Variable Control Charts Research Articles

Bagan Kendali Variansi dengan Penambahan Variabel pada Nilai Ekspor dan Berat Ekspor

To create products or services that meet certain quality standards, supervision and control need to be carried out. Quality control monitors changes in the level of variability, or the level of average, or both to observe changes that occur during the production process. The monitoring stage begins with controlling variability, followed by controlling the average level. Walter A. Shewhart (1920) introduced several variability control charts, including the S2 variance control chart, which involves one quality characteristic, Y. Riaz (2008) introduced a regression-type estimator of the variance of Y using additional correlated information X. This control chart is known as the Vr control chart and shows better results than the S2 control chart. Furthermore, Riaz (2009) introduced a Vt control chart, created based on a ratio-type estimator of the variance of Y. The accuracy of the Vt control chart increases as the value increases. The S2, Vr, Vt control chart is used to monitor the variability of export value (Y) using additional information on export weight (X). All three charts indicate that the variability in export values is out of control. Comparison of the results obtained from the Vt, Vr, and S2 control charts is made by examining the power curve of each chart. Specifically, it was observed that the Vt control chart produces more consistent and accurate conclusions.

Measuring the quality of the learning process in basic courses using the multivariate statistical process control method

The quality of learning is the key to being able to compete in the world of education. This research aims to measure the quality of the learning process in basic courses at the University of Logistics and International Business. The method used is Multivariate Statistical Control Process with subgroups whose size is not constant. In this method, multivariate control of the target process is carried out using the T2 Hotelling control diagram. Meanwhile, control of multivariate process variability is carried out using a generalized variance control chart. The sample data used in this research was taken from grades in English courses and introductory logistics courses from 20 classes with a total of 498 students. Data collection was carried out randomly from 2019-2022. The results obtained were that in the Multivariate Process Target (MPT) calculation using the T2 Hotelling control diagram it was found that class 1 was out of control. Meanwhile, in calculating Multivariate Process Variability (MPV) using a Generalized Variance (GV) based control diagram, it was found that classes 5 and 20 were out of control. Investigating the cause of the class being out of control is a part that must be explored by study program and university leaders in an effort to improve the teaching and learning process.

Variable Sample Size Control Charts for Monitoring the Multivariate Coefficient of Variation Based on Median Run Length and Expected Median Run Length

The monitoring of a well-functioning process system has always held significant importance. In recent times, there has been notable attention towards employing control charts to oversee both univariate and multivariate coefficients of variation (MCV). This shift is in response to the concern of erroneous outcomes that can arise when traditional control charts are applied under the condition of dependent mean and standard deviation, as highlighted by prior research. To address this, the remedy lies in adopting the coefficient of variation. Furthermore, this study underscores the application of MCV in scenarios where multiple quality attributes are simultaneously under surveillance within an industrial process. This aspect has demonstrated considerable enhancement in chart performance, especially when incorporating the variable sample size (VSS) feature into the MCV chart. Adaptive VSS, evaluated through metrics like median run length (MRL) and expected median run length (EMRL), is also integrated for MCV monitoring. In contrast to earlier studies that predominantly focused on average run length (ARL), this research acknowledges the potential inaccuracies in ARL measurement. In this study, two optimal designs for VSS MCV charts are formulated by minimizing two criteria: firstly, MRL; and secondly, EMRL, both accounting for deterministic and unknown shift sizes. Additionally, to assess the distribution's variability in run lengths, the study provides the 5th and 95th percentiles. The research delves into two VSS schemes: one with a defined small sample size (nS), and another with a predetermined large sample size (nL) for the initial subgroup (n(1)). The approach taken involves the development of a Markov chain method for designing and deriving performance measures of the proposed chart. These measures include MRL and EMRL. Moreover, a comparative analysis between the proposed chart's performance and the standard MCV chart (STD) is presented in terms of MRL and EMRL criteria. The outcomes illustrate the superiority of the proposed chart over the STD MCV chart for all shift sizes, whether they are upward or downward, and when n(1) equals nS or nL.

Application of the control chart for variables in a vehicle assembly plant in the south of the state of Rio de Janeiro

Vehicle assemblers have quality as a prerequisite for the proper functioning of their process. The monitoring of the quality of this type of industrial activity is carried out by means of control charts by variables. The objective of this article is to show a case study carried out in a company in the south of the State of Rio de Janeiro that used this type of control chart, more specifically the control chart of the mean and amplitude to evaluate a process carried out by three machines. The results showed the need for some adjustments and managerial attitudes will be taken to improve the process.

A combined adaptive double sampling and variable sampling interval control chart for monitoring three-level products

Three-level control charts have been developed for monitoring processes where the quality of products is characterized by classifying the product characteristic into three discrete levels. In this article, a combined double sampling and variable sampling interval (DSVSI) attribute control chart is developed for monitoring three-level products. This research is motivated by recent studies done on combining the DSVSI scheme with traditional attribute charts and their results recommend the application of the DSVSI attribute charts. The proposed DSVSI three-level chart is compared with the existing standard, adaptive, and EWMA three-level charts. The results approve the superiority of the proposed scheme and recommend it as an efficient three-level control chart in application. An example is also provided to illustrate the application of the proposed chart.

Optimal designs of variable sample size control chart for monitoring the multivariate coefficient of variation in short production runs

Short production runs are common in industries that require high flexibility and variety in manufacturing. Only a limited amount of researches on multivariate control charts in short production runs exists in the literature. This article proposes two one-sided adaptive charts for monitoring the multivariate coefficient of variation (MCV) in short production runs by varying the sample size (called the VSS MCV SPR charts). The two one-sided adaptive charts are the upper-sided and lower-sided VSS MCV SPR charts for monitoring increasing and decreasing shifts, respectively, in the process MCV. The optimal parameters of the VSS MCV SPR charts in minimizing the out-of-control truncated average run length (TARL) value, for various shift sizes, are presented. The proposed VSS MCV SPR charts outperform their non-adaptive short production runs Shewhart MCV counterparts (called the SH MCV SPR charts), as the former have smaller out-of-control TARL value than the latter, for the same shift size. The sensitivity of the VSS MCV SPR charts, in terms of the probability of signaling an alarm within I inspections is also studied, where the VSS MCV SPR charts surpass their corresponding SH MCV SPR charts. An example for implementing the VSS MCV SPR charts is provided.

Economic statistical model of the np chart for monitoring defectives

When monitoring manufacturing processes, managing an attribute quality characteristic is easier and faster than a variable quality characteristic. Yet, the economic-statistical design of attribute control charts has attracted much less attention than variable control charts in the literature. This study develops an algorithm for optimizing the economic-statistical performance of the np chart for monitoring defectives, based on Duncan’s economic model. This algorithm has the merit of the economic model to minimize expected total cost, and the benefit of the statistical design to enhance the effectiveness of detecting increasing shifts in defectives. The effectiveness of the developed np chart is investigated under different operational scenarios. The results affirm a considerable superiority of the proposed np chart over the traditional np chart. Real-life data are used to demonstrate the applicability of the proposed np scheme, in comparison to the traditional np chart.

A variable sampling interval one-sided CUSUM control chart for monitoring the multivariate coefficient of variation

Monitoring techniques based on the multivariate coefficients of variation (MCV) have received a great deal of attention in quality control. Numerous studies have shown that adaptively changing the charting parameters based on the past sample information can improve the performance of a chart in detecting process changes. In view of the performance benefits of adaptive strategies, two one-sided cumulative sum (CUSUM) charts are proposed to monitor the MCV and a variable sampling interval (VSI) strategy is incorporated into these charts. By using the Markov chain method, the formulas for calculating the average and standard deviation of time to signal measures of the VSI CUSUM MCV control charts are derived. Then for the known and unknown shift sizes, the optimization algorithms for obtaining the charting parameters are presented. The superiority of the proposed control charts is confirmed by comparing their performance with two existing MCV charts. Finally, an example using real investment data demonstrates the practical application of the proposed charts.

Development of robust X‐bar charts with unequal sample sizes

AbstractThe traditional variable control charts, such as the chart, are widely used to monitor variation in a process. They have been shown to perform well for monitoring processes under the general assumptions that the observations are normally distributed without data contamination and that the sample sizes from the process are all equal. However, these two assumptions may not be met and satisfied in many practical applications and thus make them potentially limited for widespread application especially in production processes. In this paper, we alleviate this limitation by providing a novel method for constructing the robust control charts, which can simultaneously deal with both data contamination and unequal sample sizes. The proposed method for the process parameters is optimal in a sense of the best linear unbiased estimation. Numerical results from extensive Monte Carlo simulations and a real data analysis reveal that traditional control charts seriously underperform for monitoring process in the presence of data contamination and are extremely sensitive to even a single contaminated value, while the proposed robust control charts outperform in a manner that is comparable with the traditional ones, whereas they are far superior when the data are contaminated by outliers.

A sensitized variable selection control chart based on a classification algorithm for monitoring high‐dimensional processes

AbstractDuring the last decade, variable‐selection‐based (VS) control charts have gained much popularity for process monitoring and diagnosis. These charts have been proven efficient for the detection of sparse mean shifts in high‐dimensional processes. VS charts usually assume that in‐control (IC) data are the only information used to determine the control limits. In modern industrial processes, however, out‐of‐control (OC) data can be easily collected. Detecting a specific shift in a data‐rich environment without utilizing OC data information will limit the development of a process monitoring scheme. In this paper, a novel variable selection control chart that is combined with a classification algorithm is proposed, which is expected to benefit from both the classification and variable selection approaches. In contrast to alternative charts, the proposed sensitized variable selection chart can capture the potential shifted variables using both IC and OC information, which can improve the sensitivity of the chart in a specific direction. Extensive Monte Carlo simulations demonstrate that the proposed chart outperforms the alternatives in a data‐rich and high‐dimensional environment. A real‐life example of cellular localization is also included to support the findings of our study.

Case of Preferential Selection of Attribute over Variable Control Charts in Trend Analysis of Microbiological Count in Water

Case of Preferential Selection of Attribute over Variable Control Charts in Trend Analysis of Microbiological Count in Water

Comparing the performance of Kernel PCA Mix Chart with PCA Mix Chart for monitoring mixed quality characteristics

Along with the development of information and technology, the quality characteristics of a product cannot be monitored separately in the different types of control charts. In the past, conventional control charts were developed to monitor only one type of quality characteristic. The variable control charts are used to observe the variable or metric quality characteristics. Meanwhile, in monitoring non-metric characteristics or categorical data, attribute control charts are employed. To accommodate these two types of data, the PCA Mix control chart is suggested to simultaneously monitor these two types of data in one chart. However, some drawbacks occur when this chart is applied to monitor non-metric data which has an imbalanced proportion. Therefore, the Kernel PCA Mix control chart is created to overcome the gaps that occurred in the PCA Mix chart. Similar to the previous chart, this chart is also constructed using Hotelling’s T2 statistics with Kernel Density Estimation control limit. Several simulations are used to evaluate the performance of the proposed control charts. The simulation results show that the proposed chart has a better result than the previous control chart, especially for a small mean shift with an imbalanced proportion of non-metric data. However, the PCA Mix chart has a similar performance to the proposed chart when it is applied to monitor the balanced proportion of categorical data with a large mean shift. The application with simulated data with various scenarios and the real-world case also shows that the Kernel PCA Mix chart performs better compared to the performance of the PCA Mix chart.

Extreme Value Charts and ANOM Based on Gumbel Distribution

The quality is assessable by its feature is implicit with a probability model which follow Gumbel distribution. From each subgroups extreme values are used to construct extreme value charts and variable control charts. Probability model of the extreme order statistics and the size of each sub group are used in control chart constants. To find the decision lines of Gumbel distribution we implement a method of analysis of means (ANOM). The proposed ANOM decision lines are constructed for given number of subgroup within means category and between means category given by Ott (1967). These decision lines are illustrated by giving few examples.

A resubmission-based variable control chart

In this paper, an attempt is made to develop a new variable control chart under the resubmitted sampling scheme. The resubmission of a sample allows retaking a sample to pass through inspection/analyzing if there is a question on the inspection of the sample at any stage. The proposed control chart includes the X-bar chart as a special case. The performance of the proposed control chart is assessed by determining the in-control and out-of-control average run lengths for the various parametric settings. For illustrative purposes, a real-life example is presented to explain a detailed implementation of the proposed control chart.

STATISTICAL CONTROL ANALYSIS OF THE STUDENT’S FINAL ASSIGNMENT COMPLETION PERIOD AT THE MATHEMATICS AND NATURAL SCIENCES FACULTY

The final assignment is one of the requirements to get a bachelor’s degree for college students at the Faculty of Mathematics and Natural Sciences (FMIPA) University of Lambung Mangkurat (ULM). The average period of completion of the final assignment in the year 2015 until 2019 is 8 months, while the determined specification by the guideline is 6 months. The aim of this research is to identify the quality control of the final assignment completion process and whether satisfy the determined specification using statistical quality control. The used data in this research is the student’s final assignment completion period (variable data) and the nonconforming proportion of data (attribute data). The and control charts are used for variable data and control chart for attribute data and process capability analysis. The result of variable data is that the average period of final assignment completion is statistically in control with a control limit of months. For attribute data concluded that final assignment completion is statistically in control with a big average proportion that is . For the capability analysis process by index and value sequentially is and for the DPU value is . This shows that the completion period of the student’s final assignment of FMIPA ULM is not capable to fulfill the specified standard of the period.

Statistical design of an adaptive synthetic X¯$\bar{X}$ control chart for autocorrelated processes

AbstractThis paper aims to design a variable parameters synthetic control chart for first‐order AR(1) autocorrelated data following a Gaussian process. To improve the statistical performance in detecting small changes and maintaining a low false alarm rate, the variable parameters control chart was combined with the Conforming Run Length (CRL) sub‐chart to determine when to implement tight or relaxed control and intervene to identify an assignable cause. The statistical design of the proposed chart was performed under a discrete‐time Markov chain approach and a non‐linear programming mathematical model to obtain, using a genetic algorithm (GA), the values of the design parameters that minimise the average time to signal the out‐of‐control state (). A sensitivity analysis was performed to examine the behaviour of the in the face on changes in the parameters. Also, a performance evaluation was conducted to compare the proposed chart with other adaptive synthetic charts, the synthetic control chart and the chart developed by Costa and Machado. Our results indicate that this proposal is faster to detect small changes in the process mean considering the autocorrelation of the data.

Taguchi's robust parameter design to analyse ordered categorical data using inverse omega transformation

The manufacturing industry is striving hard to gain an edge over its competitors as far as the product quality is concerned. The product may have both variable and attribute quality characteristics. The variable cases are addressed using Shewhart's variable control charts, process capability analysis etc. Most of the attribute cases are addressed using 'fraction defective'; this serves as a quality measure. When such attributes of the product are categorised according to their severity, then the same case may be dealt with as 'ordered categorical data'. This research work presents the use of Taguchi's parameter design to improve the product quality during spline hob operation of a shaft. The visual defects that occur during this operation are treated as ordered categorical data and the analysis of this data is carried out using inverse omega transformation. The paper has resulted in determining the optimum settings for the process parameters in the spline hob operation.

A Comparison Between the MEWMA and Mahalanobis Distance Control Chart

Statistical Process Control (SPC) is approaching that uses statistical techniques to monitor the process. The methods of quality control are widely used in controlling any strategy—the widely used control charts. A traditional variable control chart includes three lines: the Centre Line (CL), the Upper Control Limit (UCL), and the Lower Control Limit (LCL), all of which are represented by numeric values—represented by numeric values. A control chart illustrates the centerline of the average value of the quality feature under investigation.
 Depending on numeric observation values, a process is either "in control" or "out of control."
 Considering the current, there are no questions regarding the observations and their values during the production process. However, when these observations include human judgments, assessments, and choices, a continuous random variable (xi) of a manufacturing process should be made up of the variable.
 The MEWMA and Mahalanobis distance control chart techniques are used when more than one variable is involved.
 This paper aims to compare the MEWMA and Mahalanobis distance chart for three compounds for water drinking production in the ALA -Factory in the Sulaimani-Iraq region.
 So, linguistic terms can be used instead of the exact value of the continuous random variable. Today, quality control has become one of the most essential techniques for studying all variables to control production or consumption decision factors. Quality control's primary aim is to guarantee that the goods, services, or processes delivered satisfy particular standards and are reliable and satisfactory. The factor's direct approach is based on the product's quality.

Remote sensing based on time variance control in configurable area partitioning

Abstract. In this paper a sensor data fusion approach for characteristics field monitoring, based on time variance control model, is proposed. Distributed sensing and remote processing are the basic features of the employed architecture. In fact, in order to obtain meaningful information about the temporal and spatial variations, which characterize the field levels of some characteristics (electromagnetic, air pollution, seismic, etc), a distributed network of wireless and mobile smart-sensors has been designed.Starting from the partitioned configuration of a monitored geographic areas, this model allows to take into account the different levels of degradation over time in the sensors' performances associated with the different geographic partitions, progressively increasing the severity of the control. To this end, through the introduction of a reliability curve, a revised traditional control chart for variables is proposed.The proposed approach, further constituting an element of the scientific debate, aims to be a useful operational tool for professionals and managers employed in the environment control.

Exact computational methods for univariate and multivariate control charts under runs rules

This article proposes efficient computational methods for designing and evaluating phases of Shewhart type control charts under runs rules. The efficient computational methods include exact equations or formulas for computing the probability of single-point and run-length properties of control charts. The run-length properties include average, variance, standard deviation, coefficient of variation, and moments. The study implements the proposed computational methods in the design and evaluation phases of well known univariate and multivariate control charts. In this regard, the research considers mean, variance, standard deviation, multivariate Hotelling and generalized variance control charts. Also, various procedures and a code in R language are provided to exemplify the applications of proposed computational methods in control charts. A comprehensive analysis of the behaviour of run-length properties of control charts under runs rules is conducted by considering various choices of factors such as sample size, amount of shift, and choice of runs rules. The proposed efficient computational methods provide the desired results with additional features such as reducing the computational burden, time efficient and being practitioner friendly. Finally, the article presents some real-life examples of univariate and multivariate control charts from manufacturing and winds turbine processes.