Individual Control Charts Research Articles

Evaluating students’ performance in mathematics and other subjects using fixed and individual control chart grading methods

Evaluating students’ performance in mathematics and other subjects using fixed and individual control chart grading methods

Applying the six-sigma methodology to determine the limits of quality control (QC) tests for a specific linear accelerator.

We aimed to show the framework of the six-sigma methodology (SSM) that can be used to determine the limits of QC tests for the linear accelerator (Linac). Limits for QC tests are individually determined using the SSM. The SSM is based on the define-measure-analyze-improve-control (DMAIC) stages to improve the process. In the "define" stage, the limits of QC tests were determined. In the "measure" stage, a retrospective collection of daily QC data using a Machine Performance Check platform was performed from January 2020 to December 2022. In the "analyze" stage, the process of determining the limits was proposed using statistical analyses and process capability indices. In the "improve" stage, the capability index was used to calculate the action limits. The tolerance limit was established using the larger one of the control limits in the individual control chart (I-chart). In the "control" stage, daily QC data were collected prospectively from January 2023 to May 2023 to monitor the effect of action limits and tolerance limits. A total of 798 sets of QC data including beam, isocenter, collimation, couch, and gantry tests were collected and analyzed. The Collimation Rotation offset test had the min-Cp, min-Cpk, min-Pp, and min-Ppk at 2.53, 1.99, 1.59, and 1.25, respectively. The Couch Rtn test had the max-Cp, max-Cpk, max-Pp, and max-Ppk at 31.5, 29.9, 23.4, and 22.2, respectively. There are three QC tests with higher action limits than the original tolerance. Some data on the I-chart of the beam output change, isocenter KV offset, and jaw X1 exceeded the lower tolerance and action limit, which indicated that a system deviation occurred and reminded the physicist to take action to improve the process. The SSM is an excellent framework to use in determining the limits of QC tests. The process capability index is an important parameter that provides quantitative information on determining the limits of QC tests.

A Recently Formulated Individual Control Chart Designed for Quality Control Applications within the Health-care Domain

Quality control charts are based on data that is also used for various statistical analyses, such as regression, time series analysis, and other types of analyses. This implies that the data used to create these charts may contain outliers, potentially compromising their accuracy. To eliminate any potential noise or pollution from the data, a researcher proposed using wavelet shrinkage with a threshold and comparing the resulting data with Shewart's individual chart. Based on this, a new quality control chart was proposed and built using a universal approach for assessing the level of thresholding, representing the individual chart for wavelet haar with soft and hard thresholding. Following that, a comparison was performed between them as well as with Shewart's individual chart. This letter's most significant conclusion is that, in addition to using two real data points—triglyceride, which was recorded by a laboratory blood analyzer in Al-Jumhuri and at the specialized Center for Cardiology Hospital in Erbil Governorate—it may be possible to use wavelet shrinkage with a threshold to address issues of noise or pollution when Shewart's individual chart was made and used. Moreover, the wavelet method effectively reduces deviation, as demonstrated in both sets of data.

Performance analysis of agricultural machinery with aid digital agriculture

Digital agriculture has increasingly gained strength in the countryside, as it is considered a byproduct of growing globalization. As the search for production optimization, cost reduction, and productivity increase continues, these tools become the great allies of the producer in the final agricultural production process.Therefore, agricultural operations must also follow this evolution in the development of technological improvements, which carry positive aspects for large-scale production. In this context, the objective of this work was to evaluate the performance of seeders-fertilizers with different input distribution mechanisms. Since one of the biggest expenses in the production process is the acquisition of seeds and fertilizer, any savings in production costs become a significant advantage for the producer, who will have a greater net income. The experimental design used to evaluate the data followed the premises of Statistical Process Control (SPC), and the results were assessed using individual value control charts. It was concluded that the production process was negatively affected by the performance of the seeders-fertilizers, as in one area, more seeds were falling than necessary, increasing the cost per hectare and not adhering to the principles of cost minimization and profit maximization. Conversely, in the second area evaluated, the machinery's performance resulted in fewer seeds being deposited than planned. Consequently, according to the results, the producer lost the opportunity to produce 5.85 sc/ha without reducing costs in the operation, as the seeder simply did not deposit the seeds, thereby reducing the gain per area, which could have been more productive, increasing final profitability.

INDIVIDUAL CONTROL CHARTS FOR NON-NORMAL DATA

Individual control charts are a suitable option to consider when the processes being studied change slowly. If obtaining standard samples for Shewhart control charts is expensive or in the case of studying statistical characteristics of the technological process, they are used. Control charts are used to control technological processes in the case of a normal distribution of the possible values of the controlled parameter. Sometimes a quasi-normal distribution of the studied parameter is allowed. In practice, it is often necessary to deal with technological processes in which samples are not distributed according to a normal distribution. In such cases, using individual control charts can lead to type I and II errors. This is because the control limits of the charts are calculated for the mean and standard deviation of the normal distribution. Control charts of individual values are most sensitive to the deviation of the distribution from the normal one since individual values are used to construct the limits, to which the central limit theorem does not apply, as in the case of control charts of mean values. Therefore, it is extremely important to develop methods of applying the individual control charts for random samples, the general population of which is not normally distributed. The study examines the application of individual control charts for a random process that is non-normally distributed. This is achieved by using the normalization method to transform samples of the studied parameter into samples that are distributed normally or quasi-normally. The normalization is performed using the Box-Cox method with further construction of control charts based on the transformed samples. The mathematical apparatus of the individual control chart application for samples with non-normal distribution is described. Numerical modeling of the application of individual control charts for the chi-square distributed samples, which have a significant distribution asymmetry for small values of the shape factor, and for the samples obtained by normalizing the chi-square one, was performed. According to the research findings, the utilization of individual control charts for samples exhibiting a significantly asymmetric distribution results in a higher likelihood of type I errors being detected. However, when the method of sample normalization is employed, this issue is almost entirely eliminated. Modeling process disruption, by changing a certain individual value, also demonstrated the emergence of false signals of process disruption.

Economic modelling and optimisation of SPRT-based quality control schemes for individual observations

In many industrial processes, it may not be practical to obtain sample sizes larger than one due to various reasons. As a result, practitioners must rely on control charts based on individual observations for statistical process monitoring and control. The sequential probability ratio test (SPRT) chart is an appropriate solution for such situations. Existing literature predominantly delves into the statistical aspects of designing or optimising an SPRT chart, neglecting the economic and associated design aspects. However, past experience suggests that statistical design may not always be optimal from an economic perspective. This paper aims to bridge this research gap by proposing a two-stage Markov chain approach to develop an economic model for the optimal design of the SPRT chart with individual observations. Following the principles of economic-statistical designs, optimal parameters are determined by solving a mixed-integer non-linear programming problem that minimises the long-run cost per item while ensuring compliance with practical constraints. Through an extensive study, we find that the economic performance of the SPRT chart surpasses that of competing individual control charts in many cases. This indicates that the economic-statistical design of the SPRT chart can yield significant economic benefits while maintaining desirable statistical properties. Moreover, enhancements have been introduced to refine the optimal design of the SPRT chart, retaining excellent overall performance across a wide range of shifts. Finally, we provide two industrial examples to illustrate the effectiveness of the proposed SPRT chart.

Remaining Useful Life Prediction of Lithium-Ion Battery Using ICC-CNN-LSTM Methodology

In recent years, lithium-ion batteries have gained significant attention due to their crucial role in various applications, such as electric vehicles and renewable energy storage. Accurate prediction of the remaining useful life (RUL) of these batteries is essential for optimizing their performance and ensuring reliable operation. In this paper, we propose a novel methodology for RUL prediction using an individual control chart (ICC) to identify and remove degraded data, a convolutional neural network (CNN) to smooth the noise of sensor data and long short-term memory (LSTM) networks to effectively capture both spatial and temporal dependencies within battery data, enabling accurate RUL estimation. We evaluate our proposed model using a comprehensive dataset, and experimental results demonstrate its superior performance compared to existing methods. Our findings highlight the potential of ICC-CNN-LSTM for RUL prediction in lithium-ion batteries and provide valuable insights for future research.

Guaranteed performance of individual control chart used in gamma passing rate-based patient-specific quality assurance

PurposeTo assess the effect of sampling variability on the performance of individual charts (I-charts) for PSQA and provide a robust and reliable method for unknown PSQA processes. Materials and methodsA total of 1327 pretreatment PSQAs were analyzed. Different datasets with samples in the range of 20–1000 were used to estimate the lower control limit (LCL). Based on the iterative “Identify-Eliminate-Recalculate” and direct calculation without any outlier filtering procedures, five I-charts methods, namely the Shewhart, quantile, scaled weighted variance (SWV), weighted standard deviation (WSD), and skewness correction (SC) method, were used to compute the LCL. The average run length (ARL0) and false alarm rate (FAR0) were calculated to evaluate the performance of LCL. ResultsThe ground truth of the values of LCL, FAR0, and ARL0 obtained via in-control PSQAs were 92.31%, 0.135%, and 740.7, respectively. Further, for in-control PSQAs, the width of the 95% confidence interval of LCL values for all methods tended to decrease with the increase in sample size. In all sample ranges of in-control PSQAs, only the median LCL and ARL0 values obtained via WSD and SWV methods were close to the ground truth. For the actual unknown PSQAs, based on the “Identify-Eliminate-Recalculate” procedure, only the median LCL values obtained by the WSD method were closest to the ground truth. ConclusionsSampling variability seriously affected the I-chart performance in PSQA processes, particularly for small samples. For unknown PSQAs, the WSD method based on the implementation of the iterative “Identify-Eliminate-Recalculate” procedure exhibited sufficient robustness and reliability.

Correlation between patient-specific quality assurance in volumetric modulated arc therapy and 2D dose image features

In radiotherapy, air-filled ion chamber detectors are ubiquitously used in routine dose measurements for treatment planning. However, its use has been restricted by intrinsic low spatial resolution barriers. We developed one procedure for patient-specific quality assurance (QA) in arc radiotherapy by coalescing two adjacent measurement images into a single image to improve spatial resolution and sampling frequency, and investigated how different spatial resolutions affect the QA results. PTW 729 and 1500 ion chamber detectors were used for dosimetric verification via coalescing two measurements with 5 mm-couch shift and the isocenter, and only isocenter measurement, which we call coalescence and standard acquisition (SA). Statistical process control (SPC), process capability analysis (PCA), and receiver operating characteristic (ROC) curve were used to compare the performance of the two procedures in determining tolerance levels and identifying clinically relevant errors. By analyzing 1256 γ values calculated on interpolated data points, our results indicated that detector 1500 showed higher averages in coalescence cohorts at different tolerance criteria and the dispersion degrees were spread out smaller. Detector 729 yielded a slightly lower process capability of 0.79, 0.76, 1.10, and 1.34, but detector 1500 exhibited somewhat different results of 0.94, 1.42, 1.19, and 1.60 in magnitude. The results of SPC individual control chart showed that cases in coalescence cohorts with γ values lowering its lower control limit (LCL) were greater than those in SA cohorts for detector 1500. A combination of the width of multi-leaf collimator (MLC) leaf, the cross-sectional area of the single detector, and the spacing between adjacent detectors might lead to discrepancies in percent γ values across diverse spatial resolution scenarios. The accuracy of reconstructed volume dose is mainly determined by the interpolation algorithm used in dosimetric systems. The magnitude of filling factor in the ion chamber detectors determined its ability to detect dose deviations. SPC and PCA results indicated that coalescence procedure could detect more potential failure QA results than SA while enhancing action thresholds.

Monitoring performance indicators of mechanized agricultural operations through a systemic method

Key performance indicators (KPI) are essential to decision-making in an organization, but the approach to analysis and composition used in the formulation of the KPIs can lead to errors. Analysis based only on averages does not allow for discriminating between variations that are natural to the process or special cases which require investigation. The use of control charts can identify this differentiation. However, when several charts are presented encompassing different measurement units and scales, systemic interpretation can be impaired. To assist in this interpretation, this research study aimed at proposing a method to facilitate the analysis of control charts when multiple indicators are employed in the monitoring of agricultural operations. Based on the data obtained over 26 weeks from a mechanized sugarcane (Saccharum officinarum L.) harvesting front, six indicators were defined and analyzed through individual control charts and, systemically, through a standardized group control chart. Results show that the points identified as being outside the control zone (special causes of variation) according to the standardized group control chart were the same as those identified by the six individual charts, which demonstrates the potential of this method to summarize the information with no loss of quality of analysis.

A Modified Mahalanobis Distance Metric Used to Optimize Mahalanobis Space and Improve Classification Performance of MTS

The Mahalanobis–Taguchi system (MTS) is a diagnostic and forecasting technique in a multidimensional system that integrates the Mahalanobis distance (MD) and robust engineering of Taguchi. To implement MTS, a set of observations from a normal group is selected to construct the Mahalanobis space (MS). With this MS as a reference, new observations from an unknown group can be judged to be normal or abnormal, and the degree of abnormality can be determined. MD is very sensitive to data changes, so the data quality of normal samples used to construct the MS directly affects the accuracy of classification. In practical applications, the selection of normal samples depends on the experience and subjective judgment of experts and lacks an objective selection mechanism. In this paper, a modified MD metric is proposed, which is combined with the individual control chart to obtain a robust MS. First, the initial MS is constructed according to the normal samples selected by experts, and the MD of each normal sample is calculated by the initial MS. Then, the MD of each normal sample in the corresponding reduced MS is computed, and the incremental MD is used as the new distance metric to establish the individual control charts. The stability rules of the control chart are employed to eliminate abnormal points, and the MS of the stable state is obtained. To evaluate the effectiveness of the modified MD metric, a numerical simulation experiment is implemented, and the results show that the proposed method is effective and improves the classification performance of MTS. Finally, the improved MTS method is applied to a real medical diagnosis case.

Application of Statistical Process Control for Structural Health Monitoring of a High-Speed Railway Track System

To make full use of the massive monitoring data accumulated in China high-speed railways, an improved statistical process control (SPC) framework was introduced to analyze the discontinuous monitoring data of the track system on a high-speed railway elevated station. Multilinear regression models and time series difference equation (TSDE) models were first developed to separate common-cause variations in the monitoring data. Then, individual control charts, moving range control charts, and exponentially weighted moving average control charts were constructed to detect special-cause variations. Results showed that the variations of girder displacement and track slab–girder relative displacements mainly resulted from temperature effects and linear trends related with material damages. Moreover, visible serial dependence was found in the regression model residuals, which could be effectively captured by the TSDE model. Numerous outliers were detected at the measuring points of rail–track slab displacement 15 and track slab–girder relative displacement 17 by more than three control charts, implying higher sensitivity to special causes. With respect to the special causes triggering the anomalous responses of local and overall track systems, sixteen and twenty-eight significant special events were detected, respectively.

Spatial variability characterization of acoustic discomfort and zone of admissible noise caused by micro-tractor

Agricultural development requires greater adoption of machinery by producers to avoid damage to the worker’s health due to excessive noise. In this scenario, this study aimed to analyze the noise magnitude emitted by a micro-tractor using geostatistics and Statistical Process Control (SPC) in mapping spatial variability to identify healthy zones for workers. The study was carried out at the Federal University of Lavras (UFLA), where noise levels were collected at points distributed in a regular 2.0×2.0 m sample grid around the machine. The spatial dependence of noise was analyzed by adjusting the wave-type semivariogram and interpolating by ordinary kriging and the SPC through individual control charts. It was possible to observe alarming noise values above 85 dB(A) in a radius of up to 6 m around the tractor in operation. The maximum value of 91 dB(A) was obtained from the operator’s seat, thus allowing maximum daily exposure of 3.5 h. In addition, it was observed that people located at distances greater than 4 m from the micro-tractor do not need to wear personal protective equipment for an exposure of 8 h of work.

A patient risk model to determine the optimal output constancy check frequency for a radiotherapy machine.

The output constancy check, a basic quality control (QC) item for radiotherapy machines, is performed daily according to suggestions in technical reports by experienced experts. In this study, a patient risk model was built to determine the optimal frequency of an output constancy check for a specific radiotherapy machine. The method was based on the patient risk model and comprised three steps: 1) the power function graph was used to select a proper QC rule and the average number of QC measurements per QC rule evaluation. 2) The optimal QC frequency was determined by the minimum integer value of expected patients treated between QC measurements. 3) The individual control chart (I-Chart) was used to evaluate the effectiveness of the model. The model was implemented on the output constancy check of a Tomotherapy machine. The QC rule with the limits set to the mean±3 standard deviations and 5 measurements per QC were selected according to the power function graph. The optimal frequency was observed every 21 patients. The I-Chart showed that the optimal frequency detected the machine failure earlier compared to the conventional daily frequency. The model could monitor whether Tomotherapy machine was in good condition and predicted the time to adjust the machine. The optimal output constancy check frequency of a radiotherapy machine is determined by the number of patients, which uses patient risk model. The optimal frequency is superior to the conventional daily frequency in identifying machine failure earlier.

Model-Based Monitoring of Patient Response to Staged Thyroidectomy

The goal of this study is to develop a model-based control chart for monitoring patient behavior in a staged thyroidectomy considering risk factors and clinical prescription. prospectively collected data are gathered from thyroid surgery unit of a hospital located in Tehran, Iran for 80 staged thyroidectomy patients discharged from 2009 to 2013. A risk adjusted state space model is developed based on the staged thyroidectomy. Variables to be included in the model are determined as a part of the model building process. Performance criteria, clinical prescription and patient risk factors are three variable components for the model. The appropriate risk factors are directly involved in the model and no scoring system is used for the model construction. Model identification is performed in two steps; model order selection and parameter estimation. In the first step, Hankel singular value decomposition (HSVD) is used for detecting the model order and in the second step, unknown parameters are estimated by the prediction error minimization (PEM) method. For monitoring patient responses, a group individual (GI) control chart is introduced and applied to a real-world problem. Results indicate that the suggested control chart can monitor the staged thyroidectomy patient’s behavior with an acceptable accuracy. Also, computer aided diagnosis (CAD) systems can be developed based on the proposed identification and monitoring method.

Highest Posterior Distribution (HPD) Control Chart for Individual Observation

Highest Posterior Distribution (HPD) is one of the methods to determine the interval estimator of data having both symmetric and asymmetric distributions. On the symmetric distribution, the Lower Control Limit (LCL) and the Upper Control Limit (UCL) of Individual control chart will automatically have the equilibrium density value. However, the LCL and the UCL of Individual control chart for asymmetric distribution will never have the equilibrium density value. This research is aimed to propose HPD control chart based on the concept of equilibrium density. The simulation studies provide the control limits of Individual and HPD control charts for both symmetric and asymmetric distributions of data. The Average Run Length (ARL) of both Individual and HPD control charts are calculated by generating the data which follow normal distribution and some asymmetric distributions such as weibull, gamma, beta, and lognormal. The in-control ARL (ARL0) of Individual control chart for various asymmetric distributions violate the ARL0 target. Even for asymmetric distribution, the ARL0 of HPD control chart is convergent to certain value of ARL0 target. Hence, HPD control chart is appropriate to monitor both symmetric and asymmetric distribution of data.

Analysis and control of the paper moisture content variability by using fuzzy and traditional individual control charts

For several decades, the fuzzy theory has been used to develop the so-called fuzzy control charts to analyze process data in a more reliable and flexible way than traditional control charts. Control charts are more commonly used in the papermaking processes to check the stability of the data source. These charts are conceived as devices that enhance routine time-by-time adjustments during the production process, so their value is incomparable. A critical variable that must be controlled during the papermaking process is the moisture content of the paper. However, due to the paper’s hygroscopic characteristics, its moisture content values may carry some uncertainty derived from measurement systems and the nature of the papermaking process. Therefore, an alternative approach that includes fuzz control charts to handle these uncertainties is proposed in this paper. The method to convert individual data to fuzzy numbers is based on the sigma level process as a first stage, and then, the fuzzy individual and moving range control charts are introduced using the α−cut fuzzy midrange approach. Data from the moisture content of a 240 ​g coated paper sample is used to prove the performance of the fuzzy individual control charts. According to the proposed methodology, findings show that fuzzy individual and moving range control charts have greater flexibility than traditional individual control charts by reflecting a larger amplitude of their control limits, in addition to a lower number of “out of control” values.

Productive diagnosis of Girolando cows on a farm in Alto Sertão Sergipano

Girolando breed has several blood grades, from 1/4 Dutch (Hol) x 3/4 Gir (G), to 7/8 Hol x 1/8 G. These animals have good milk production characteristics inherited from the Dutch breed and a good acquired rusticity of the Gir breed. In view of this, this work aimed to evaluate the productive performance of three different blood grades of the Girolando breed on a farm in the Alto Sertão Sergipano. For the research, the data used referred to the highest production in 305 days of distinct lactations, between the first and the fourth lactation. The blood grades evaluated were: 1/2 HG (G1); 3/4 HG (G2) and 7/8 HG (G3). For the diagnosis, the Individual Control Chart was used, which is one of the tools of the Statistical Process Control (SPC), with the purpose of evaluating and controlling, in a global way, all the production. The results obtained do not demonstrate superiority of production among the three genetic groups. However, the G1 group showed the highest regularity in milk production, with the highest average production and the lowest average range. However, in order to obtain a better diagnosis of milk production, more studies are needed addressing milk production in 305 days with different blood grades of the Girolando breed, in the Alto Sertão Sergipano region.

Preliminary study on monitoring patient-specific volumetric modulated arc therapy quality assurance process with statistical process control methodology on the basis of TG-218 report

Patient-specific volumetric modulated arc therapy (VMAT) quality assurance (QA) process is an important component of the implementation process of clinical radiotherapy. The tolerance limit and action limit of discrepancies between the calculated dose and the delivered radiation dose are the key parts of the VMAT QA processes as recognized by the AAPM TG-218 report, however, there is no unified standard for these two values among radiotherapy centers. In this study, based on the operational recommendations given in the AAPM TG-218 report, treatment site-specific tolerance limits and action limits of gamma pass rate in VMAT QA processes when using ArcCHECK for dose verification were established by statistical process control (SPC) methodology. The tolerance limit and action limit were calculated based on the first 25 in-control VMAT QA for each site. The individual control charts were drawn to continuously monitor the VMAT QA process with 287 VMAT plans and analyze the causes of VMAT QA out of control. The tolerance limits for brain, head and neck, abdomen and pelvic VMAT QA processes were 94.56%, 94.68%, 94.34%, and 92.97%, respectively, and the action limits were 93.82%, 92.54%, 93.23%, and 90.29%, respectively. Except for pelvic, the tolerance limits for the brain, head and neck, and abdomen were close to the universal tolerance limit of TG-218 (95%), and the action limits for all sites were higher than the universal action limit of TG-218 (90%). The out-of-control VMAT QAs were detected by the individual control chart, including one case of head and neck, two of the abdomen and two of the pelvic site. Four of them were affected by the setup error, and one was affected by the calibration of ArcCHECK. The results show that the SPC methodology can effectively monitor the IMRT/VMAT QA processes. Setting treatment site-specific tolerance limits is helpful to investigate the cause of out-of-control VMAT QA.

Stability assessment of sulphur (II) compounds in medicinal water from B-8b Michał intake in Busko-Zdrój

Abstract In this paper, the stability of sulphur (II) compounds determined as the sum of hydrogen sul-phide, hydrosulphides and sulphides was evaluated in groundwater sourced from the B-8b Michał intake. Sulphide waters are a valuable raw material used as a basis for spa treatment in Busko-Zdrój. Based on the chemical composition analyses conducted in the years 1946–2018, a general analysis of random variability and statistical analysis of data was performed using PS IMAGO 5.0.1 software. Stability assessment was carried out on the data set for the 2009–2018 period on the basis of individual measurement control charts. Trend analysis was also performed using the GWSDAT software.