Shewhart Control Charts Research Articles

Simultaneous monitoring of the mean vector and covariance matrix of multivariate multiple linear profiles with a new adaptive Shewhart-type control chart

There has been a growing interest in research regarding monitoring a process through a regression model (called a profile) rather than a simple quality characteristic. This paper proposes a new monitoring scheme to simultaneously monitor the multivariate multiple linear profiles’ parameters. This scheme is based on the Shewhart control chart concept and only has one single (max-type) control chart for monitoring regression coefficients and error’s variation, which uses a new statistic to improve the variability (error’s variance-covariance matrix) shift detection in multivariate profiles. To increase the sensitivity and capability of the proposed scheme, especially in detecting small to moderate shift sizes, we add a variable parameters (VP) adaptive scheme to the developed control chart as well, considering that no adaptive monitoring schemes have so far been developed for monitoring the multivariate multiple linear profiles and neither are there any VP adaptive features for all profile monitoring schemes. Next, we develop a Markov chain model to compute the time to signal and run length performance measures. After that, we perform extensive numerical analyses to first compare the proposed control chart with the best available control charts and then evaluate its performance under different shift scenarios as well as different dimensions. The results show that the new monitoring scheme performs well compared to the best available monitoring schemes, and more importantly, it is more applicable in real practice. Finally, an illustrative example is presented to show the implementation of the proposed scheme in practice.

ПРИМЕНЕНИЕ МЕТОДА КОНТРОЛЬНЫХ КАРТ ПРИ ИССЛЕДОВАНИИ ХАОТИЧЕСКОЙ ДИНАМИКИ КАРДИОИНТЕРВАЛОВ

The article analyzes literature on the use of Shewhart control charts for various purposes and presents examples of applying a proposed statistical method in medicine. The study demonstrates that it is possible to identify situations common for the transferring stage from one functional condition to another (including pathologic one) using Shewhart control charts for prediction of critical conditions in the biosystem and its parameters (on the example of time series of cardiovascular system’s RR intervals).

Refinement of the Process Capability Index Сalculation

The variability of product performance is the reason for the introduction of special methods to ensure product quality, particularly statistical methods. These include introducing statistical process control (SPC) in production and calculating the process capability index to determine the manufacturing ability to meet the product’s quality requirements. To a large extent, the ability of a process to meet the requirements was determined by the location of the process or the mathematical expectation of the controlled quality characteristic value. Process setup center variability within the boundaries of the Shewhart control chart of the average values was supposed to be the natural state for a statistically controlled process. However, the calculation of the process capability index did not consider the possibility of a shift in the actual value of the process setup center for a controlled characteristic from its mathematical expectation. It was proposed to adjust the process capability index for the setup center’s possible deviation. It demonstrated the possibility of critical errors in determining the ability of a production process to meet requirements without considering the process setup center. The effectiveness of the proposed solutions was also demonstrated by the example of determining the ability of the welding wire manufacturing process to meet the requirements for metal yield strength of the welded joint of metal bridge span constructions.

Alternative Design of One-Sided Shewhart Control Charts for the Multivariate Coefficient of Variation

The control charting technique is an approach to quality control and was implemented in various industries. There are many control charts, where the coefficient of variation control chart was one of the common charts and greatly used in Statistical Process Control. Since most processes are multivariate, the multivariate coefficient of variation charts has received great attention in the past few years. However, the existing multivariate coefficient of variation control charts was evaluated in terms of the average run length criterion, which may misinterpret the actual performance of the charts. This paper designs an alternative for the Shewhart multivariate coefficient of variation chart by considering the median run length and expected median run-length criteria to circumvent this problem. The research on the multivariate coefficient of variation chart is very limited in the existing literature by considering the median run length criterion. This proposed chart in this paper can minimize this research gap. The formulas and algorithms of the proposed chart are presented. The outputs of the proposed charts are shown by examining the different upward and downward process shifts. Additionally, the sample sizes, the process shifts, and the variation of the run-length distribution are investigated for their effects on the proposed chart. The findings reveal that the run-length distribution’s variation is inversely proportional to the shift size. Furthermore, it shows that the variation decreases if the shift size increases.

Simulation-Based Fault Detection Remote Monitoring System for Small-Scale Photovoltaic Systems

A small-scale grid-connected PV system that is easy to install and is inexpensive as a remote monitoring system may cause economic losses if its failure is not found and it is left unattended for a long time. Thus, in this study, we developed a low-cost fault detection remote monitoring system for small-scale grid-connected PV systems. This active monitoring system equipped with a simulation-based fault detection algorithm accurately predicts AC power under normal operating conditions and notifies its failure when the measured power is abnormally low. In order to lower the cost, we used a single board computer (SBC) with edge computing as a data server and designed a monitoring system using openHAB, an open-source software. Additionally, we used the Shewhart control chart as a fault detection criterion and the ratio between the measured and predicted ac power for the normal operation data as an observation. As a result of the verification test for the actual grid-connected PV system, it was confirmed that the developed remote monitoring system was able to accurately identify the system failures in real-time, such as open circuit, short circuit, partial shading, etc.

Fault Detection of Wind Turbine Pitch Motors Based on Ensemble Learning Approach

Machine learning-based condition monitoring of wind turbines’ critical components is an active area of research, especially for pitch systems, which suffer from a high failure rate. In this work, we successfully predicted and detected the high-temperature fault of the electric pitch motor by analyzing SCADA data through the ensemble learning-based approach. For that, normal behavior models to predict pitch motor temperature were constructed respectively for three pitch motors by gradient boosting tree regression. Residual evolution before the reported high-temperature fault was studied by the sliding window approach. A Shewhart control chart was applied to detect the anomalies of temperature. The proposed approach successfully gave an early warning for the potential high-temperature fault of electric pitch motors around ten days prior to the SCADA system.

Constructing control charts for autocorrelated data using an exhaustive systematic samples pooled variance estimator

SPC with positive autocorrelation is well known to result in frequent false alarms if the autocorrelation is ignored. The autocorrelation is a nuisance and not a feature that merits modeling and understanding. This paper proposes exhaustive systematic sampling, which is similar to Bayesian thinning except no observations are dropped, to create a pooled variance estimator that can be used in Shewhart control charts with competitive performance. The expected value and variance are derived using quadratic forms that is nonparametric in the sense no distribution or time series model is assumed. Practical guidance for choosing the systematic sampling interval is offered to choose a value large enough to be approximately unbiased and not too big to inflate variance. The proposed control charts are compared to time series residual control charts in a simulation study that validates using the empirical reference distribution control limits to preserve stated in-control false alarm probability and demonstrates similar performance.

TECHNICAL DIAGNOSTICS OF HYDRAULIC ROTATOR

This article deals with the design of a technical diagnostics system for hydraulic rotators and the successful implementation of a unique hydraulic test bench. Based on an analysis of the design and function of all types of hydraulic rotators available on the world market, a system of requirements for the test bench and its place in the test centre was formulated. Furthermore, four diagnostic parameters from the group of deformation diagnostics and hydraulic systems diagnostics are proposed and used to evaluate the technical condition of the Indexator IR25 hydraulic rotator. For the evaluation of individual parameter values, a modified Shewhart control chart method is proposed for individual values and moving ranges of each parameter. Based on the measurements of 30 rotators, control limits were designed for statistical evaluation of the technical condition of the mentioned hydraulic rotator.

Improving Duration of Antibiotics for Skin and Soft-tissue Infections in Pediatric Urgent Cares.

National guidelines recommend a 5- to 7-day course of antibiotics for most skin and soft-tissue infections (SSTIs). Our aim was to increase the percentage of pediatric patients receiving 5 to 7 days of oral antibiotics for SSTIs in our pediatric urgent care clinics (UCCs) from 60% to 75% by December 31, 2021. We performed cause-and-effect analysis and surveyed UCC providers to uncover reasons for hesitation with short antibiotic courses for SSTIs. Plan- Do-Study-Act (PDSA) cycle 1 provided an update on current guidelines for UCC providers and addressed providers' concerns. PDSA cycle 2 modified the electronic health record to display antimicrobial prescription sentences from shortest to longest duration. PDSA cycle 3 provided project outcome and balancing measure updates to UCC providers at regular intervals. We created a monthly report of patients 90 days and older in UCCs with a final diagnosis of SSTIs. We used a Shewhart control chart to identify special cause variations. After completing our PDSA cycles, we found that the percentage of children receiving 5 to 7 days of oral antibiotics for SSTIs exceeded 85%. The improvement was sustained over multiple months. There was no increase in the proportion of patients returning to the UCCs with an SSTI diagnosis within 14 days. By addressing primary drivers uncovered through quality improvement methodology, we shortened the antibiotic course for children seen in our UCCs with SSTIs. Outpatient antimicrobial stewardship programs may apply similar methods to other diagnoses to further improve duration of antibiotic prescriptions.

A Method for Statistical Processing of Magnetic Field Sensor Signals for Non-Invasive Condition Monitoring of Synchronous Generators.

Condition monitoring of synchronous generators through non-invasive methods is widely requested by maintenance teams for not interfering the machine operation. Among the techniques used, external magnetic field monitoring is a recent strategy with great potential for detecting incipient faults. In this context, this paper proposes the application of a simple strategy with low computational cost to process data of external magnetic field time derivative signals for the purposes of condition monitoring and fault detection in synchronous machines. The information of interest is extracted from changes in the magnetic signature of the synchronous generator, obtained from frequency spectra of monitored signals using induction magnetic field sensors. The process forms a set of time series that reflects constructive and operational characteristics of the machine. The Shewhart control chart method is applied for anomaly detection in these time series, allowing the detection of changes in the machine magnetic signature. This method is employed in an algorithm for continuous condition monitoring of synchronous generators, presenting as output a global change indicator for the multivariable problem associated with magnetic signature monitoring. Correlation matrices are used to improve the algorithm response, filtering series with similar variation patterns associated with detected events. The proposed method is validated through tests on an experimental bench that allows the controlled imposition of faults in a synchronous generator. The proposed global change indicator allows the automatic detection of stator and rotor faults with the machine synchronized with the commercial power grid. The proposed methodology is also applied on data obtained from an equipment installed in a 305 MVA synchronous generator of a hydroelectric power plant where the evolution of an incipient fault, i.e., a mechanical vibration fault, has been detected.

Monitoring a labeled degree‐corrected stochastic block model

AbstractThe stochastic block model (SBM) is a random graph model that focuses on partitioning the nodes into blocks or communities. A degree‐corrected stochastic block model (DCSBM) considers degree heterogeneity within nodes. Investigation of the type of edge label can be useful for studying networks. We have proposed a labeled degree‐corrected stochastic block model (LDCSBM), added the probability of the occurrence of each edge label, and monitored the behavior of this network. The LDCSBM is a dynamic network that varies over time; thus, we applied the monitoring process to both the US Senate voting network and simulated networks by defining structural changes. We used the Shewhart control chart for detecting changes and studied the effect of Phase I parameter estimation on Phase II performance. The efficiency of the model for surveillance has been evaluated using the average run length for estimated parameters.

About Shewhart control charts to monitor the Weibull mean based on a Gamma distribution

AbstractA control chart for the mean of a process whose quality characteristic follows a Weibull distribution is evaluated. In this sense, a transformation that follows an exponential distribution is used involving the parameters of scale and form of a Weibull distribution. Such a transformation allows to obtain analytically the control limits to monitor the mean using the Gamma distribution. Compared with recent results in the literature, lower average run lengths after a change (ARL1) values are measured without the need to use intensive Monte Carlo simulation to obtain the control limits as well as to calculate the ARL1 values. A numerical example is presented in detail to illustrate the efficiency and effectiveness of the developed control chart.

Moving Average Control Chart for Generalized Poisson Distribution

This study aim to propose a moving average control chart explicit formula based on the Generalized Poisson distribution (MAGP ) and to compare the performance of the MAGP control chart with that of the Shewhart control chart (CGP ). The average run length (ARL) is used to consider the performance. The ARL results indicated that the MAGP control chart is superior to the CGP control chart based on the Generalized Poisson distribution for detecting small shifts. Practitioners will find this explicit formula to be accurate as well as simple to apply and use.

A phase II EWMA chart for the balanced one‐way random effects model

AbstractStatistical process control (SPC) techniques are used in applications where more than one sources of variation are present, for example, in a one‐way random effects (variance components) model. The Shewhart control charts for this situation have been studied by several researchers. However, exponentially weighted moving average (EWMA) charts are generally recommended in Phase II, as they are more sensitive to detecting smaller process mean shifts. We consider EWMA charts for the one‐way random effects model in the balanced case, properly accounting for the effects of parameter estimation while designing and implementing the control charts. In the sequel we derive and calculate the corrected (adjusted) control limits for Phase II applications. Following the recent literature, the limits are formulated under two perspectives, the unconditional and the conditional. Tabulations of the charting constants are provided under both perspectives along with an illustration with some actual data. A simulation study examining in‐control (IC) robustness performance is conducted under both perspectives. Finally, some conclusions are given. An R package is provided to support deployment of the proposed control chart in practice.

Application of Shewhart Control Chart in Controlling Adverse Events in Patients with Severe Acute Organophosphorus Pesticide Poisoning Undergoing Blood Purification.

Objective To explore the application effect of the Shewhart control chart in controlling adverse events in patients with severe acute organophosphorus pesticide poisoning (AOPP) undergoing blood purification. Methods A retrospective analysis was performed on the clinical data of 102 patients with severe AOPP admitted to the hospital between January 2020 and December 2021, including 47 cases in the control group and 55 cases in the observation group. The control group was given routine emergency nursing, while the observation group was given emergency nursing under the guidance of the Shewhart control chart on the basis of the control group. The specialized operations, basic operations, specialized theory, and basic theory of nursing staffs were scored to compare the comprehensive nursing quality. The total incidence of adverse nursing events in both groups was statistically analyzed. The dosage of atropine, disappearance time of muscarinic symptoms, recovery time of CHE activity to 60%, and hospitalization time in both groups were recorded. The total incidence of complications in both groups was statistically analyzed. The satisfaction of family members was statistically analyzed by a satisfaction questionnaire. Results The scores of specialized operations, basic operations, specialized theory, and basic theory of nursing staffs in the observation group were significantly higher than those in the control group (P < 0.05), total incidence of adverse nursing events was significantly lower than that in the control group (P < 0.05), dosage of atropine, disappearance time of muscarinic symptoms, recovery time of CHE activity to 60%, and hospitalization time were significantly lower than those in the control group (P < 0.05), total incidence of complications was significantly lower than that in the control group (P < 0.05), and scores of nursing attitude, communication process, psychological relief, and drug preparation were significantly higher than those in the control group (P < 0.05). Conclusion The Shewhart control chart can effectively improve the clinical effect, comprehensive nursing quality, and satisfaction of patients with severe AOPP and effectively reduce complications and adverse events.

Synthetic-type control charts for monitoring general inflated poisson processes

The statistical monitoring of count data has received much attention in the recent years, with applications in several areas of applied research. The basic tool for monitoring an integer-valued process is the Shewhart control chart. In this work we investigate the performance of two Synthetic-type charts in the monitoring of a general inflated Poisson process. Synthetic charts are considered as viable alternatives to Shewhart charts, when we are interested in detecting quickly small and moderate shifts in the process parameters. Moreover, they retain the simplicity in design, operation, and interpretation of the Shewhart chart. We present the results of a numerical study regarding the statistical design and the performance of the proposed Synthetic charts. Finally, we provide two real-data examples that demonstrate the implementation of the proposed charts.

Insights into Variations in COVID-19 Infections in Malaysia

The present study aims to visualize the variations in the number of confirmed daily COVID-19 infections during the third wave in Malaysia through the application of control charts. This study also attempts to propose the target number of daily new cases that would bring the pandemic situation in Malaysia under control by utilizing the confirmed daily cases in Malaysia starting from 8th September 2020 until 30th June 2021. A modified Shewhart control chart was adopted to monitor the variations before and after the commencement of National Immunisation Programme (NIP). The chart shows a declining trend in the number of cases after the rollout of NIP whereby several days were brought to a state of statistical-in-control. But in less than three months after NIP commencement, there were huge variations in COVID-19 cases leading to drastic increase in the mean number of cases. These signal the presence of unnatural or assignable causes of variations which could be attributed to failure of curbing the risks of transmission, existence of various variants in the community, easing of containment measures and less adherence to the COVID-19 Standard Operating Procedures (SOPs). Significant shifts in the mean values prompt the development of a 3-phase modified Shewhart control chart. From the 3-phase chart, a series of daily number new cases that can be set as the target value to bring the pandemic situation in Malaysia under control, while flattening the epidemiological curve in the very near term.

A Control-Chart-Based Detector for Small-Amount Electricity Theft (SET) Attack in Smart Grids

For achieving the goal of two-way communication and power flows, smart grids are integrated with much state-of-the-art hardware and software. However, these newly added components also introduce a lot of vulnerabilities into the power systems, which results in that malicious users can launch various cyber-physical attacks to steal electricity. Existing electricity theft detection techniques suffer from an implicit assumption that malicious users tamper with smart meter readings to values much less than their actual electricity consumptions. These are called Large-amount Electricity Theft (LET) attacks. Nevertheless, in the real world, some malicious users may be cautious enough to deliberately launch Small-amount Electricity Theft (SET) attacks where smart meter readings are manipulated to numbers slightly lower than actual values, mainly to escape detection. To address this limitation, we propose a detector able to deal with both LET and SET attacks effectively. This detector applies a cumulative sum (CUSUM) control chart and a Shewhart control chart together to analyze users’ reported readings and measurements of a central observer meter. It consists of an electricity theft detection phase which aims to detect the existence of LET/SET attacks timely and a malicious user identification phase which aims to identify malicious users exactly. Extensive experiments are conducted to evaluate the proposed detector, and the results show that it has good performance in terms of several metrics.

Three-Dimensional Control Charts for Regulating Processes Described by a Two-Dimensional Normal Distribution

In the statistical management of processes in the initial phase, the stability of the technological process is determined based on the available samples. If the process is not stable, eliminating possible causes is brought into a statistically controlled position. At the same time, simple Shewhart control charts are used. In practice, some methods bring the process to a stable state (ISO standards, standards of various states). After the process has become stable, the boundaries of control charts are found for further management. Then, with the help of new samples, the process is managed. The article considers a process modeled by a two-dimensional normal distribution. New control charts have been found to check the normality and correlation of two-dimensional random variable components. The process is regulated using these charts, preserving the shape of the density of the individual components of the normal vector and linearity of these components. When constructing control charts, the Kolmogorov-Smirnov type agreement criterion and the Fisher criterion on the strength of the linear coupling of components were used. A concrete example shows the course of the introduction of these charts in production. The work results can be used in the initial phase of regulation and during the control check of the process under study. We used these control charts to assess product quality and quality control coming from the machine that produces the sleeves. It presents statistical methods for analyzing problems in factory practice and solutions for their elimination.

Veterinary syndromic surveillance using swine production data for farm health management and early disease detection

The use of syndromic surveillance (SyS) has grown in animal health since the 2010s, but the use of production data has been underexplored due to methodological and practical challenges. This paper aimed to tackle some of those challenges by developing a SyS system using production data routinely collected in pig breeding farms. Health-related indicators were created from the recorded data, and two different time-series types emerged: the weekly counts of events traditionally used in SyS; and continuous time-series, where every new event is a new observation, and grouping by time-unit is not applied. Exponentially Weighted Moving Average (EWMA) and Shewhart control charts were used for temporal aberration detection, using three detection limits to create a “severity” score. The system performance was evaluated using simulated outbreaks of porcine respiratory and reproduction syndrome (PRRS) as a disease introduction scenario. The system proved capable of providing early detection of unexpected trends, serving as a useful health and management decision support tool for farmers. Further research is needed to combine results of monitoring multiple parallel time-series into an overall assessment of the risk of reproduction failure.