scholarly journals Treating Measurement Errors in the Run Rule Schemes Integrated with Shewhart X ¯ Chart

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
TingTing Shan ◽  
WeiDong Huang
Keyword(s):  
Quality Control ◽  
Measurement Errors ◽  
Average Run Length ◽  
Error Model ◽  
Quality Characteristic ◽  
Control Applications ◽  
Run Length ◽  
Negative Effect ◽  
Characteristic Two ◽  
Run Rules

In modern quality control applications, there often exist significant measurement errors because observations are measured quickly in time order. As a result, the errors influence the power of a control chart to detect a given change in the process parameter(s) of a quality characteristic. In this paper, by using a covariate error model, the properties of the Shewhart X ¯ chart integrated with run rules are investigated when errors exist in the measurement of quality characteristic. Two metrics, the average run length and 95% quantile of the run length, are adopted to evaluate the chart’s performance for different mean shifts and sample sizes. Numerous simulations are conducted, and the results indicate that the errors in the measurement significantly affect the performance of the run rule X ¯ chart, especially when the errors are large. To reduce this negative effect on the run rule X ¯ chart, measuring more times of each item in each subgroup and increasing the coefficient in the covariate error model are shown to be good choices for practitioners.

Combined effect of autocorrelation and measurement errors on the adaptive X¯ monitoring schemes

2020 ◽  
pp. 014233122093529 ◽  
Author(s):  
Sandile Charles Shongwe ◽  
Jean-Claude Malela-Majika
Keyword(s):  
Measurement Errors ◽  
Length Distribution ◽  
Real Life ◽  
Adaptive Designs ◽  
Combined Effect ◽  
Sampling Strategies ◽  
Run Length ◽  
Variable Sampling ◽  
Negative Effect ◽  
Run Length Distribution

For independent and identically distributed observations, and those with measurement errors only, the adaptive designs (i.e. variable sampling sizes (VSS), variable sampling intervals (VSI) and the latter two combined to form VSSI) have been thoroughly discussed. However, no research exists for processes under the combined effect of autocorrelation and measurement errors; thus, such adaptive Shewhart [Formula: see text] schemes are proposed. The Markov chain approach for adaptive designs are used to evaluate the run-length distribution properties with two special sampling strategies (i.e. s-skip and multiple measurements) incorporated to reduce the combined negative effect of autocorrelation and measurement inaccuracy. Using numerous run-length metrics, it is shown that the combination of the two sampling strategies with the VSSI design reduces this negative effect considerably and improves the detection ability of the [Formula: see text] scheme by a significant margin as compared with using the fixed sample size and sampling interval (FSSI), VSS and VSI designs. Autocorrelation level has a higher negative effect as compared with the measurement inaccuracy level. For high levels of autocorrelation ([Formula: see text]0.8), the s-skip strategy has little influence in reducing the negative effect; but the VSSI design maintains better performance than the other designs. Finally, a real-life example is used to illustrate its implementation.

scholarly journals Precision Analysis of Poisson Control Chart Based on Sample Size

2020 ◽  
Vol 16 (3) ◽  
pp. 325
Author(s):  
Elsa Resa Sari
Keyword(s):  
Quality Control ◽  
Sample Size ◽  
Control Chart ◽  
Average Run Length ◽  
Statistical Quality Control ◽  
Sample Sizes ◽  
Precision Analysis ◽  
Run Length ◽  
Statistical Quality ◽  
Result Show

One technique used in performing statistical quality control is by poisson control chart. Poisson control chart used in data that have the same mean and varians for monitoring the number of defects in the study. In some cases, the different sample sizes influence the control chart performance. The control chart performance can be measured using average run length (ARL). The smaller ARL’s value, the better type of control chart. In this study, we used different sample sizes  that is  and mean . The result show the best performance of control chart is when  and m = 200, because its has a smaller ARL’s value.                            

scholarly journals Nonparametric Double EWMA Control Chart for Process Monitoring

2016 ◽  
Vol 39 (2) ◽  
pp. 167 ◽  
Author(s):  
Muhammad Riaza ◽  
Saddam Akber Abbasib
Keyword(s):  
Standard Deviation ◽  
Control Chart ◽  
Average Run Length ◽  
Location Parameter ◽  
Quality Characteristic ◽  
Quadratic Loss ◽  
Run Length ◽  
Ewma Control Chart ◽  
Monitoring Process ◽  
Nonparametric Techniques

<p>In monitoring process parameters, we assume normality of the quality characteristic of interest, which is an ideal assumption. In many practical sit- uations, we may not know the distributional behavior of the data, and hence, the need arises use nonparametric techniques. In this study, a nonparametric double EWMA control chart, namely the NPDEWMA chart, is proposed to ensure efficient monitoring of the location parameter. The performance of the proposed chart is evaluated in terms of different run length properties, such as average, standard deviation and percentiles. The proposed scheme is compared with its recent existing counterparts, namely the nonparametric EWMA and the nonparametric CUSUM schemes. The performance mea- sures used are the average run length (ARL), standard deviation of the run length (SDRL) and extra quadratic loss (EQL). We observed that the pro- posed chart outperforms the said existing schemes to detect shifts in the process mean level. We also provide an illustrative example for practical considerations.</p>

scholarly journals One-sided 4-out-of-5 Run Rules Charts for the Multivariate Coefficient of Variation in the Finite Horizon Process

2021 ◽  
Vol 20 ◽  
pp. 455-460
Author(s):  
Khai Wah Khaw ◽  
Xin Ying Chew ◽  
Ming Ha Lee ◽  
Wai Chung Yeong ◽  
Sajal Saha
Keyword(s):  
Process Monitoring ◽  
Coefficient Of Variation ◽  
Flexible Manufacturing ◽  
Average Run Length ◽  
Past Research ◽  
Finite Horizon ◽  
Run Length ◽  
Multivariate Coefficient Of Variation ◽  
Run Rules ◽  
Made In

Quality improvement has been receiving great attention in industries. In recent years, the finite horizon process is commonly encountered in industries due to flexible manufacturing production. Past research works on finite horizon process monitoring are still limited. Because of this, one-sided 4-out-of-5 run rules charts are proposed to monitor the multivariate coefficient of variation in a finite horizon process. The performance measures of the proposed charts are derived using the Markov-chain approach. The proposed schemes can serve as a framework for practitioners who wish to perform process monitoring easily and efficiently. Numerical comparisons between the proposed and existing charts have been made, in terms of the truncated average run length and the expected truncated average run length criteria. The findings reveal that the proposed charts outperform the existing charts for detecting small and moderate process shifts in the finite horizon process.

scholarly journals An Analysis of Multirules for Monitoring Assay Quality Control

2019 ◽  
Vol 51 (1) ◽  
pp. 94-98
Author(s):  
Brandon S Walker ◽  
Lauren N Pearson ◽  
Robert L Schmidt
Keyword(s):  
Quality Control ◽  
Average Run Length ◽  
Computer Code ◽  
Microsoft Excel ◽  
Run Length ◽  
Excel Spreadsheet ◽  
R Language ◽  
Rule Set ◽  
The Mean ◽  
Power Curves

AbstractBackgroundMultirules are often employed to monitor quality control (QC). The performance of multirules is usually determined by simulation and is difficult to predict. Previous studies have not provided computer code that would enable one to experiment with multirules. It would be helpful for analysts to have computer code to analyze rule performance.ObjectiveTo provide code to calculate power curves and to investigate certain properties of multirule QC.MethodsWe developed computer code in the R language to simulate multirule performance. Using simulation, we studied the incremental performance of each rule and determined the average run length and time to signal.ResultsWe provide R code for simulating multirule performance. We also provide a Microsoft Excel spreadsheet with a tabulation of results that can be used to create power curves. We found that the R4S and 10x rules add very little power to a multirule set designed to detect shifts in the mean.ConclusionQC analysts should consider using a limited-rule set.

scholarly journals The effect of measurement errors on the performance of the homogenously weighted moving average X¯ monitoring scheme

2020 ◽  
pp. 014233122097356
Author(s):  
Maonatlala Thanwane ◽  
Jean-Claude Malela-Majika ◽  
Philippe Castagliola ◽  
Sandile Charles Shongwe
Keyword(s):  
Measurement Errors ◽  
Moving Average ◽  
Real Life ◽  
Error Model ◽  
Measuring Instruments ◽  
Monitoring Scheme ◽  
Real Life Situation ◽  
Negative Effect ◽  
Multiple Measurements ◽  
Weighted Moving Average

Monitoring schemes are typically designed under the assumption of perfect measurements. However, in real-life applications, data tend to be subjected to measurement errors, that is, a difference between the real quantities and the measured ones mostly exist even with highly sophisticated advanced measuring instruments. Thus, in this paper, the negative effect of measurement errors on the performance of the homogenously weighted moving average (HWMA) scheme is studied using the linear covariate error model for constant and linearly increasing variance. Monte Carlo simulations are used to evaluate the performance of the proposed HWMA scheme in terms of the run-length characteristics. It is observed that as the smoothing parameter increases, measurement errors have a higher negative effect on the performance of the HWMA [Formula: see text] scheme. More importantly, it is shown that the negative effect of measurement errors is reduced by using multiple measurements and/or by increasing the slope coefficient of the covariate error model. Moreover, the performance of the HWMA [Formula: see text] scheme is compared with the corresponding exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) [Formula: see text] schemes. An illustrative example is provided to help in implementing this monitoring scheme in a real-life situation.

scholarly journals A Nonparametric Shewhart-Type Quality Control Chart for Monitoring Broad Changes in a Process Distribution

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Saad T. Bakir
Keyword(s):  
Quality Control ◽  
Control Chart ◽  
Control Charts ◽  
Probability Distributions ◽  
Average Run Length ◽  
Training Sample ◽  
Statistical Quality Control ◽  
Test Statistic ◽  
Run Length ◽  
Quality Control Chart

This paper develops a distribution-free (or nonparametric) Shewhart-type statistical quality control chart for detecting a broad change in the probability distribution of a process. The proposed chart is designed for grouped observations, and it requires the availability of a reference (or training) sample of observations taken when the process was operating in-control. The charting statistic is a modified version of the two-sample Kolmogorov-Smirnov test statistic that allows the exact calculation of the conditional average run length using the binomial distribution. Unlike the traditional distribution-based control charts (such as the Shewhart X-Bar), the proposed chart maintains the same control limits and the in-control average run length over the class of all (symmetric or asymmetric) continuous probability distributions. The proposed chart aims at monitoring a broad, rather than a one-parameter, change in a process distribution. Simulation studies show that the chart is more robust against increased skewness and/or outliers in the process output. Further, the proposed chart is shown to be more efficient than the Shewhart X-Bar chart when the underlying process distribution has tails heavier than those of the normal distribution.

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 ON THE UNIFORM CONVERGENCE OF DECONVOLUTION ESTIMATORS FROM REPEATED MEASUREMENTS

2021 ◽  
pp. 1-22
Author(s):  
Daisuke Kurisu ◽  
Taisuke Otsu
Keyword(s):  
Multivariate Analysis ◽  
Measurement Error ◽  
Uniform Convergence ◽  
Measurement Errors ◽  
Convergence Rates ◽  
Free Variable ◽  
Error Model ◽  
Repeated Measurements ◽  
Empirical Characteristic Function ◽  
Measurement Error Model

This paper studies the uniform convergence rates of Li and Vuong’s (1998, Journal of Multivariate Analysis 65, 139–165; hereafter LV) nonparametric deconvolution estimator and its regularized version by Comte and Kappus (2015, Journal of Multivariate Analysis 140, 31–46) for the classical measurement error model, where repeated noisy measurements on the error-free variable of interest are available. In contrast to LV, our assumptions allow unbounded supports for the error-free variable and measurement errors. Compared to Bonhomme and Robin (2010, Review of Economic Studies 77, 491–533) specialized to the measurement error model, our assumptions do not require existence of the moment generating functions of the square and product of repeated measurements. Furthermore, by utilizing a maximal inequality for the multivariate normalized empirical characteristic function process, we derive uniform convergence rates that are faster than the ones derived in these papers under such weaker conditions.

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