword(s):  
Control Chart ◽  
Control Charts ◽  
Statistical Power ◽  
Average Run Length ◽  
Probability Model ◽  
Maxwell Model ◽  
Performance Measure ◽  
Underlying Assumption ◽  
Novel Design ◽  
Statistical Development

The normality assumption is a significant part of the development of control charts. This underlying assumption of normality most likely does not hold true in real scenarios. One of such designs usually devised to observe the target parameter σ 2 of the Maxwell quality characteristics is the V -control chart. In general, quality practitioners preferably have to observe the scale parameter σ rather than σ 2 in examined processes. The contemporary V -control chart is relying on the V -statistic which does not hold the unbiasedness property with respective to parameter σ of the Maxwell probability model. In view of this, implementation of the V -chart is not an appropriate design in monitoring a real parameter of the underlying Maxwell data. To accommodate the monitoring of the parameter σ of the Maxwell model, a novel design of the V S Q -chart is mainly proposed in this work. To support a statistical understanding of the V S Q -chart, power function, characteristic function, and the average run length ARL have been essentially established. The parameters of the V S Q -chart are determined from the results of the sampling distribution of the derived statistic. Analytical findings are further applied to determine the performance of the study proposal with its existing counterpart. Substantially, the better performance of the proposed technique has been observed because of statistical power used as a performance measure. Eventually, the computational plan of the V S Q -chart is considered both for the simulated and real datasets with the aim of illustrating the theory of the proposed design.

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.

SURVEILLANCE OF DIABETES PREVALENCE RATE THROUGH THE DEVELOPMENT OF A MARKOV-BASED CONTROL CHART

2012 ◽  
Vol 12 (04) ◽  
pp. 1250083
Author(s):  
PERSHANG DOKOUHAKI ◽  
RASSOUL NOOROSSANA
Keyword(s):  
Control Chart ◽  
Control Charts ◽  
High Performance ◽  
Discrete Data ◽  
Correlated Data ◽  
Statistical Process ◽  
Control Charting ◽  
Attribute Quality ◽  
Related Process

In the field of statistical process control (SPC), usually two issues are addressed; the variables and the attribute quality characteristics control charting. Focusing on discrete data generated from a process to be monitored, attributes control charts would be useful. The discrete data could be classified into two categories; the independent and auto-correlated data. Regarding the independence in the sequence of discrete data, the typical Shewhart-based control charts, such as p-chart and np-chart would be effective enough to monitor the related process. But considering auto-correlation in the sequence of the data, such control charts would not workanymore. In this paper, considering the auto-correlated sequence of X1, X2,…, Xt,… as the sequence of zeros or ones, we have developed a control chart based on a two-state Markov model. This control chart is compared with the previously developed charts in terms of the average number of observations (ANOS) measure. In addition, a case study related to the diabetic people is investigated to demonstrate the applicability and high performance of the developed chart.

scholarly journals Monitoring process mean with a new EWMA control chart

Production ◽  
2011 ◽  
Vol 21 (2) ◽  
pp. 217-222 ◽  
Author(s):  
Yang Su-Fen ◽  
Tsai Wen-Chi ◽  
Huang Tzee-Ming ◽  
Yang Chi-Chin ◽  
Cheng Smiley
Keyword(s):  
Control Chart ◽  
Control Charts ◽  
Population Distribution ◽  
Average Run Length ◽  
Process Data ◽  
Ewma Chart ◽  
Ewma Control Chart ◽  
Simple Statistic ◽  
Run Lengths ◽  
Proper Values

In practice, sometimes the process data did not come from a known population distribution. So the commonly used Shewhart variables control charts are not suitable since their performance could not be properly evaluated. In this paper, we propose a new EWMA Control Chart based on a simple statistic to monitor the small mean shifts in the process with non-normal or unknown distributions. The sampling properties of the new monitoring statistic are explored and the average run lengths of the proposed chart are examined. Furthermore, an Arcsine EWMA Chart is proposed since the average run lengths of the Arcsine EWMA Chart are more reasonable than those of the new EWMA Chart. The Arcsine EWMA Chart is recommended if we are concerned with the proper values of the average run length.

scholarly journals X̅ and R control charts based on marshall-olkin inverse log-logistic distribution for positive skewed data

2020 ◽  
Vol 1 (1) ◽  
pp. 9-16
Author(s):  
O. L. Aako ◽  
J. A. Adewara ◽  
K. S Adekeye ◽  
E. B. Nkemnole
Keyword(s):  
Control Chart ◽  
Control Charts ◽  
Average Run Length ◽  
Logistic Distribution ◽  
Skewed Data ◽  
Process Data ◽  
And Performance ◽  
Set Up ◽  
Control Limits ◽  
Normally Distributed

The fundamental assumption of variable control charts is that the data are normally distributed and spread randomly about the mean. Process data are not always normally distributed, hence there is need to set up appropriate control charts that gives accurate control limits to monitor processes that are skewed. In this study Shewhart-type control charts for monitoring positively skewed data that are assumed to be from Marshall-Olkin Inverse Loglogistic Distribution (MOILLD) was developed. Average Run Length (ARL) and Control Limits Interval (CLI) were adopted to assess the stability and performance of the MOILLD control chart. The results obtained were compared with Classical Shewhart (CS) and Skewness Correction (SC) control charts using the ARL and CLI. It was discovered that the control charts based on MOILLD performed better and are more stable compare to CS and SC control charts. It is therefore recommended that for positively skewed data, a Marshall-Olkin Inverse Loglogistic Distribution based control chart will be more appropriate.

scholarly journals Evaluasi Kinerja Bagan Kendali Fm Pada Proses Short-Run

2018 ◽  
Vol 17 (1) ◽  
Author(s):  
Darmanto Darmanto
Keyword(s):  
Control Chart ◽  
Control Charts ◽  
Job Shop ◽  
Average Run Length ◽  
Just In Time ◽  
Multivariate Normal ◽  
Sensitivity Level ◽  
Short Run ◽  
Control Limits ◽  
Vector Shift

<p><em>The manufacturing production process that is currently trend is short-run. Short-run process is a job shop and a just in-time. These causes the process parameters to be unknown due to unavailability of data and generally a small amount of product. The control chart is one of the control charts which  designed for the short run. The procedure of the control chart follows the concept of succesive difference and under the assumption of the multivariate Normal distribution. The sensitivity level of a control chart is evaluated based on the average run length (ARL) value. In this study, the ARL value was calculated based on the shift simulation of the average vector by recording the first m-point out of the control limits. The average vector shift simulation of the target () is performed simultaneously with the properties of a positive shift (=+ δ). Variations of data size and many variables in this study were m = 20, 50 and p = 2, 4, 8, respectively. Each scheme (a combination of δ, m and p) is iterated 250,000 times. The simulation results show that for all schemes when both parameters are known ARL<sub>0 </sub>≈ 370. But, when parameters are unknown, ARL<sub>1</sub> turn to smaller. This conclusion also implied when the number of p and n are increased, it reduce the sensitivity of the control chart.</em></p>

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