Standard Deviation Of Run Length Research Articles

Integration of hybrid score functions to design new adaptive EWMA control chart to monitor the process mean shift

Small-to-moderate shifts in the process parameters can be detected using the traditional Exponentially Weighted Moving Average (EWMA) control chart. The classical EWMA control chart's parameter helps only to identify the specific size of the shift. However, various shifts occur in real-world processes, so the conventional EWMA control chart performs inefficiently for off-target shifts. This problem has been confronted by applying an adaptive EWMA (AEWMA) control chart, an advanced version of the classical EWMA control chart. The score functions are utilized to design the AEWMA control chart. Generally, the Huber and Bi-square (score) functions have unique characteristics, such as monotone and redescended, respectively.There has not been any investigation into the simultaneous and/or joint deployment of score functions. So, by taking this point as motivation, this study aims to propose a new score function by blending the Huber and Bi-square characteristics into one hybrid formulation and then utilize it to design a new AEWMA control chart to monitor different sizes of the shift in the process location parameter. To evaluate the proposed control chart performance against other control charts, Monte Carlo simulation is applied to obtain the run length properties under zero-state and steady-state environments. Performance measures, such as average run length, standard deviation of run length, and median of run length, are considered to evaluate the performance at a single shift. In contrast, extra quadratic loss, relative average run length, and performance comparison index are utilized to evaluate effectiveness for a specific range of shifts. The comparison based on performance measures and visual presentation reveals the superiority of the proposed control chart. Besides, the proposed control chart is employed in the real-world chemical engineering process industry problem, demonstrating excellent detection ability of anomalies in air pollutant data. The comparison based on performance measures and visual presentation reveals the good performance of the proposed control chart.

Monitoring autocorrelated multivariate multiple linear profiles

AbstractIf the quality of a process can be represented by a functional relationship, a collection of this quality data is called a profile. In monitoring schemes, profile monitoring is used to evaluate the stability of a relationship. In some applications, quality data collected from continuous processes have time correlations and can thus be characterized by a linear relationship between more than one response and explanatory variables. Therefore, we investigate this type of multivariate multiple linear regression model with between‐profile correlations in this study. We propose two exponentially weighted moving average control charts for monitoring the regression parameters and the covariance matrix of the model. Our simulation results reveal that our proposed scheme has satisfactory performance in terms of the average run length and standard deviation run length criteria. Finally, we present an example using real data to demonstrate the applicability of the proposed scheme.

Adaptive EWMA control chart using Bayesian approach under ranked set sampling schemes with application to Hard Bake process

The memory-type control charts, such as cumulative sum (CUSUM) and exponentially weighted moving average control chart, are more desirable for detecting a small or moderate shift in the production process of a location parameter. In this article, a novel Bayesian adaptive EWMA (AEWMA) control chat utilizing ranked set sampling (RSS) designs is proposed under two different loss functions, i.e., square error loss function (SELF) and linex loss function (LLF), and with informative prior distribution to monitor the mean shift of the normally distributed process. The extensive Monte Carlo simulation method is used to check the performance of the suggested Bayesian-AEWMA control chart using RSS schemes. The effectiveness of the proposed AEWMA control chart is evaluated through the average run length (ARL) and standard deviation of run length (SDRL). The results indicate that the proposed Bayesian control chart applying RSS schemes is more sensitive in detecting mean shifts than the existing Bayesian AEWAM control chart based on simple random sampling (SRS). Finally, to demonstrate the effectiveness of the proposed Bayesian-AEWMA control chart under different RSS schemes, we present a numerical example involving the hard-bake process in semiconductor fabrication. Our results show that the Bayesian-AEWMA control chart using RSS schemes outperforms the EWMA and AEWMA control charts utilizing the Bayesian approach under simple random sampling in detecting out-of-control signals.

Generalized new exponentially weighted moving average control charts (NEWMA) for monitoring process dispersion

PurposeThis work aims to focuse on improving the performance of the new exponentially weighted moving average (NEWMA) scheme for monitoring process dispersion. The authors use the generalized time-varying fast initial response (GFIR) to further enhance the detection ability of variability NEWMA control charts at the process startup. The performance of the proposed chart and other schemes discussed in this article are evaluated; and compared using the average run length (ARL) and standard deviation run length (SDRL) measures. It is observed that the ARL of the proposed scheme is quicker in detecting small and moderate shifts in the process dispersion than its counterparts. The real-life application of the proposed scheme is presented.Design/methodology/approachThe dynamic parameter of GFIR is used to enhance the detection ability of variability NEWMA control charts. The authors apply GFIR to the control limit of variability NEWMA scheme. This further narrows the control limit, hence enabling it to swiftly detect small and moderate changes in process dispersion.FindingsThe authors present the performance comparisons by examining the ARL properties of the proposed chart and its counterparts. The performance comparison shows that the proposed chart is highly sensitive in detecting small and intermediate process shifts. The real-life application presented also supports the study’s conclusion from the simulation studies. The performance comparison of the proposed chart and its counterparts shows that the proposed scheme is efficient in detecting process abnormalities, especially at the startup.Originality/valueIn terms of the control limits, the proposed chart is the generalized variability NEWMA control chart in which all the previously proposed NEWMA variant schemes can be obtained. Also, the newly proposed control scheme is more efficient in detecting small or moderate persistent shifts in the process dispersion.

An unbiased function‐based Poisson adaptive EWMA control chart for monitoring range of shifts

AbstractFor monitoring the number of nonconformities per unit in industrial processes during the inspection, Poisson control charts are most widely deployed. These charting structures are referred to as attribute control charts as the quality characteristic under study is based on a nominal scale other than a quantitative or measured scale. In this study, Poisson adaptive exponentially weighted moving average (PAEWMA) has been designed and the performance of the said chart under a steady‐state situation along with the zero‐state condition has been studied for detecting changes over an unknown range of shifts. The enactment of the proposed PAEWMA design with existing schemes has been evaluated and compared using run‐length (RL) profiles such as; average RL (ARL), the standard deviation of RL (SDRL), and some percentile points of the RL distribution. The extra quadratic loss and relative mean index measures have been used for comparing the range of shifts. The comparison reveals that the proposed PAEWMA chart under the steady‐state situations performs far better than the competitors. The effect of estimation of the process parameter is also a part of the study. The three applications of the proposal have been included; which are taken from the artificial dataset, from past study monitoring dataset, and the other from the aircraft accident monitoring data for the implementation of the proposal.

Enhanced fault detection models with real-life applications

<abstract> <p>Nonconforming events are rare in high-quality processes, and the time between events (TBE) may follow a skewed distribution, such as the gamma distribution. This study proposes one- and two-sided triple homogeneously weighted moving average charts for monitoring TBE data modeled by the gamma distribution. These charts are labeled as the THWMA TBE charts. Monte Carlo simulations are performed to approximate the run length distribution of the one- and two-sided THWMA TBE charts. The THWMA TBE charts are compared to competing charts like the DHWMA TBE, HWMA TBE, THWMA TBE, DEWMA TBE, and EWMA TBE charts at a single shift and over a range of shifts. For the single shift comparison, the average run length (ARL) and standard deviation run length (SDRL) measures are used, whereas the extra quadratic loss (EQL), relative average run length (RARL) and performance comparison index (PCI) measures are employed for a range of shifts comparison. The comparison reveals that the THWMA TBE charts outperform the competing charts at a single shift as well as at a certain range of shifts. Finally, two real-life data applications are presented to evaluate the applicability of the THWMA TBE charts in practical situations, one with boring machine failure data and the other with hospital stay time for traumatic brain injury patients.</p> </abstract>

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.

A generalized multiple dependent state sampling chart based on ridge penalized likelihood ratio for high-dimensional covariance matrix monitoring

Online monitoring of high-dimensional processes variability in which the number of variables is larger than the sample size is a challenging issue for quality practitioners because the sample covariance matrix is not invariable. To deal with this challenge, a generalized multiple dependent state sampling (GMDS) chart based on ridge penalized likelihood ratio (RPLR) statistic is developed for Phase II monitoring of multivariate process variability under high-dimensional setting. The developed control chart benefits from three advantages: (1) departing from the conventional covariance matrix charts, it can be efficiently employed for both spars and non-spars covariance matrices; (2) it is able to detect spars shift patterns in which only a few covariance matrix elements are deviated from their nominal values; and (3) it outperforms the detectability of the RPLR chart in terms of average run length (ARL) and standard deviation of run length (SDRL). The performance of RPLR, MDS-RPLR, and GMDS-RPLR charts are compared using extensive simulation studies by considering different diagonal and/or off-diagonal covariance matrix disturbance. Moreover, sensitivity analysis are provided to analyze how the number of process variables and GMDS parameter affect the run length properties of the developed chart.

Performance of new nonparametric Tukey modified exponentially weighted moving average-Moving average control chart.

Control charts are an amazing and essential statistical process control (SPC) instrument that is commonly used in monitoring systems to detect a specific defect in the procedure. The mixed Tukey modified exponentially weighted moving average - moving average control chart (MMEM-TCC) with motivation detection ability for fewer shifts in the process mean under symmetric and non-symmetric distributions is proposed in this paper. Average run length (ARL), standard deviation of run length (SDRL), and median run length (MRL) were used as efficiency criteria in the Monte Carlo simulation, and their efficiency was compared to existing control charts. Furthermore, the expected ARL (EARL) is a method for evaluating the performance of control charts beyond a specific range of shift sizes. The distinguishing feature of the proposed chart is that it performs efficiently in detecting small to moderate shifts. There are applications for PM 2.5 and PM 10 data that demonstrate the performance of the proposed chart.

Max-EWMA Chart Using Beta and Simplex Distributions for Time and Magnitude Monitoring

Control charts are used to detect assignable causes in different manufacturing and nonmanufacturing processes. This study presents a new maximum exponentially weighted moving average (Max-EWMA) chart for joint unit interval time and magnitude monitoring. To this end, beta distribution is considered for time whereas simplex distribution is used for magnitude. Average run length (ARL), standard deviation of run length (SDRL), and different quantiles are used to evaluate the performance of the Max-EWMA chart. A real data example is also included in the study to show the application of the proposed chart. The results provide evidences that the Max-EWMA chart is efficient in detecting small- to medium-sized shifts.

New modified exponentially weighted moving average-moving average control chart for process monitoring

The mixed control chart is proposed to improve detection performance with fewer process shifts. In this study, we proposed the modified exponentially weighted moving average - moving average control chart (MMEM), a new mixed control chart for observing the changes in the process mean. Average run length, standard deviation of run length, and median run length can be used to examine the effectiveness of detecting changes in the proposed chart with Shewhart, Moving Average (MA), Modified Exponentially Weighted Moving Average (MEWMA), and Mixed Moving Average - Modified Exponentially Weighted Moving Average (MMME) control charts in parametric and nonparametric distributions that use Monte Carlo simulation. The results demonstrate that the proposed chart outperforms other control charts mostly in the detection of small-to-moderate shifts. To illustrate the application of the proposed chart, chemical process temperature data and dataset on survival times of a group of patients suffering from head and neck cancer disease and treated with radiotherapy were provided, and it was discovered that the proposed chart performs better than other control charts.

Design Tukey’s Control Chart and mix with CUSUM Control Chart

Statistical process control is a collection of valuable tools for detecting alteration in a process. It has wide application in many areas field and other fields where variation is being monitored. The variation may be a natural cause variation or a particular cause variation. Statistical process control deals with the monitoring process to detect disturbances in the process. These disturbances may be from the process mean or variance. This study proposes efficient charts for detecting early shifts in dispersion parameters by applying the Fast Initial Response feature. We propose and compare the performance of different cumulative sum (CUSUM)control charts for phase II monitoring of location based on mean and median. The (CUSUM) control chart, which is a method of data analysis based on John Tukey's principles control chart (TCC), is used to compare the proposed charts with their existing counterparts is used to evaluate new charts to existing charts using performance measures such as average run length, the standard deviation of run length, additional quadratic loss, relative average run length, and performance comparison . The proposed charts detect early shifts in the process dispersion faster and have better overall. This article is a similar effort to design an improved charting structure in the form of mixed or using Tukey -CUSUM chart together, to show the process control chart., and drawing the Average Run Length ARL value.

An Adaptive EWMA Control Chart Based on Principal Component Method to Monitor Process Mean Vector

The special causes of variations, which is also known as a shift, can occur in a single or more than one related process characteristics. Statistical process control tools such as control charts are useful to monitor shifts in the process parameters (location and/or dispersion). In real-life situation, the shift is emerging in different sizes, and it is hard to identify it with classical control charts. Moreover, more than one process of characteristics required special attention because they must monitor jointly due to the association among them. This study offers two adaptive control charts to monitor the different sizes of a shift in the process mean vector. The novelty behind this study is to use dimensionally reduction techniques such as principal component analysis (PCA) and an adaptive method such as Huber and Bi-square functions. In brief, the multivariate cumulative sum control chart based on PCA is designed, and its plotting statistic is utilized as an input in the classical exponentially weighted moving average (EWMA) control chart. The run length (RL) properties of the proposed and other control charts are obtained by designing algorithms in MATLAB through a Monte Carlo simulation. For a single shift, the performance of the control charts is assessed through an average of RL, standard deviation of RL, and standard error of RL. Likewise, overall performance measures such as extra quadratic loss, relative ARL, and the performance comparison index are also used. The comparison reveals the superiority over other control charts. Furthermore, to emphasize the application process and benefits of the proposed control charts, a real-life example of the wind turbine process is included.

Multivariate ELR control chart with estimated mean vector and covariance matrix

Recently, simultaneous monitoring of multivariate process mean and variability has received increasing attention in the literature of statistical process monitoring (SPM). However, the deleterious impact of parameter estimation on the capability of control charts designed for simultaneous monitoring of the mean vector and covariance matrix of multivariate processes has been clearly neglected. In this paper, we study the effect of estimation error on both in-control and out-of-control properties of the multivariate exponentially weighted moving average (EWMA)-based generalized likelihood ratio (MELR) chart. Simulation studies in terms of the average run length (ARL), the standard deviation of run length (SDRL), and the median run length (MRL) metrics are conducted to explore how the amount of Phase I reference samples affects the performance of the MELR chart. The results show that extra variability due to estimation error reduces the detecting capability of the MELR chart while increases its false alarm rate. Meanwhile, a real-life data is provided to illustrate poor Phase I estimation results in more false alarms than expected.

Max-EWMA chart for time and magnitude monitoring using generalized exponential distribution

Joint monitoring of time and magnitude is an important issue in many industrial and non-industrial fields and several proposals exist in the literature. The aim of this article is to propose a new maximum exponentially weighted moving average (Max-EWMA) chart assuming generalized exponential distribution for time as well as magnitude. As the test-statistic of Max-EWMA chart consists of two EWMA statistics, it is easy to identify the out-of-control signal raised by the chart. The performance of the chart is evaluated using different run length characteristics including, average run length (ARL), standard deviation of run length (SDRL), and quantiles of the run length distribution. Besides extensive simulation studies, a real data set is also used to show the practicality of the proposed chart. The results show that the proposed chart is efficient in detecting different size of small to moderate shifts.

The Performance of Triple Sampling x̄ Control Chart with Measurement Errors

ABSTRACT The presence of measurement errors can seriously alter the statistical performance of Phase II control charts. Up today, no research on designing the triple sampling control charts taking into account the gauge measurement errors is reported in the existing literature. In this paper, we study the adverse effect of measurement errors on detecting performance of triple sampling (TS)- control chart based on an additive covariate model. Three multiple measurement based triple sampling (MMBTS) schemes are developed to reduce the undesired impact of gauge inability on detecting performance of TS- chart. Through simulation studies in terms of average run length (ARL) and standard deviation of run length (SDRL), it is indicated that the run length characteristics of the TS- is significantly affected by the measurement errors. The results also confirm that all proposed remedial approaches can effectively reduce the undesired impact of imprecise measurements on performance of TS- chart. A sensitivity analysis is also carried out to evaluate how the covariate model parameters affect the detection performance of the TS- chart. Finally, using a real industrial data obtained from the spring production system, we demonstrate the performance of TS- chart when the measurement errors exist.

Phase II monitoring of zero inflated Poisson regression profiles

In many quality control applications, the quality of some products or processes is best characterized by a functional relationship (profile) between a response variable and one or more explanatory variables. Profile monitoring involves the use of control charts to monitor the stability of this type of quality control processes. Several studies have discussed the problem of monitoring normal response profiles. More recently, researchers started studying the case where the response variable follows a discrete distribution such as the Poisson or the Bernoulli distributions. Due to recent technological advancement and the high level of automation used in almost all manufacturing processes, there exist near-zero defect manufacturing processes, hence, the zero-inflated Poisson distribution is expected to be more appropriate than the ordinary Poisson distribution for monitoring such processes. This study aims at extending three of the existing methods for phase II monitoring of profiles namely; MEWMA, Hotelling’s T2, and EWMA-R to the case of zero-inflated Poisson profiles. A simulation study is used to compare the performance of the competing approaches in terms of the average run length (ARL) and the standard deviation run length (SDRL). The results revealed that the EWMA-R chart is generally superior to the other competing methods.

Unit Interval Time and Magnitude Monitoring Using Beta and Unit Gamma Distributions

Quick detection of an assignable cause is necessary for process accuracy with respect to the specifications. The aim of this study is to monitor the time and magnitude processes based on unit-interval data. To this end, maximum exponentially weighted moving average (Max-EWMA) control chart for simultaneous monitoring time and magnitude of an event is proposed. To be precise, beta and unit gamma distributions are considered to develop the Max-EWMA chart. The chart’s performance is accessed using average run length (ARL), the standard deviation of run length (SDRL), and different quantiles of the run length distribution through extensive Monte Carlo simulations. Besides a comprehensive simulation study, the proposed charting methodology is applied to a real data set. The results show that the proposed chart is more efficient in detecting small to medium-sized shifts. The results also indicate that simultaneous shifts are detected more quickly as compared to the pure shift.

A parameter free Bayesian adaptive EWMA mean chart under different loss functions

AbstractThe adaptive exponentially weighted moving average (AEWMA) control chart is more sensitive than the exponentially weighted moving average (EWMA) control chart for the mean shifts. The EWMA control chart is used to monitor the small or moderate shifts, and the Shewhart control chart is used to monitor only large shifts in the process mean. The AEWMA control chart is useful to monitor the small to large mean shifts. We proposed a new parameter free Bayesian AEWMA mean chart under different loss functions (LFs). We used two different LFs as symmetric LF namely squared error loss function (SELF) and asymmetric LF namely Linex loss function (LLF) with both informative and non‐informative priors for posterior and posterior predictive distributions. The average run length (ARL) and the standard deviation of run length (SDRL) are used to measure the performance of the proposed parameter free Bayesian AEWMA control chart under different LFs. A Monte Carlo simulation study is used to evaluate the proposed control chart under different LFs. A real data example is used for implementation purposes.

MEWMA based control charts with runs rules for monitoring multivariate simple linear regression profiles in Phase II

In this article, three control charts including MEWMA, MEWMA/ and DMEWMA equipped with proposed runs rules schemes, are developed to improve the performance of existing control charts in monitoring multivariate simple linear profiles. Using five criteria of average run length, percentile of the run length, standard deviation of run length, relative mean index and relative standard deviation index the behavior of the suggested control schemes has been assessed. The results of our study demonstrate that the suggested schemes have a better performance compared to current charts for detecting shifts. Ultimately, using an actual calibration application case in the automotive industry, the suggested control charts applicability is depicted.