Small Mean Shifts Research Articles

Monitoring high-dimensional heteroscedastic processes using rank-based EWMA methods

Monitoring high-dimensional processes is a challenging task, as the underlying dependency structure among variables is often too complicated to estimate accurately. The inherent volatility of dependence, so-called heteroscedasticity, is rarely mentioned nor considered in process monitoring problems. We consider time-dependent heteroscedasticity a common cause variability and propose an integrated scheme for monitoring and diagnosis of changes in the location parameters of high-dimensional processes. Our proposed method consists of rank-based EWMA control charts which are designed to detect mean shifts in a small subset of variables. A bootstrap algorithm determines the control limits by achieving a pre-specified false alarm probability. A post-signal diagnosis strategy is executed to cluster the shifted variables and estimate a time window for the change point. Simulation results show that the proposed methodology is robust to heteroscedasticity and sensitive to small and moderate sparse mean shifts. It can efficiently identify out-of-control variables and the corresponding change points. A real-life example of monitoring online vibration data for predictive maintenance applications illustrates the proposed methodology.

Amplified cortical neural responses as animals learn to use novel activity patterns

Cerebral cortex supports representations of the world in patterns of neural activity, used by the brain to make decisions and guide behavior. Past work has found diverse, or limited, changes in the primary sensory cortex in response to learning, suggesting that the key computations might occur in downstream regions. Alternatively, sensory cortical changes may be central to learning. We studied cortical learning by using controlled inputs we insert: we trained mice to recognize entirely novel, non-sensory patterns of cortical activity in the primary visual cortex (V1) created by optogenetic stimulation. As animals learned to use these novel patterns, we found that their detection abilities improved by an order of magnitude or more. The behavioral change was accompanied by large increases in V1 neural responses to fixed optogenetic input. Neural response amplification to novel optogenetic inputs had little effect on existing visual sensory responses. A recurrent cortical model shows that this amplification can be achieved by a small mean shift in recurrent network synaptic strength. Amplification would seem to be desirable to improve decision-making in a detection task; therefore, these results suggest that adult recurrent cortical plasticity plays a significant role in improving behavioral performance during learning.

Run-length distribution for Shewhart control charts with runs rules

The Shewhart control chart is simple to apply to the actual production process. When the change is large, it is sensitive to detect the changes. However, if the change is small, it is not sensitive. Several methods have been developed to improve the sensitivity of the Shewhart control chart. Western Electronic Company applied runs rules to have sensitivity in cases of small shifts. To calculate the ARL of the control chart, we use the finite Markov chain imbedding method of Fu and Koutras and calculate ARLs in cases of several mean and variance shifts. In this thesis, according to the small shifts in mean and variance, the two control charts were compared through ARL. The control chart with runs rules has been more decreased ARL in small shifts compared the traditional Shewhart control charts. That is, it can be seen that the control chart with runs rules detects more sensitively than the Shewhart control chart when there are small shifts.

Neutrosophic multivariate EWMA control chart

The MEWMA chart is one of the traditional multivariate charts which are widely employed in inspecting the quality of manufacturing and services. This chart is created through monitoring the small shifts of mean vectors of variable quality characteristics. Often in practice, the measurement of a quality characteristic produces uncertain, incomplete values, so that ambiguous numbers are obtained. In this condition, a neutrosophic-based control chart can overcome the problem resulting from the ambiguous data. The paper’s objective is to construct a new multivariate monitoring scheme based on a neutrosophic chart, namely the neutrosophic Multivariate EWMA (NMEWMA). Furthermore, the performance of the new multivariate monitoring scheme is evaluated in detecting process shifts employing the Average Run Length (ARL) and Standard Deviation Run Length (SDRL). This control chart is an innovation in the quality monitoring of uncertain data. The research result obtained indicates that the NMEWMA chart performs better than the MEWMA in finding the small mean shifts as well as in the real case application.

The Role of Tourism Education in the Promotion of Tourism. The Case of Greece in the Period 2005-2020 with Particular Reference to the Pandemic Era

Nowadays, tourism appears to be one of the most developing sciences to research and study. Over the last decades, the industry of travel and tourism has evolved significantly, increasing its pace of common development year by year. For the Greek Economy, tourism is a central pillar of development and growth with significant contribution to Gross Domestic Product increase, employment, and investment. The rich cultural heritage, extensive coastline and natural environment are some of the basic advantages that make the country one of the most important tourist destinations worldwide. Considering the impact tourism has on our country, we understand the role that tourism education can play in the shaping of tourism consciousness and, consequently, in promoting social and economic development. Thus, it is necessary to study some elements in order to reach conclusions that will help to improve our tourism consciousness. In this paper, we will deal with tourism data (referring to the period 2005-2020 https://insete.gr/bi/inbound-tourism-total-country) using statistical process control, specifically time series control charts. We use Box-Jenkins methodology to find models of time series in Annual Changes of Income from 2005-2020, of Arrivals from 2010-2020 and the Average per capital expenses from 2005-2020. Specifically, we test models’ sensitivity in detecting even small shifts in mean which may indicate financial instability. This analytical approach is widely applicable and therefore of theoretical and practical interest. Based on the results of this approach could propose the inclusion of introductory tourism education courses in all levels of education. The Greek tourism industry is thus expected to benefit from the financial and wider benefits of education.

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.

One-sided Adaptive Truncated Exponentially Weighted Moving Average X¯ Schemes for Detecting Process Mean Shifts

ABSTRACT One-sided type schemes are known to be more appropriate for monitoring a process when the direction of a potential mean shift can be anticipated. The one-sided adaptive truncated exponentially weighted moving average (ATEWMA) scheme recommended in this paper is a control chart that combines a Shewhart scheme and a new one-sided EWMA scheme together in a smooth way for rapidly detecting the upward (or downward) mean shifts. The truncation method used in this paper helps to improve the sensitivity of the recommended scheme for detecting both small and large mean shifts simultaneously. To further improve the detection efficiency of the recommended scheme, we also suggest integrating a variable sampling interval (VSI) feature into the recommended scheme. Markov chain models are established to analyze the run length (RL) properties of the recommended scheme in both the zero-state and the steady-state cases. Comparison results show that the recommended one-sided ATEWMA scheme works better than the conventional adaptive EWMA (AEWMA) chart and the improved one-sided EWMA chart in detecting a wide range of mean shifts. Finally, a numerical example is presented to illustrate the usage of the proposed one-sided ATEWMA scheme for detecting process mean shifts.

A parameter-free adaptive EWMA chart with variable sample sizes and variable sampling intervals for the process mean

In this article, a parameter-free adaptive EWMA (AE) chart, which adopts the variable sample size (VSS), variable sampling interval (VSI) or both (VSSVSI) features, is developed to monitor the mean of a normal process. The simulation method is employed to compute the run-length profiles of the proposed VSS, VSI and VSSVSI based AE charts. The extra quadratic loss and integral relative average run-length/time-to-signal measures are used as a performance criterion in order to evaluate the sensitivities of the control charts. The run-length evaluation shows that the proposed VSS, VSI and VSSVSI based AE charts surpass the VSS, VSI and VSSVSI based EWMA charts, respectively, in detecting small mean shifts but the latter prevails in detecting moderate to large mean shifts. The proposed charts also outperform their fixed sampling rate based AE counterparts. An example is given to compare the implementation of the existing and proposed charts.

Vector Autoregressive-Based Maximum MCUSUM Control Chart for Monitoring the Quality of White Crystal Sugar

The white crystal sugar which is widely consumed sugar has two critical to qualities, namely the index of solution colour and the level of sulphur dioxide. These quality characteristics have small mean and variability shifts, as well as autocorrelation pattern. This research aims to propose residual-based Maximum Multivariate Cumulative Sum (Max-MCUSUM) control chart, one of the single control charts to monitor small shifts of mean and variability simultaneously, for monitoring the quality of white crystal sugar. The vector autoregressive (VAR) model is utilized to model the daily solution colour index and the daily sulphur dioxide level, then the residuals are monitored using Max-MCUSUM chart. The VAR-based Max-MCUSUM chart employs bootstrap, one of the nonparametric resampling methods, to estimate the control limit. The results of white crystal sugar quality control show that the processes in the last week of August 2020 need to be improved. Monitoring the white crystal sugar data using conventional control chart leads to many false alarm signals. Furthermore, the proposed control chart is more sensitive than the residual-based MEWMA and residual-based Hotelling’s T 2 charts in case of monitoring the quality of white crystal sugar.

A side-sensitive group runs median control chart with measurement errors

The Shewhart median (denoted as ) chart can be used in place of the Shewhart chart for detecting mean shifts when outliers are present because the sample mean is easily affected by outliers. However, the Shewhart median chart is slow in detecting small and moderate mean shifts. In this study, the side-sensitive group runs median (called SSGR ) chart is proposed to enhance the speed of the Shewhart median chart in detecting small and moderate mean shifts. Additionally, by adopting a linear covariate error model, the effect of measurement errors on the performance of the SSGR chart is studied. The average run length (ARL) and standard deviation of the run length (SDRL) criteria are used as performance measures, for cases with and without measurement error. The Markov chain method is used to compute the ARL and SDRL values of the SSGR and competing charts. Performance analyses show that the SSGR chart surpasses the synthetic chart for detecting all shift sizes but for detecting small shifts, the exponentially weighted moving average (EWMA) chart performs better than the SSGR chart. Finally, the application of the SSGR chart is described with an example.

On the conditional performance of the synthetic chart with unknown process parameters using the exceedance probability criterion.

Recent researches on the control charts with unknown process parameters have noticed the large variability in the conditional in-control average run length (ARL) performance of control charts, especially when a small number of Phase I samples is used to estimate the process parameters. Some research works have been conducted on the conditional ARL performance of different types of control charts. In this paper, by simulating the empirical distribution of the conditional ARL and especially using the exceedance probability criterion (EPC), we study the conditional ARL performance of the synthetic chart. Our results show that a large amount of Phase I samples is needed to obtain a specified EPC of the synthetic chart. For the available number of Phase I samples, the control limits of the synthetic chart are adjusted using the EPC method to improve its conditional in-control performance. It is shown that, for small mean shift sizes, a tradeoff should be made between the conditional in-control and out-of-control performances. For moderate to large shifts, the conditional performance of the synthetic chart using the adjusted control limits is generally satisfied. By comparing the results with the ones using the bootstrap approach, it can also be concluded that the conditional performances of both approaches are comparable. While the method proposed in this paper requires much less computation work than the bootstrap approach.

A Penalized Convolution Model for Oil Leakage Detection in Electrohydraulic Railway Point Systems

The railway point is one of the most critical systems in railway, which enables trains to be guided from one track to another. Failures of railway point systems often lead to service delays and hazardous situations. With the ever-increasing railway operation, the stable and safe operation of railway point systems becomes more and more important. The electrohydraulic railway point system is widely adopted due to its high efficiency and long service life. However, its operation highly relies on a sufficient volume of oil, which usually leaks gradually due to many practical issues, e.g., the wear of joint rings and the aging and corrosion of oil pipes. The gradual oil leakage often causes failures of electrohydraulic railway point systems, so it is important to develop the effective and reliable technologies for the early detection of slow oil leakage. To achieve this goal, the static oil level is used to construct the monitoring statistic since it is a direct indicator of the oil volume and more suitable for railway point systems than the hydraulic pressure due to the discrete demand for operations and the short duration of every operation. However, it is very challenging to utilize the oil level directly for oil leakage detection due to the large variability caused by the environmental temperature. Therefore, in this article, we propose a penalized convolution-based model to capture the relationship between the temperature and the oil level, whose parameters are estimated by using least squares with a smooth penalty. With the trained model, we obtain the residuals by removing the effect of temperature from the oil-level signal. Then, the CUSUM chart is employed to monitor the residual signal since it is sensitive to the small mean shift. Finally, the proposed method is evaluated through a case study by using in situ data collected from a real point system in Changsha Railway Station.

On autoregressive model selection for the exponentially weighted moving average control chart of residuals in monitoring the mean of autocorrelated processes

AbstractWith the development of automation technologies, data can be collected in a high frequency, easily causing autocorrelation phenomena. Control charts of residuals have been used as a good way to monitor autocorrelated processes. The residuals have been often computed based on autoregressive (AR) models whose building needs much experience. Data have been assumed to be first‐order autocorrelated, and first‐order autoregressive (AR(1)) models have been employed to obtain residuals. But for a pth‐order autocorrelated process, how the AR(1) model affects the performance of the control chart of residuals remains unknown. In this paper, the control chart of exponentially weighted moving average of residuals (EWMA‐R) is used to monitor the pth‐order autocorrelated process. Taking the mean and standard deviation of run length as performance indicators, two types of EWMA‐R control charts, with their residuals obtained from the pth‐order autoregressive AR(p) and AR(1) models, respectively, are compared. The results of the numerical experiment show that for detecting small mean shifts, EWMA‐R control charts based on AR(1) models outperform ones based on AR(p) models, whereas for detecting large shifts, they are sometimes slightly worse. A practical application is used to give a recommendation that a large number of samples are necessary for determining an EWMA‐R control chart before using it.

A synthetic control chart for monitoring the small shifts in a process mean based on an attribute inspection

In this paper, a synthetic control chart is proposed by integrating the salient features of the npx chart and the CRL chart. The synthetic chart achieves higher detection effectiveness on both small and large mean shifts while retaining the operational simplicity of the attribute charts owing to only using attribute inspection. Both statistical and economic design of the synthetic chart are considered and numerical tests have indicated that the synthetic chart has a higher power for detecting mean shifts than the npx chart, MON chart and CUSUM chart. In addition, sensitivity analyses are also performed under both the statistical and economic design model.

Double exponentially weighted moving average control chart with supplementary runs-rules

ABSTRACTEnhancing the sensitivity of control charts for detecting small process shift is desirable and may be done in different ways. In this paper, we propose the double exponentially weighted moving average (DEWMA) control chart using the 2-of-2 and 1-of-1 or 2-of-2 runs-rules schemes for monitoring process mean shifts. The performances of the resulting control schemes are investigated in terms of the average run-length (), standard deviation of the run-length () and selective percentiles of the run-length (). In addition, the overall performance of the proposed runs-rules charts are examined and compared with those of the existing charts in terms of the , average extra quadratic loss (), average ratio of the average run-length () and performance comparison index () values. It is observed that the proposed control schemes are more efficient in many situations and improve the ability of the existing DEWMA schemes in detecting small, moderate and large mean shifts.

A study on the variable sampling interval EWMA chart when the process parameters are unknown

The exponentially weighted moving average (EWMA) chart is well known in statistical process control for detecting small and moderate process mean shift. A variablesampling-interval (VSI) control scheme of the EWMA chart is able to enhance the speed of detection when the process is out-of-control as the intervals switch according to the value of the previous sample statistics. Generally, the performance of the VSI EWMA chart is investigated under the assumption of known process parameters. However, in reality, these parameters are usually unknown and are estimated from a historical Phase-I dataset. Hence, the performance of the VSI EWMA chart is significantly affected when the process parameters are unknown. This is due to estimation errors. In this paper, we investigate the effects of parameter estimation on the performance of the VSI EWMA chart in terms of the average time to signal and standard deviation of the time to signal. Suggestions on the required number of Phase-I samples and sample sizes in designing the VSI EWMA chart with unknown process parameters, are provided for practitioners’ fast implementation.

An effective multivariate control chart for detecting small mean shifts using support vector data description

Conventional multivariate cumulative sum control charts are more sensitive to small shifts than [Formula: see text] control charts, but they cannot get the knowledge of manufacturing process through the learning of in-control data due to the characteristics of their own structures. To address this issue, a modified multivariate cumulative sum control chart based on support vector data description for multivariate statistical process control is proposed in this article, which is named [Formula: see text] control chart. The proposed control chart will have both advantages of the multivariate cumulative sum control charts and the support vector data description algorithm, namely, high sensitivities to small shifts and learning abilities. The recommended values of some key parameters are also given for a better application. Based on these, a bivariate simulation experiment is conducted to evaluate the performance of the [Formula: see text] control chart. A real industrial case illustrates the application of the proposed control chart. The results also show that the [Formula: see text] control chart is more sensitive to small shifts than other traditional control charts (e.g. [Formula: see text] and multivariate cumulative sum) and a D control chart based on support vector data description.

Adaptive control charts for skew‐normal distribution

AbstractThe standard Shewhart‐type chart, named FSS‐ chart, has been widely used to detect the mean shift of process by implementing fixed sample and sampling frequency schemes. The FSS‐ chart could be sensitive to the normality assumption and is inefficient to catch small or moderate shifts in the process mean. To monitor nonnormally distributed variables, Li et al [Commun Stat‐Theory Meth. 2014; 43(23):4908‐4924] extended the study of Tsai [Int J Reliab Qual Saf Eng. 2007; 14(1):49‐63] to provide a new skew‐normal FSS‐ (SN FSS‐ ) chart with exact control limits for the SN distribution. To enhance the sensitivity of the SN FSS‐ chart on detecting small or moderate mean shifts in the process, adaptive charts with variable sampling interval (VSI), variable sample size (VSS), and variable sample size and sampling interval (VSSI) are introduced for the SN distribution in this study. The proposed adaptive control charts include the normality adaptive charts as special cases. Simulation results show that all the proposed SN VSI‐ , SN VSS‐ , and SN VSSI‐ charts outperform the SN FSS‐ chart on detecting small or moderate shifts in the process mean. The impact of model misspecification on using the proposed adaptive charts and the sample size impact for using the FSS‐ chart to monitor the mean of SN data are also discussed. An example about single hue value in polarizer manufacturing process is used to illustrate the applications of the proposed adaptive charts.

A new double exponentially weighted moving average control chart using repetitive sampling

PurposeThe purpose of this paper is to propose a double exponentially weighted moving average control chart using repetitive sampling (RS-DEWMA) for a normally distributed process variable to improve the efficiency of detecting small process mean shift.Design/methodology/approachThe algorithm for the implementation of the proposed chart is developed and the formulae for the in-control and out-of-control average run lengths (ARLs) are derived. Tables of ARLs are presented for various process mean shift. The performance of the proposed chart is investigated in terms of the average run-length for small process mean shift and compared with the existing DEWMA control chart. Numerical examples are given as illustration of the design and implementation of the proposed chart.FindingsThe proposed control chart is more efficient than the existing DEWMA control chart in the detection of small process mean shifts as it consistently gives smaller ARL values and quickly detects the process shift. However, the performance of the proposed chart relatively deteriorates for large smoothing constants.Practical implicationsThe application of repetitive sampling in the control chart literature is gaining wide acceptability. The design and implementation of the RS-DEWMA control chart offers a new approach in the detection of small process mean shift by process control personnel.Originality/valueThis paper fills a gap in the literature by examining the performance of the repetitive sampling DEWMA control chart. The use of repetitive sampling technique in the control chart is discussed in the literature, however, its use based on the DEWMA statistic has not been considered in this context.

SBRT in the Post-Prostatectomy Setting: Analysis of Interfraction Variability

Our institution has a phase 1 clinical trial evaluating acute toxicity in the setting of SBRT to the prostate fossa following prostatectomy. Patients enrolled on this trial are simulated and treated with fiducial markers in the prostate fossa, a rectal balloon and a daily ultrasound (US) of the bladder for immobilization and target visualization. This study reports the interfraction motion analysis based on the described immobilization technique. At this point, the study has enrolled 12 patients onto dose levels 1 and 2 (3.6Gy/fraction x 15 fractions and 4.7Gy/fraction x 10 fractions, respectively). All patients had a rectal balloon for consistency in rectal volume and immobilization of the prostate bed. Patients were treated with a full bladder that was within 20% of the bladder volume on the day of CT simulation as verified by daily US. All patients were implanted with three gold fiducial markers into the prostate bed. KV and CBCT were performed on day 1 to verify fiducial placement and bladder and rectal volume. Daily kV and weekly CBCT were used for daily alignment based on fiducial markers. For 10 out of 12 patients, the patients’ shift data were gathered and a shift vector was calculated. The mean shifts for this cohort of the patients was -0.2 mm, 0.4 mm, -1.1 mm in anterior and posterior, superior and inferior, and left and right, respectively. The standard deviation was 4.0 mm, 3.7 mm, -3.4 mm in anterior and posterior, superior and inferior and left and right, respectively. It was demonstrated that the current bladder filling and IGRT protocol resulted in minimal systematic shift (small mean shifts). Most shifts were random which were reflected in the standard deviation. The mean and standard deviation of the shift vector was 5.3 mm and 3.9 mm, respectively. The calculated percentage bladder volume compared to bladder volume during the CT simulation had a mean of 3.6% and standard deviation of 8.9%. No correlation was found between magnitudes of patient shifts and bladder filling for this cohort of patients. With the current rectal/bladder immobilization and IGRT protocol, this cohort of the patients had a mean shift of no more than 1.1 mm but a relatively large standard deviation of 4.0 mm in each direction. Setup variation did not follow a specific pattern based on bladder or rectal filling. For the subset of the patients who have reasonable CBCT volumetric information, dosimetric analysis will be performed by deforming planning CT and dose to CBCT using VelocityTM.