Design Of Control Charts Research Articles

Monitoring Lifetime Data for a Failure Censoring Reliability Test with Replacement Using Shewhart Type and Exponentially Weighted Moving Average Control Charts

Lifetime data has two distinguishing features: they are usually censored and have non-normal distributions. Generally speaking, censoring schemes can be classified into (i) censoring schemes with replacement and (ii) censoring schemes without replacement. Replacement during a life testing means that once observing a failure item, it is replaced by a new one. While there is a relatively large body of literature regarding control charts under censoring schemes without replacement, i.e., the second type schemes, designing control charts for the first type schemes has not yet received considerable attention. In this paper, two types of control charts are developed to monitor the lifetime data of an exponentially distributed item. To obtain the information of the lifetime data, failure censoring is conducted: n items are randomly selected and put on the test simultaneously. The test continues until observing r (r≤n) failures. During the test, once observing a failure time, it is replaced by a new one. Development of Shewhart type and exponentially weighted moving average control charts under failure censoring with replacement is the main novelty of the current study. Comparative and simulation studies are conducted. ARL curves are also derived with respect to different parameters of the process.

Monitoring of location and dispersion parameters of production processes using hybrid control charts

In practical terms, the measurement data from production processes are usually contaminated which may translate into failure to meet the assumed normality. In consequence, using classical Shewhart control charts to monitor the stability of production processes leads to the occurrence of numerous false signals. The purpose of this article is to propose hybrid control charts and to investigate their performance in monitoring the parameters of location and variability of production processes for which there occurs contamination of measurement data appearing at the stage of monitoring production cycles. To construct the control charts proposed by the authors, we should use extended control limits of classical Shewhart charts for means and ranges (Phase I) and robust estimators as test statistics to control the production cycle (Phase II). The article demonstrates the conducted simulation testing of classical and robust estimators for location and dispersion in terms of their effectiveness, as well as determining the relationship between them. These analyses have contributed to the design of hybrid control charts. Comparative simulation tests of classic and hybrid control charts performance have confirmed the effectiveness of the suggested measures. It follows that the proposed control charts can replace the classic counterparts, because they do not respond to an acceptable level of measurement data contamination, thanks to which it is possible to avoid taking unnecessary corrective actions in the production process. The theoretical portion is closed by a case study based on actual data which aims to illustrate the proposed approach.

Optimization design of control charts for statistical monitoring QA system

Optimization design of control charts for statistical monitoring QA system

Economic Design of EWMA Control Charts with Variable Sampling Intervals for Monitoring the Mean and Standard Deviation under Preventive Maintenance and Taguchi’s Loss Functions

The control chart and the maintenance management need to control process quality and reduce out-of-control cost. They are two key tools in the production process; however, they have usually been analyzed separately in the literature. Moreover, the existing studies integrating these two concepts suffer from three significant drawbacks as follows: (1) using control charts with fixed parameters to monitor the process, so that the small and middle shifts are detected slowly; (2) monitoring the mean and standard deviation separately, whereas, in real condition, the mean and standard deviation should be monitored simultaneously; (3) quality loss function is not usually used to design economic model, which leads to a large social quality loss in the monitoring process of control chart. To eliminate these weaknesses, the economic design of the exponential weighted moving average (EWMA) control chart with variable sampling intervals (VSI) for monitoring the mean and standard deviation under preventive maintenance and Taguchi’s loss functions is proposed. The optimal values of the parameters are determined to minimize the loss-per-item in an average cycle process. In addition, a genetic algorithm is used in a numerical example to search for the optimal values of the parameters. According to the sensitivity analysis, the effect of the model parameters on the solution of the economic model is obtained. Finally, the comparison study shows that the VSI EWMA control charts designed by the joint economic model are expected to reduce loss.

Earned Duration Management Control Charts: Role of Control Limit Width Definition for Construction Project Duration Monitoring

AbstractThe design of control charts refers to the selection of the sample, the sampling interval, and the width of the control limits. The literature on the use of control charts for project monit...

Residuals based EWMA control charts with risk adjustments for zero‐inflated Poisson models

AbstractCount data are widely available in many fields and numerous studies have designed control charts for them to monitor count processes. However, these control charts have limited effect on the ”zero‐inflated” data who have excess zeros. Zero‐inflated Poisson (ZIP) models are important methods to deal with the data and some control charts based on them have been proposed. Unfortunately, there are still some limitations in these works, such as lack of risk adjustments, inability to monitor two parameters of ZIP models simultaneously, or insufficient sensitivity to small shifts. Therefore, in this paper, we propose residuals based exponentially weighted moving average (EWMA) control charts with risk adjustments for ZIP models to detect small shifts in zero‐inflated data. With taking Pearson and deviance residuals as targets, the two parameters can be monitored simultaneously. The results of simulation study via Monte Carlo methodology demonstrate that our charts have better performance than the existing charts in detecting the small changes of zero‐inflated processes. In addition, according to the results, we advise that it is best to use the EWMA chart based on deviance residuals (DR‐EWMA) to obtain the optimal monitoring performance when the likelihood function is easy to define; otherwise, that based on Pearson residuals (PR‐EWMA) can still provide better results than the existing charts. Finally, two different real data sets are used to verify the practicability of our charts.

Robust Distribution-Free Hybrid Exponentially Weighted Moving Average Schemes Based on Simple Random Sampling and Ranked Set Sampling Techniques

This paper proposes new nonparametric hybrid exponentially weighted moving average (HEWMA) control charts based on simple random sampling (SRS) and ranked set sampling (RSS) techniques using the Wilcoxon rank-sum W statistic. The in-control robustness and out-of-control (OOC) performances are thoroughly investigated using extensive simulations. The HEWMA W chart is shown to be superior to the basic exponentially weighted moving average (EWMA) and double EWMA W charts in many cases under normal and nonnormal distributions. Moreover, the OOC sensitivities of the new HEWMA W -type control charts are further improved by using supplementary 2-of-2 and 2-of-3 standard and improved runs-rules approaches. It is found that the proposed HEWMA W -type charts with runs-rules perform better than the basic HEWMA W SRS and RSS charts. Real-life data based on the impurity of iron ore are used to illustrate the design and implementation of the new control charts.

Monitoring shrimp growth with control charts in aquaculture

This work proposes a method for the statistical monitoring of the weekly weight of shrimp in a fish farm. The design of control charts for shrimp growth presents several challenges, the main ones being the presence of trend and autocorrelation. Several control charts are proposed, the most efficient being a chart based on the residuals of a second order autoregression whose parameters vary with the week. A control chart with less computational complexity is also provided. It is simply based on growth rates and works well at detecting negative weight changes. Real data from a large shrimp farm has been used for both the design and the evaluation.

Integration of Multivariate Loss Function Approach in the Hotelling’s Charts under Banerjee-Rahim (1988) Weibull Shock Models

A proper monitoring of stochastic systems is the control charts of statistical process control and drift in characteristics of output may be due to one or several assignable causes. Although many research works have been done on the economic design of control charts with single assignable cause, the economic statistical design of T^2 control chart under Weibull shock model with multiple assignable causes and considering multivariate Taguchi loss function has not been presented yet. Using Taguchi loss function in the concept of quality control charts with economic and economic statistical design leads to better decisions in the industry. Based on the optimization of the average cost per unit of time and taking into account the different combination values of Weibull distribution parameters, optimal design values ??of sample size, sampling interval and control limit coefficient were derived and calculated. Then the cost models under non-uniform and uniform sampling scheme were compared. The results revealed that the model under multiple assignable causes with Taguchi loss function has a lower cost than single assignable cause model and integrated model with non-uniform sampling has a lower cost than that with uniform sampling.

Controlling the conditional false alarm rate for the MEWMA control chart

An integral part of the design of control charts, including the multivariate exponentially weighted moving average (MEWMA) control chart, is the determination of the appropriate control limits for prospective monitoring. Methods using Markov chain analyses, integral equations, and simulation have been proposed to determine the MEWMA chart limits when the limits are based on a specified in-control average run length (ARL) value. A drawback of the usual approach is that the conditional false alarm rate (CFAR) for these charts varies over time in what might be in an unexpected and undesirable way. We define the CFAR as the probability of a false alarm given no previous false alarm. We do not condition on the results of a Phase I sample, as done by others, in studies of the effect of estimation error on control chart performance. We propose the use of dynamic probability control limits (DPCLs) to keep the CFAR constant over time at a specified value. The CFAR at any time, however, could be controlled to be any specified value using our approach. Using simulation, we determine the DPCLs for the MEWMA control chart being used to monitor the mean vector with an assumed known variance-covariance matrix. We consider cases where the sample size is both fixed and time-varying. For varying sample sizes, the DPCLs adapt automatically to any change in the sample size distribution. In all cases, the CFAR is held closely to a fixed value and the resulting in-control run length performance follows closely to that of the geometric distribution.

Monitoring mean changes in persistent multivariate time series

ABSTRACT We focus on sequential (online) monitoring of changes in the mean vector of high-dimensional persistent VARMA time series by using multivariate control charts. Applying either modified or residual control charts to the original process or to the process of VARMA residuals could be problematic when the degree of autoregressive persistence is high. To overcome these difficulties, we suggest to monitor the process of the vector first differences of the VARMA series. We derive the stochastic properties of this difference vector process which are required for the design of the multivariate control charts. Then, we illustrate the performance of our approach in a Monte Carlo simulation study for detection of various types of mean changes.

Multi-objective design of risk-adjusted control chart in healthcare systems with economic and statistical considerations

Using control charts to monitor healthcare systems has gained particular attention. In this paper, a risk-adjusted cumulative sum control chart is designed to monitor surgery outputs. Before undergoing surgery, the patients have some unique risk factors which influence the surgery outputs. Thus, risk-adjustment is carried out with the purpose of taking these risks into account using an accelerated failure time model. But the technical implementation of the chart requires determining the design parameters which should be selected in an optimal way putting the desired statistical and economic considerations into service. To this end, a multi-objective model, considering multiple assignable causes with different occurrence rates and effects, has been proposed and the model is solved with the help of a 5-stage algorithm based on the data envelopment analysis method. Then, to show the performance of the proposed procedure, a real case study has been conducted in the cardiac surgery center. Finally, sensitivity analysis on some cost parameters has been conducted. Furthermore, comparisons of the proposed multi-objective model with the pure economic and pure statistical design models have been made. The results reveal that the multi-objective design of the risk-adjusted cumulative sum chart shows acceptable performance in the presence of multiple assignable.

Monitoring Mortality Caused by COVID-19 Using Gamma-Distributed Variables Based on Generalized Multiple Dependent State Sampling.

More recently in statistical quality control studies, researchers are paying more attention to quality characteristics having nonnormal distributions. In the present article, a generalized multiple dependent state (GMDS) sampling control chart is proposed based on the transformation of gamma quality characteristics into a normal distribution. The parameters for the proposed control charts are obtained using in-control average run length (ARL) at specified shape parametric values for different specified average run lengths. The out-of-control ARL of the proposed gamma control chart using GMDS sampling is explored using simulation for various shift size changes in scale parameters to study the performance of the control chart. The proposed gamma control chart performs better than the existing multiple dependent state sampling (MDS) based on gamma distribution and traditional Shewhart control charts in terms of average run lengths. A case study with real-life data from ICU intake to death caused by COVID-19 has been incorporated for the realistic handling of the proposed control chart design.

On the design of Shewhart control charts for count time series under estimation uncertainty

This study is a first step towards a comprehensive analysis of the effects of parameter estimation on the monitoring of autocorrelated count processes. Focusing on Shewhart’s c and np charts, various types of count process with different dispersion properties and model structures are considered. The pure effect of discreteness of observations is contrasted with the additional consequences of estimation uncertainty on the control limits of the charts as well as on the resulting run length performance. The main parameter regarding a trustworthy chart design is the actual dispersion of the count process, which, in turn, might be connected to the extent of serial dependence for certain types of process. For some low-dispersion scenarios, the effect of parameter estimation on the design parameters might even fully vanish. The acquired results are illustrated with two real-data examples, where a parametric bootstrap approach is used to judge the reliability of the obtained chart design.

Statistical design of a VSI-EWMA control chart for monitoring the communications among individuals in a weighted social network

Statistical design of a VSI-EWMA control chart for monitoring the communications among individuals in a weighted social network

Joint planning of maintenance, buffer stock and quality control for unreliable, imperfect manufacturing systems

A stochastic model is developed in this study for joint planning of maintenance, production and quality control in manufacturing systems. The process may deteriorate during the production and the process state may transit from an in-control to an out-of-control. The state transition time follows a general distribution. Sampling inspections are conducted on the process during the production run and the collected information is plotted on a proper control chart to monitor the process. With respect to the process state, PM action or CM action is conducted on the process. The time duration to conduct maintenance actions was considered as a continuous random variable. During conducting maintenance action the production process is interrupted and the demand is satisfied from a safety stock. The aim of the model is to integrate the decisions on the sampling inspections, control chart design, maintenance schedule and stock level determination to minimize the total cost. A numerical study was conducted and the sensitivity of the model was analyzed for important parameters. A genetic algorithm was applied for optimization and finally, the integrated model of three aspects and the mathematical model of maintenance and production were compared to investigate the impact of joint planning of these aspects on the management of manufacturing systems.

Economic Statistical Design for Three-level Control Charts with Variable Sample Size

The problem of Statistical Process Control with some discrete level classification scheme, have been recently discussed by some authors. This paper presents economic and economic-statistical designs for variable sample size (VSS) of the three-level control charts. The expected cost per unit of time is derived with the use of the cost model developed for the control chart proposed by Costa and Rahim. The genetic algorithm is employed to search for the optimal values of model parameters. Finally, the expected cost per unit of time of VSS and fixed ratio sampling (FRS) three-level control charts is compared.

Controlling the exponentially weighted moving average S2 control chart false alarm behavior when the in‐control variance level must be estimated

AbstractInvestigating the problem of setting control limits for an exponentially weighted moving average (EWMA) chart in the case of parameter uncertainty is more accessible when monitoring the variance because only one parameter has to be estimated. Simply ignoring the induced uncertainty frequently leads to control charts with poor false alarm performances. Adjusting the unconditional in‐control (IC) average run length (ARL) makes the situation even worse. Guaranteeing a minimum conditional IC ARL with some given probability is another very popular approach to solving these difficulties. However, it is very conservative as well as more complex and more difficult to communicate. We utilize the probability of a false alarm within the planned number of points to be plotted on the control chart. It turns out that adjusting this probability produces notably different limit adjustments compared to controlling the unconditional IC ARL. We then develop numerical algorithms to determine the respective modifications of the upper and two‐sided EWMA charts based on the sample variance for normally distributed data. These algorithms are made available within an R package. Finally, the impacts of the EWMA smoothing constant and the size of the preliminary sample on the control chart design and its performance are studied.

Economic design of a CEV x̄ control chart for determining optimal right-censored times

ABSTRACT Lifetime is a crucial quality characteristic of electronic products that must be monitored using control charts. Lifetime may provide right-censored data. A conditional expected value (CEV) x̄ control chart was developed to monitor type I right-censored data. Researchers had always assumed that the censored time is a known constant when designing control charts. This study provides an economic design model for optimizing CEV x̄ charts and type I right-censored time for reducing costs associated with quality control and life tests. This method was employed on a practical case of a liquid crystal display module. A sensitivity analysis was also conducted on the influence of the model parameters on the design and censored time of the CEV x̄ chart.

Statistical-Economic Design of Control Chart If The Vector of Target Values of Multi-Variables Shifts With Time

In this paper, the statistical-economic design of a multivariate special triangle control chart is proposed to control the processes of the quality characteristics or financial indices shifting with time. A multi-objective programming with several constraints is used to determine optimal solutions of control region (probability of false alarm), the power of finding out assignable cause(s), sample interval and sample size. An application of the statistical-economic design of a Multivariate special triangle control chart is illustrated to control the soundness of insurers of U.S