Exploring Variability in Sea Level at a Tide Gauge Station through Control Charts

Monitoring temporal changes in sea level is important in assessing coastal risk.Sea level anomalies at a tide gauge station,if kinematically conceived,include systematic variations such as trend,acceleration,periodic oscillations,and random disturbances.Among them,the non-stationary nature of the random sea level variations of known or unknown origin at coastal regions has been long recognized by the sea level community.This study proposes the analyses of subgroups of random residual statistics of a rigorously formulated kinematic model solution of tide gauge variations using X-bar and S control charts.The approach is demonstrated using Key West,Florida tide gauge records.The mean and standard errors of 5-year-long subgroups of the residuals revealed that sea level changes at this location have been progressively intensifying from 1913 to the present.Increasing oscillations in sea level at this locality may be attributed partly to the thermal expansion of seawater with increasing temperatures causing larger buoyancy-related sea level fluctuations as well as the intensification of atmospheric events including wind patterns and the impact of changes in inverted barometer effects that will alter coastal risk assessments for the future.

Ranked-Set Sampling Based Distribution Free Control Chart with Application in CSTR Process

Nonparametric(distribution-free)control charts have been introduced in recent years when quality characteristics do not follow a specific distribution.When the sample selection is prohibitively expensive,we prefer ranked-set sampling over simple random sampling because ranked set sampling-based control charts outperform simple random sampling-based control charts.In this study,we proposed a nonparametric homogeneously weighted moving average based on theWilcoxon signed-rank test with ranked set sampling(NPHWMARSS)control chart for detecting shifts in the process location of a continuous and symmetric distribution.Monte Carlo simulations are used to obtain the run length characteristics to evaluate the performance of the proposed NPHWMARSS control chart.The proposed NPHWMARSS control chart’s performance is compared to that of parametric and nonparametric control charts.These control charts include the exponentially weighted moving average(EWMA)control chart,Wilcoxon signed-rank with simple random sampling based the nonparametric EWMA control chart,the nonparametric EWMA sign control chart,Wilcoxon signed-rank with ranked set sampling-based the nonparametric EWMA control chart,and the homogeneously weighted moving average control charts.The findings show that the proposed NPHWMARSS control chart performs better than its competitors,particularly for the small shifts.Finally,an example is presented to demonstrate how the proposed scheme can be implemented practically.

Memory-Type Control Charts Through the Lens of Cost Parameters

A memory-type control chart utilizes previous information for chart construction.An example of a memory-type chart is an exponentially-weighted moving average(EWMA)control chart.The EWMA control chart is well-known and widely employed by practitioners for monitoring small and moderate process mean shifts.Meanwhile,the EWMA median chart is robust against outliers.In light of this,the economic model of the EWMA and EWMA median control charts are commonly considered.This study aims to investigate the effect of cost parameters on the out-of-control average run lengthðARL_(1)Þin implementing EWMA and EWMA median control charts.The economic model was used to compute the ARL_(1) parameter.The 14 input parameters were identified and the analysis was carried out based on the one-parameter-at-a-time basis.When the input parameters change based on a predetermined percentage,the ARL_(1) is affected.According to the results of the EWMA chart,nine input parameters had an effect andfive input parameters had no effect on the ARL_(1) parameter.Further,only seven of the 14 input parameters had an effect on the ARL_(1) of the EWMA median chart.However,the effect of each input parameter on the ARL_(1) was different.Moreover,the ARL_(1) for the EWMA median chart was smaller than the EWMA chart.This analysis is crucial to observe and determine the input parameters that have a significant impact on the ARL_(1) of the EMWA and EWMA median control charts.Hence,practitioners can obtain an overview of the influence of the input parameters on the ARL_(1) when implementing the EWMA and EWMA median control charts.

Tool Condition Monitoring Based on Nonlinear Output Frequency Response Functions and Multivariate Control Chart

Tool condition monitoring(TCM)is a key technology for intelligent manufacturing.The objective is to monitor the tool operation status and detect tool breakage so that the tool can be changed in time to avoid significant damage to workpieces and reduce manufacturing costs.Recently,an innovative TCM approach based on sensor data modelling and model frequency analysis has been proposed.Different from traditional signal feature-based monitoring,the data from sensors are utilized to build a dynamic process model.Then,the nonlinear output frequency response functions,a concept which extends the linear system frequency response function to the nonlinear case,over the frequency range of the tooth passing frequency of the machining process are extracted to reveal tool health conditions.In order to extend the novel sensor data modelling and model frequency analysis to unsupervised condition monitoring of cutting tools,in the present study,a multivariate control chart is proposed for TCM based on the frequency domain properties of machining processes derived from the innovative sensor data modelling and model frequency analysis.The feature dimension is reduced by principal component analysis first.Then the moving average strategy is exploited to generate monitoring variables and overcome the effects of noises.The milling experiments of titanium alloys are conducted to verify the effectiveness of the proposed approach in detecting excessive flank wear of solid carbide end mills.The results demonstrate the advantages of the new approach over conventional TCM techniques and its potential in industrial applications.

基于Shewhart Control Chart的生鲜乳中兽药残留风险预警方法研究

针对生鲜乳中兽药残留水平动态变化的特点,本研究探索构建一种基于历史数据的生鲜乳中兽药残留动态预警方法。基于Shewhart Control Chart理论,建立了兽药残留超标预警、检出率异常预警和平均值标准偏差预警方法。对中国某大型乳企的生鲜乳中氟甲喹和达氟沙星检测数据分析发现,无需触发风险预警,同时对假定出现的检出率异常和平均值异常预警情况进行了分析。

Construction of Control Charts for Monitoring Various Parameters Related to the Management of the COVID-19 Pandemic

To monitor the quality characteristics of a process, appropriate graphical and statistical tools must be used. These tools are capable of showing the evolution over time of the behavior of the quality characteristics (measurable or countable) and detecting situations that seem to present certain anomalies. The control chart is one of these tools widely used in quality management. In the process of managing the COVID-19 pandemic, this tool will make it possible to know at all times whether the parameters monitored such as the positivity rate, the recovery rate, and the mortality rate, are under control and to act accordingly. Monitoring cure and mortality rates will also show us the effectiveness of the treatments used.

Calculation of One-Valued Control Limits by Control Chart of Angles

The data we use to express angle or direction are entitled directional data. In a plan right angled coordinate system the traditional control chart can’t solve the quality control problem which the characteristic value is angle. This paper analyses and calculates the one valued control limits by control chart of angles.

Automated Identification of Basic Control Charts Patterns Using Neural Networks

The identification of control chart patterns is very important in statistical process control. Control chart patterns are categorized as natural and unnatural. The presence of unnatural patterns means that a process is out of statistical control and there are assignable causes for process variation that should be investigated. This paper proposes an artificial neural network algorithm to identify the three basic control chart patterns;natural, shift, and trend. This identification is in addition to the traditional statistical detection of runs in data, since runs are one of the out of control situations. It is assumed that a process starts as a natural pattern and then may undergo only one out of control pattern at a time. The performance of the proposed algorithm was evaluated by measuring the probability of success in identifying the three basic patterns accurately, and comparing these results with previous research work. The comparison showed that the proposed algorithm realized better identification than others.

Computation of Average Run Length for Residual-Based T^2 Control Chart for Multivariate Autocorrelated Processes

The expression of residual is obtained according to its dynamic response to mean shift, then the distribu- tion of T2 statistic applied to the residual is derived, thus the probability of the 7a statistic lying outside the control limit is calculated. The above-mentioned results are substituted into the infinite definition expression of the average run length （ARL）, and then the final finite ARL expression is obtained. An example is used to demonstrate the procedures of the proposed method. In the comparative study, eight autocorrelated processes and four different mean shifts are performed, and the ARL values of the proposed method are compared with those obtained by simulation method with 50 000 replications. The accuracy of the proposed method can be illustrated through the comparative results.

Control charts for the Pareto distribution

The Pareto distribution plays an important role in various areas of research. In this paper, the average run length （ARL） unbiased control charts, which monitor the shape and threshold parameters of the Pareto distribution respectively, are proposed when the incontrol parameters are known. The effects of parameter estimation on the performance of the proposed control charts are also studied. Results show that the control charts with the estimated parameters are not suitable to be used in the known parameter case, thus the ARL-unbiased control charts for the shape and threshold parameters with the desired ARLo, which consider the variability of the parameter estimates, are further developed. The performance of the proposed control charts is investigated in terms of the ARL. Finally, an example is given to illustrate the proposed control charts.

Economic Design of & S Control Charts Based on Taguchi's Loss Function and Its Optimization

Much research effort has been devoted to economic design of X ＆ S control charts,however,there are some problems in usual methods.On the one hand,it is difficult to estimate the relationship between costs and other model parameters,so the economic design method is often not effective in producing charts that can quickly detect small shifts before substantial losses occur;on the other hand,in many cases,only one type of process shift or only one pair of process shifts are taken into consideration,which may not correctly reflect the actual process conditions.To improve the behavior of economic design of control chart,a cost ＆ loss model with Taguchi＇s loss function for the economic design of X ＆ S control charts is embellished,which is regarded as an optimization problem with multiple statistical constraints.The optimization design is also carried out based on a number of combinations of process shifts collected from the field operation of the conventional control charts,thus more hidden information about the shift combinations is mined and employed to the optimization design of control charts.At the same time,an improved particle swarm optimization（IPSO） is developed to solve such an optimization problem in design of X ＆ S control charts,IPSO is first tested for several benchmark problems from the literature and evaluated with standard performance metrics.Experimental results show that the proposed algorithm has significant advantages on obtaining the optimal design parameters of the charts.The proposed method can substantially reduce the total cost（or loss） of the control charts,and it will be a promising tool for economic design of control charts.

A Cause-Selecting Control Chart Method for Monitoring and Diagnosing Dependent Manufacturing Process Stages

Many industrial products are normally processed through multiple manufacturing process stages before it becomes a final product.Statistical process control techniques often utilize standard Shewhart control charts to monitor these process stages.If the process stages are independent,this is a meaningful procedure.However,they are not independent in many manufacturing scenarios.The standard Shewhart control charts can not provide the information to determine which process stage or group of process stages has caused the problems(i.e.,standard Shewhart control charts could not diagnose dependent manufacturing process stages).This study proposes a selective neural network ensemble-based cause-selecting system of control charts to monitor these process stages and distinguish incoming quality problems and problems in the current stage of a manufacturing process.Numerical results show that the proposed method is an improvement over the use of separate Shewhart control chart for each of dependent process stages,and even ordinary quality practitioners who lack of expertise in theoretical analysis can implement regression estimation and neural computing readily.

Control Charts for the Shape Parameter of Power Function Distribution under Different Classical Estimators

In practice,the control charts for monitoring of process mean are based on the normality assumption.But the performance of the control charts is seriously affected if the process of quality characteristics departs from normality.For such situations,we have modified the already existing control charts such as Shewhart control chart,exponentially weighted moving average(EWMA)control chart and hybrid exponentially weighted moving average(HEWMA)control chart by assuming that the distribution of underlying process follows Power function distribution(PFD).By considering the situation that the parameters of PFD are unknown,we estimate them by using three classical estimation methods,i.e.,percentile estimator(P.E),maximum likelihood estimator(MLE)and modified maximum likelihood estimator(MMLE).We construct Shewhart,EWMA and HEWMA control charts based on P.E,MLE and MMLE.We have compared all these control charts using Monte Carlo simulation studies and concluded that HEWMA control chart under MLE is more sensitive to detect an early shift in the shape parameter when the distribution of the underlying process follows power function distribution.

The New Neutrosophic Double and Triple Exponentially Weighted Moving Average Control Charts

The concept of neutrosophic statistics is applied to propose two monitoring schemes which are an improvement of the neutrosophic exponentially weighted moving average(NEWMA)chart.In this study,two control charts are designed under the uncertain environment or neutrosophic statistical interval system,when all observations are undermined,imprecise or fuzzy.These are termed neutrosophic double and triple exponentially weighted moving average(NDEWMA and NTEWMA)control charts.For the proficiency of the proposed chart,Monte Carlo simulations are used to calculate the run-length characteristics(such as average run length(ARL),standard deviation of the run length(SDRL),percentiles(P_(25),P_(50),P_(75)))of the proposed charts.The structures of the proposed control charts are more effective in detecting small shifts while these are comparable with the other existing charts in detecting moderate and large shifts.The simulation study and real-life implementations of the proposed charts show that the proposed NDEWMA and NTEWMA charts perform better in monitoring the process of road traffic crashes and electric engineering data as compared to the existing control charts.Therefore,the proposed charts will be helpful in minimizing the road accident and minimizing the defective products.Furthermore,the proposed charts are more acceptable and actual to apply in uncertain environment.

Truss structural damage identification based on principal component analysis and multivariate control chart

The present paper addresses the subject of truss damage identification using measured frequency response functions (FRF). Damage identification matrix is formed using measured FRFs obtained from truss dynamic test. Then using principal component analysis (PCA),the variable space dimensions of damage identification matrix can be reduced,and original data characters of FRFs can be analyzed and extracted from lower dimension variable space. Thus truss damages can be identified using the multivariate control chart of first several order principal components which contain almost all of original data information. Without the need for modal parameters,the method avoids the errors of modal fitting. In order to validate the reliability of the method,a whole size truss was tested with six types of damage case concerning single or two element damages. The experimental result shows that the proposed method is straightforward and reliable for truss damage identification. Especially,the method has good applicability for the truss under noisy environment and non-linear cases.

The Principle of Mathematical Induction Applied to the Generalized Model for the Economic Design of X-Control Charts

Rahim and Banerjee [1] developed a general model for the optimal design of x-control charts. The model minimizes the expected cost per unit time. The heart of the model is a theorem that derives the expected total cost and the expected cycle length. In this paper an alternative simple proof for the theorem is provided based on mathematical induction.

Parameters optimization for exponentially weighted moving average control chart using generalized regression neural network

As a useful alternative of Shewhart control chart, exponentially weighted moving average （EWMA） control chat has been applied widely to quality control, process monitoring, forecast, etc. In this paper, a method was introduced for optimal design of EWMA and multivariate EWMA （MEWMA） control charts, in which the optimal parameter pair （ λ, k） or （ λ, h ） was searched by using the generalized regression neural network （GRNN）. The results indicate that the optimal parameter pair can be obtained effectively by the proposed strategy for a given in-control average running length （ARLo） and shift to detect under any conditions, removing the drawback of incompleteness existing in the tables that had been reported.

EWMA control chart based on its first hitting time and coronavirus alert levels for monitoring symmetric COVID-19 cases

Objective:To define the alert levels for the total number of COVID-19 cases derived by using quantile functions to monitor COVID-19 outbreaks via an exponentially weighted moving-average(EWMA)control chart based on the first hitting time of the total number of COVID-19 cases following a symmetric logistic growth curve.Methods:The cumulative distribution function of the time for the total number of COVID-19 cases was used to construct a quantile function for classifying COVID-19 alert levels.The EWMA control chart control limits for monitoring a COVID-19 outbreak were formulated by applying the delta method and the sample mean and variance method.Samples were selected from countries and region including Thailand,Singapore,Vietnam,and Hong Kong to generate the total number of COVID-19 cases from February 15,2020 to December 16,2020,all of which followed symmetric patterns.A comparison of the two methods was made by applying them to a EWMA control chart based on the first hitting time for monitoring the COVID-19 outbreak in the sampled countries and region.Results:The optimal first hitting times for the EWMA control chart for monitoring COVID-19 outbreaks in Thailand,Singapore,Vietnam,and Hong Kong were approximately 280,208,286,and 298 days,respectively.Conclusions:The findings show that the sample mean and variance method can detect the first hitting time better than the delta method.Moreover,the COVID-19 alert levels can be defined into four stages for monitoring COVID-19 situation,which help the authorities to enact policies that monitor,control,and protect the population from a COVID-19 outbreak.

Monitoring Freeway Incident Detection Using a Hotelling T2 Control Chart

In real-life freeway transportation system, a few number of incident observation （very rare event） is available while there are large numbers of normal condition dataset. Most of researches on freeway incident detection have considered the incident detection problem as classification one. However, because of insufficiency of incident events, most of previous researches have utilized simulated incident events to develop freeway incident detection models. In order to overcome this drawback, this paper proposes a wavelet-based Hotelling 7a control chart for freeway incident detection, which integrates a wavelet transform into an abnormal detection method. Firstly, wavelet transform extracts useful features from noisy original traffic observations, leading to reduce the dimensionality of input vectors. Then, a Hotelling T2 control chart describes a decision boundary with only normal traffic observations with the selected features in the wavelet domain. Unlike the existing incident detection algorithms, which require lots of incident observations to construct incident detection models, the proposed approach can decide a decision boundary given only normal training observations. The proposed method is evaluated in comparison with California algorithm, Minnesota algorithm and conventional neural networks. The experimental results present that the proposed algorithm in this paper is a promising alternative for freeway automatic incident detections.

Analysis of the Effect of Subgroup Size on the X-Bar Control Chart Using Forensic Science Laboratory Sample Influx Data

This paper analyzes the effect of subgroup size on the x-bar chart characteristics using sample influx (SIF) into forensic science laboratory (FSL). The characteristics studied include changes in out-or-control points (OCP), upper control limit UCLx, and zonal demarcations. Multi-rules were used to identify the number of out-of-control-points, Nocp as violations using five control chart rules applied separately. A sensitivity analysis on the Nocp was applied for subgroup size, k, and number of sigma above the mean value to determine the upper control limit, UCLx. A computer code was implemented using a FORTRAN code to create x-bar control-charts and capture OCP and other control-chart characteristics with increasing k from 2 to 25. For each value of k, a complete series of average values, Q(p), of specific length, Nsg, was created from which statistical analysis was conducted and compared to the original SIF data, S(t). The variation of number of out-of-control points or violations, Nocp, for different control-charts rules with increasing k was determined to follow a decaying exponential function, Nocp = Ae–α, for which, the goodness of fit was established, and the R2 value approached unity for Rule #4 and #5 only. The goodness of fit was established to be the new criteria for rational subgroup-size range, for Rules #5 and #4 only, which involve a count of 6 consecutive points decreasing and 8 consecutive points above the selected control limit (σ/3 above the grand mean), respectively. Using this criterion, the rational subgroup range was established to be 4 ≤ k ≤ 20 for the two x-bar control chart rules.