Types Of Control Charts Research Articles

A distribution-free Shewhart-type Mann–Whitney control chart for monitoring finite horizon productions

Distribution-free control charts have been proposed in recent years to monitor processes with insufficient information about the distribution of observations. A promising field of application of these charts is the small production of finite batches of products, where the number of scheduled inspections is limited to a few tens. Following the machine reconfiguration after a process set-up, the quality practitioner cannot rely on past production runs to get knowledge about the distribution of the observations: this scenario can be referred to as the Case U (Unknown) condition in statistical process monitoring. Here, we investigate the issues related to the implementation of Mann–Whitney (MW) type control charts for monitoring the location in a finite horizon production (FHP) process. The practitioner-to-practitioner variability is considered while designing the control limits. The in-control and out-of-control chart performances are investigated over a wide set of scenarios and some graphical tools are proposed to help practitioners during the decision-making process. A comparison with the Shewhart Sign control chart for FHP processes is also presented. An illustrative example is provided to demonstrate the implementation of the proposed chart on a real industrial dataset.

A review of dispersion control charts for multivariate individual observations

A multivariate control chart is designed to monitor process parameters of multiple correlated quality characteristics. Often data on multivariate processes are collected as individual observations, i.e., as vectors one at a time. Various control charts have been proposed in the literature to monitor the covariance matrix of a process when individual observations are collected. In this study, we review the literature on control charts based on individual observations from multivariate continuous processes, where we find 30 relevant articles from the period 1987–2019. We group the articles into five categories. We observe that less research has been done on CUSUM, high-dimensional and non-parametric type control charts for monitoring the process covariance matrix. We describe each proposed method, state their advantages, and limitations. Finally, we give suggestions for future research.

The comparison of exponentially weighted moving variance and double moving average-S control charts based on neoteric ranked set sampling

In manufacturing industry, quality is very important, because it can determine customers’ satisfaction and distinguish the product from others. The effort that can be made by companies to maintain the products quality is by monitoring and controlling them. One of the statistical methods that can be used for monitoring and controlling quality is control charts. Generally, there are two types of control charts, control chart for mean and control chart for variability. Three models of control charts, recently, have been developed, such as Shewhart, Cumulative Sum (CUSUM), and Exponentially Weighted Moving Average (EWMA). This research will be stated Exponentially Weighted Moving Variance (EWMV) and Double Moving Average-S (DMA-S) for monitoring variability based on Neoteric Ranked Set Sampling (NRSS). EWMV and DMA-S control charts can detect small shifts, and NRSS has better performance than Simple Random Sampling (SRS) and Ranked Set Sampling (RSS). Furthermore, the performance of EWMV based on NRSS and DMA-S basd on NRSS control charts will be compared and evaluated by using Average Run Length (ARL) value with Monte Carlo simulation approach to detect any particular shifts. Both of the control chart models will be applied in Combined Cycle Power Plant (CCPP) case. By this evaluation, the result shows that the DMA-S control chart based on NRSS performs better than the EWMV control chart based on NRSS.

Precision Analysis of Poisson Control Chart Based on Sample Size

One technique used in performing statistical quality control is by poisson control chart. Poisson control chart used in data that have the same mean and varians for monitoring the number of defects in the study. In some cases, the different sample sizes influence the control chart performance. The control chart performance can be measured using average run length (ARL). The smaller ARL’s value, the better type of control chart. In this study, we used different sample sizes that is and mean . The result show the best performance of control chart is when and m = 200, because its has a smaller ARL’s value.

An Application of Univariate and Multivariate Control Charts in Monitoring Water Quality

Control chart is a tool for detecting an out-of-control signal in statistical process control (SPC). It is widely used in process monitoring in order to detect changes in process mean or process dispersion. This study aims to illustrate the application of multivariate control charts in monitoring water quality at one of the water treatments plants in Kota Kinabalu, Sabah. The tested water quality variables in this study are turbidity, pH value, dissolved oxygen (DO) and concentration of ferum. Two multivariate control charts, Hotelling’sT2 and MCUSUM control charts are constructed under the violation of the multivariate normality assumption. The purpose is to study the effect of non-normal data upon the monitoring process using the selected multivariate control charts. By comparing the monitoring process between the two types of control charts, the consistency of the results is studied. All the univariate and multivariate control charts produced out-of-control signals from different points, hence inconclusive results obtained. Keywords: Water quality; multivariate control chart; univariate control chart; Hotelling’s T2; MCUSUM

Process control in electron beam sterilization of medical devices and a pathway to parametric release

This paper presents a review of process control methods in electron beam sterilization of medical devices. Starting from normative requirements, the proper use of different types of control charts to demonstrate that the process is in statistical control, is discussed in depth. Special emphasis is laid on the establishment of control limits. Their performance is analyzed using data from an actual electron beam process. In addition to SPC charts for monitoring doses, the concept of a performance index based on processing parameters is proposed and its implementation in control charts is discussed. It is shown that these charts allow an extraordinary tight control of the sterilization process which is superior to standard monitoring dosimetry. Especially time-weighted control (CUSUM) charts are identified as means to control a process effectively.Subsequently, the process parameter analysis approach is extended towards assessment and decision whether product specifications have been met and a potential pathway to parametric release from electron beam sterilization is outlined. A process definition method which addresses minimum and maximum dose specifications directly and does not rely on monitoring doses is presented in an example using actual data. Terminology and the treatment of uncertainties follow closely the ISO 11137 family of standards.A discussion of potential advantages of parametric release and a roadmap and requirements for this paradigm shift in electron beam sterilization of medical devices complement the paper.

A distribution-free EWMA control chart for monitoring time-between-events-and-amplitude data

ABSTRACT Many control charts have been developed for the simultaneous monitoring of the time interval T between successive occurrences of an event E and its magnitude X. All these TBEA (Time Between Events and Amplitude) control charts assume a known distribution for the random variables T and X. But, in practice, as it is rather difficult to know their actual distributions, proposing a distribution free approach could be a way to overcome this ‘distribution choice’ dilemma. For this reason, we propose in this paper a distribution free upper-sided EWMA (Exponentially Weighted Moving Average) type control chart, for simultaneously monitoring the time interval T and the magnitude X of an event. In order to investigate the performance of this control chart and obtain its run length properties, we also develop a specific method called ‘continuousify’ which, coupled with a classical Markov chain technique, allows to obtain reliable and replicable results. A numerical comparison shows that our distribution-free EWMA TBEA chart performs as the parametric Shewhart TBEA chart, but without the need to pre-specify any distribution. An illustrative example obtained from a French forest fire database is also provided to show the implementation of the proposed EWMA TBEA control chart.

A new approach to design median control charts for location monitoring

In SPC, the most effective and magnificent tool is the control chart. The structure of control charting schemes required the assumption that the process is free from disturbances with known parameters or correctly estimated from the in-control process. These assumptions need to full fill for monitoring location parameter with mean control charts. But in practical, these assumptions are not always true, due to occasionally presence of outliers. That is why the median is a suitable measure as compared to the mean in the presence of disturbances. The ranked and neoteric ranked set samplings are suggested in this study to monitor the location parameter of the process by using median estimator for and Shewhart type control charts. The run-length profile is used as a performance measure for proposed median based control charts. The results reveal that for median control charts based on neoteric ranked set sampling scheme yield excellent outcomes. The real-life application is provided of the new charting schemes.

On designing a new control chart for Rayleigh distributed processes with an application to monitor glass fiber strength

In this study, a Shewhart type control chart, namely chart, has been proposed to monitor a process that follows Rayleigh distribution. The proposed chart is implemented to monitor the single scale parameter of the Rayleigh distributed process. We have studied the proposed chart under two type of control limits namely probability and -sigma limits. The performance of the proposed chart has been assessed by using power function. In addition, we have investigated run length properties including average run length (ARL), standard deviation of run length (SDRL) and median run length (MDRL). The analysis of run length profile reveals that the proposed VR chart outperforms the existing charts including the traditional Shewhart control chart and V control charts under Rayleigh distribution. The construction process for the newly proposed chart has been demonstrated using a simulated data. Finally, a real application of the proposed chart, along with the existing chart, is presented that evaluates the strength of glass fiber in a manufacturing process.

CUSUM control charts with variable sampling interval for monitoring the ratio of two normal variables

AbstractIn many industrial manufacturing processes, the ratio between two normal random variables plays a key role in ensuring quality of products. Thus, monitoring this ratio is an important task that is well worth considering. In this paper, we combine a variable sampling interval (VSI) strategy with a cumulative sum (CUSUM) scheme to create a new type of control chart for purpose of tracking the ratio between two normal variables. The average time to signal (ATS) and the expected average time to signal (EATS) criteria are used to evaluate the performance of the new VSI CUSUM RZ control chart. The numerical results show that the proposed control chart has much more attractive performance in comparison with the standard CUSUM‐RZ control chart and the VSI EWMA‐RZ control chart.

Design of hybrid EWMln-S2 control chart

ABSTRACTMemory type control charts have built using logarithmic transformations for the normalization of unbiased sample variance for monitoring of changes in the dispersion of process. The intention of this study is to give a new hybrid exponentially weighted moving average (HEWMA) control chart for monitoring theprocess dispersion. The logarithmic transformation is used to normalize the distribution of sample variance. The execution of the proposed HEWMA control chart is evaluated in accordance with the average run length and standard deviation run length estimated with the help of Monte Carlo method. The proposed HEWMTn control chart has been compared with the corresponding existing charts to detect increase and decrease in the process variability. It showed that the proposed HEWMTn control chart is uniformly better than its parallels for detection of shifts in the process variability. A numerical study is also given to understand the operationalization of the proposed control chart.

Control charts for monitoring the ratio of two Poisson rates

AbstractIn this paper, we are concerning in monitoring the ratio ρ of two Poisson rates by control charts. Let X and Y be two independent Poisson random variables with means λ1 and λ2=λ1/ρ, respectively. The study considers that only individual observations Xi and Yi are available at each sampling time i. The performance in detecting shifts on the ratio ρ using several statistics, some based on normalized transformations, is evaluated by an extensive simulation study. Two types of control charts, Shewhart and exponentially weighted moving average (EWMA), are considered. The one‐sided control chart with upper control limit (UCL) is applied so that we are focusing on detecting when the ratio ρ shifted to higher rate in this paper. The results pointed out that EWMA control chart is a better alternative. Some guidelines indicating which statistics yield best performance are proposed for the practitioners.

The use of control chart for a continuous monitoring of the water-oil ratio in fields of the Potiguar basin/Brazil

Nowadays, petroleum is the most used energy source in the world, however it also produces a great volume of a residue denominated produced water (PW). This water has no commercial value and requires treatment, due to potential contaminants in its composition, in order to be destined for disposal or reinjection during recovery methods. In this way, the produced water management needs specific process support it, becoming costly. Therefore, the present work proposes a continuous monitoring methodology of the water-oil ratio, aiming to subsidize the field viability analyses. Once that the water-oil ratio data are auto-correlated, some adjustments are needed before the application of the control charts. Therefore, ARIMA models were adjusted to the data, evaluating the accuracy of the models, then, the control charts were built based on the residues. In this paper, the type of control charts considered was a Shewhart for the averages. The performance of the chart was evaluated through simulations and it was determined that it is efficient to detect big deviations, but slow to small deviations.

Improving the quality of Higher Education teaching through the exploitation of student evaluations and the use of control charts

Student evaluations of faculty members' teaching effectiveness are considered quite important in Higher Education (HE). In this paper, we elaborate on the framework of Nikolaidis and Dimitriadis, based mainly on Statistical Process Control techniques and tools, which enables a deeper analysis and broader exploitation of student evaluation data. More specifically, we thoroughly examine and evaluate through simulation, several popular types of control charts (CCs), identifying the most suitable among them, using as comparison criteria various statistical properties of CCs. The ultimate goal of our research is to provide decision makers in HE institutions with an easy-to-use reliable tool for not only monitoring the teaching process, but also identifying the effective and ineffective faculty members’ teaching performance to promote the quality of their Institution.

Wilcoxon-type rank-sum control charts based on progressively censored reference data

In this article, we introduce a new distribution − free Shewhart − type control chart implementing a modified Wilcoxon-type rank sum statistic based on progressive Type-II censoring reference data. The proposed chart is also a tool for monitoring the incomplete data, because the censoring scheme applied allows the protection of experimental units at an early stage of the testing procedure. The setup of the new nonparametric control chart is presented in detail, while its operating characteristic function is studied. Explicit formulae for the evaluation of Alarm Rate and Average Run Length values for both in-control and out-of-control situations are established. A numerical study carried out depicts the performance and robustness of the proposed control chart. For illustration purposes, a practical example is also discussed.

Design of a Variable Sampling Interval EWMA Median Control Chart

In the literature, median type control charts have been widely investigated as easy and efficient means to monitor the process mean when observations are from a normal distribution. In this work, a Variable Sampling Interval (VSI) Exponentially Weighted Moving Average (EWMA) median control chart is proposed and studied. The Markov chains are used to calculate the average run length to signal (ARL). A performance comparison with the original EWMA median control chart is made. The numerical results show that the proposed chart is considerably more effective as it is faster in detecting process shifts. Finally, the implementation of the proposed chart is illustrated with an example in food production process.

Analysis of the Stability of the Chemical Composition of Wastewater in the Production of Printed Circuit Boards

A method for analyzing the stability of the chemical composition of wastewater in the manufacture of printed circuit boards using statistical methods of process control is proposed. The correlation and normal distribution of the monitored indicators is evaluated. Types of control charts are selected that provide control of both the average level of the process and its dispersion. To control the stability of independent indicators, Shewhart charts are used. Monitoring of correlated indicators is carried out using the Hotelling control chart. If it is necessary to control the multidimensional dispersion of the process, generalized variance charts can be used. The proposed approach ensures the detection of process violations before the monitored indicators are out of tolerance.

Assorted control charts: An efficient statistical approach to monitor pH values in ecotoxicology lab

AbstractPrimarily, three types of control charts are employed to observe the disturbances in the process parameters. The large shifts are detected efficiently by Shewhart's control chart, whereas for small and medium instabilities, cumulative sum and exponentially weighted moving average control charts are used. This study proposes an assorted approach to monitor small, medium, and large disturbances in a single control charting procedure. For the evaluation of the proposed assorted control chart, we have used various measures like average run length, standard deviation run length, extra quadratic loss, relative average run length, and performance comparison index. A comparison of the proposed assorted control chart is presented with some typical charts including the Shewhart, cumulative sum, exponentially weighted moving average control charts, and some advanced modification such as combined Shewhart‐EWMA (CSE), combined Shewhart‐CUSUM (CSC), mixed EWMA‐CUSUM (MEC), FIR EWMA, and adaptive EWMA (AEWMA). Finally, a real‐life application example is presented to monitor the pH level of water in an ecotoxicology lab.

One-sided synthetic control charts for monitoring the multivariate coefficient of variation

ABSTRACTShewhart's type control charts for monitoring the Multivariate Coefficient of Variation (MCV) have recently been proposed in order to monitor the relative variability compared with the mean. These approaches are known to be rather slow in the detection of small or moderate process shifts. In this paper, in order to improve the detection efficiency, two one-sided Synthetic charts for the MCV are proposed. A Markov chain method is used to evaluate the statistical performance of the proposed charts. Furthermore, computational experiments reveal that the proposed control charts outperform the Shewhart MCV control chart in terms of the average run length to detect an out-of-control state. Finally, the implementation of the proposed chart is illustrated with an example using steel sleeves data.

Application of control charts for non-normally distributed data using statistical software program: A technical case study

Control charts are a valuable assessment tool in the healthcare industry. The ease of use of these trending charts is crucial to obtain timely important results with minimum time and efforts. The current case showed analysis of non-normal data to obtain control charts with useful output without using exhaustive different means of transformation and/or omitting aberrant numbers. Raw results for the quality of purified water from water treatment plant that converts municipal water to purified water were collected from two points-of-use - (ζ and Ψ). Data gathered were conductivity and total organic carbon (TOC) measurements. The statistical processing and control charts were done using commercial statistical software package. Statistical analysis of data showed that conductivity and TOC results of both points did not follow Gaussian distribution except TOC of point Ψ where it passed normality test, but they were closest to other distributions. There were several observations of outlier values from the results. Moreover, data normalization did not improve after removal of the extreme values. Data were switched to be interpreted using Laney-modified attribute control charts and compared with the original results drawn using individual-moving range (I-MR). Interestingly, both types of control charts agreed regarding control limits and some alarm points. I-MR and Laney-attribute charts could be used for non-normal data with unusual other types of distributions that may not be suitable for conventional types of control charts with the variable charts possess greater sensitivity of alarm detection over the attribute charts.