The double sampling range chart

The R chart and the S² chart are the usual charts for monitoring process dispersion; however, the double sampling (DS) scheme has only be used with the S² chart. The difficulty in obtaining the properties of the DS R chart might explain the lack of papers dealing with this type of DS chart. The S² chart has the advantage of being more efficient than the R chart, but the same is not always observed with their DS versions. Depending on the size of the 2 samples, the DS R chart performs better. The trade‐off between operational simplicity and power of detection might lead the practitioner to choose the DS R chart, even with the DS S² chart signaling faster.     

Combined double sampling and variable sampling interval X chart

In recent years several studies have shown that the X chart with variable sampling intervals (VSI), the X chart with variable size (VSS), the X chart with variable sample size and sampling intervals (VSSI) and the X chart with variable parameters (VP) detect both small and moderate shifts in the process mean more quickly than the traditional Shewhart X chart. Double sampling is the counterpart to double sampling plans. A combined double sampling variable sampling interval (DSVSI) X chart is studied in this paper. It is compared with the aforementioned charts and with the CUSUM and EWMA charts. In all cases, the DSVSI X chart is quicker at detecting small and moderate shifts in the process mean. An example is provided.     

An improved variable sample size and sampling interval S control chart

The standard deviation chart (S chart) is used to monitor process variability. This paper proposes an upper‐sided improved variable sample size and sampling interval (VSSI_t) S chart by improving the existing upper‐sided variable sample size and sampling interval (VSSI) S chart through the inclusion of an additional sampling interval. The optimal designs of the VSSI_t S chart together with the competing charts under consideration, such as the VSSI S and exponentially weighted moving average (EWMA) S charts, by minimizing the out‐of‐control average time to signal (ATS₁) and expected average time to signal (EATS₁) criteria, are performed using the MATLAB programs. The performances of the standard S, VSSI S, EWMA S, and VSSI_t S charts are compared, in terms of the ATS₁ and EATS₁ criteria, where the results show that the VSSI_t S chart surpasses the other charts in detecting moderate and large shifts, while the EWMA S is the best performing chart in detecting small shifts. An illustrative example is given to explain the implementation of the VSSI_t S chart.     

A synthetic double sampling control chart for process mean using auxiliary information

A control chart is a simple yet powerful tool that is extensively adopted to monitor shifts in the process mean. In recent years, auxiliary‐information–based (AIB) control charts have received considerable attention as these control charts outperform their counterparts in monitoring changes in the process parameter(s). In this article, we integrate the conforming run length chart with the existing AIB double sampling (AIB DS) chart to propose an AIB synthetic DS chart for the process mean. The AIB synthetic DS chart also encompasses the existing synthetic DS chart. A detailed discussion on the construction, optimization, and evaluation of the run length profiles is provided for the proposed control chart. It is found that the optimal AIB synthetic DS chart significantly outperforms the existing AIB Shewhart, optimal AIB synthetic, and AIB DS charts in detecting various shifts in the process mean. An illustrative example is given to demonstrate the implementation of the existing and proposed AIB control charts.     

An improved control chart structure for process location parameter

The article proposes a Shewhart‐type control chart, namely M_t chart, for an improved monitoring of the mean level of a quality characteristic of interest, say Y, in a process. The proposed control chart uses the information on a single auxiliary characteristic, say X, of the process and is based on product–difference‐type estimator, say M_t (in fact the spirit is to pool different styles of using information on auxiliary variable(s)). Assuming bivariate normality of the characteristic of interest Y and the auxiliary characteristic X, design structure of the proposed M_t chart is developed and its comparisons are made with those of some existing control charts used for the same purposes. The comparisons reveal an improved performance of the proposed M_t chart relative to its existing counterparts due to suggested merger of different approaches. Copyright © 2011 John Wiley & Sons, Ltd.     

An adaptive exponentially weighted moving average chart for the mean with variable sampling intervals

The AEWMA control chart is an adaptive EWMA (exponentially weighted moving average) type chart that combines the Shewhart and the classical EWMA schemes in a smooth way. To improve the detection performance of the FSI (fixed sampling interval) AEWMA control chart 7 in terms of the ATS(average time to signal), this paper proposes a new VSI (variable sampling interval) AEWMA control chart. A Markov chain approach is used to calculate the ATS values of the new VSI AEWMA control chart, and comparative results show that the proposed control chart performs better than the standard FSI AEWMA control chart and than other VSI control charts over a wide range of shifts.     

An attribute control chart for multivariate Poisson distribution using multiple dependent state repetitive sampling

In this paper, an attribute control chart for a multivariate Poisson distribution using multiple dependent state repetitive sampling (MDSRS) is presented. The evaluation of the proposed control chart is given through the average run length (ARL). The proposed control chart performs better than the existing control chart based on repetitive sampling and that using multiple dependent state sampling in terms of ARLs. A real example and a simulation study are added to explain the procedure and to demonstrate the power of the proposed control chart.     

Two successive occasions resubmitted sampling scheme-based control chart

In this paper, a resubmitted sampling-based successive sampling over two successive occasions control chart is proposed to monitor the underlying characteristic of interest. Auxiliary information of the first occasion is utilized to monitor the relative change in the study variable over the second occasion successively despite high degree of correlation. The structural and operational design is presented along with the comparative performance evaluation. The average run length is used as a performance evaluation measure and proved the argument in favor of the presented concept in comparison with the other auxiliary data control charts. The implementation is explained through two real examples.     

可变抽样区间不合格品数控制图

分析了休哈特控制图的不足,设计出具有两种抽样区间长度的可变抽样区间(VSI)np图,当点子接近控制限时,使用较短的抽样区间;当点子接近目标值时,使用较长的抽样区间.若点子超出控制限,则与固定抽样区间控制图(FSI)一样发出信号.同时还计算了在可变抽样区间下发信号前的平均时间,并与固定抽样区间np图进行比较,所设计的VSI控制图能缩短过程失控时间,从而可减少不合格品数.     

Economic design of a variable sampling rate EWMA chart

A Variable Sampling Rate (VSR) control chart is a control chart whose sampling scheme is to vary the sampling interval and the sample size for the next sample depending on the current chart statistic. A VSR EWMA chart is an EWMA chart with the VSR sampling scheme. An economic model, which was developed for a VSR chart, is also applied here to evaluate the efficiency of the VSR EWMA chart. The properties of the VSR EWMA chart are obtained by using a Markov chain approach. The model contains cost parameters which allow the specification of the costs associated with sampling, false alarms and operating off target as well as search and repair. This economic model can be used to quantify the cost saving that can be obtained by using a VSR chart instead of a Fixed Sampling Rate (FSR) chart and can also be used to gain insight into the way that a VSR chart should be designed to achieve optimal economic performance. It is shown that with some design parameter combinations the economically optimal VSR chart has a lower false alarm rate than the FSR chart.     

Hotelling's T2 control chart with variable sampling intervals

Hotelling's T₂ chart is the most widely used multivariate procedure to control changes in the mean vector of p correlated quality characteristics. In this paper, it is shown how to increase the efficiency of the test using the variable sampling interval technique. Given a control scheme with constant size and frequency of sampling, tables are produced that give a scheme, with two possible periods of time between samples, that is equivalent to the standard procedure when the process is in control. However, the new chart, as it uses two possible intervals between samples, is faster in detecting a change in the process. Various alternatives are given for the possible users of this method.     

A successive sampling control chart using multiple dependent state sampling over two successive occasions

In this paper, successive sampling (SS) mean monitoring control chart is proposed for two successive occasions using multiple dependent state (MDS) sampling and characterized as MDS-SS control chart. The sample size is selected on the basis of SS for the control statistic in two pairs of the control limits. The average run length is evaluated, and the performance of the proposed concept over the existing SS control chart is presented using a real-life example. The SS monitoring chart concept is compiled with MDS, and it becomes more sophisticated in detection of warning signs.     

An adaptive sampling method for variable-fidelity surrogate models using improved hierarchical kriging

Variable-fidelity (VF) modelling methods have been widely used in complex engineering system design to mitigate the computational burden. Building a VF model generally includes two parts: design of experiments and metamodel construction. In this article, an adaptive sampling method based on improved hierarchical kriging (ASM-IHK) is proposed to refine the improved VF model. First, an improved hierarchical kriging model is developed as the metamodel, in which the low-fidelity model is varied through a polynomial response surface function to capture the characteristics of a high-fidelity model. Secondly, to reduce local approximation errors, an active learning strategy based on a sequential sampling method is introduced to make full use of the already required information on the current sampling points and to guide the sampling process of the high-fidelity model. Finally, two numerical examples and the modelling of the aerodynamic coefficient for an aircraft are provided to demonstrate the approximation capability of the proposed approach, as well as three other metamodelling methods and two sequential sampling methods. The results show that ASM-IHK provides a more accurate metamodel at the same simulation cost, which is very important in metamodel-based engineering design problems.     

A double generally weighted moving average exceedance control chart

Since the inception of control charts by W. A. Shewhart in the 1920s, they have been increasingly applied in various fields. The recent literature witnessed the development of a number of nonparametric (distribution‐free) charts as they provide a robust and efficient alternative when there is a lack of knowledge about the underlying process distribution. In order to monitor the process location, information regarding the in‐control (IC) process median is typically required. However, in practice, this information might not be available due to various reasons. To this end, a generalized type of nonparametric time‐weighted control chart labeled as the double generally weighted moving average (DGWMA) based on the exceedance statistic (EX) is proposed. The DGWMA‐EX chart includes many of the well‐known existing time‐weighted control charts as special or limiting cases for detecting a shift in the unknown location parameter of a continuous distribution. The DGWMA‐EX chart combines the better shift detection properties of a DGWMA chart with the robust IC performance of a nonparametric chart, by using all the information from the start until the most recent sample to decide if a process is IC or out‐of‐control. An extensive simulation study reveals that the proposed DGWMA‐EX chart, in many cases, outperforms its counterparts.     

The variable sampling interval X̄ chart with estimated parameters

The VSI chart has been investigated by many researchers under the assumption of known process parameters. However, in practice, these parameters are usually unknown and it is necessary to estimate them from the past data. In this paper, we evaluate and compare the performance of the VSI chart in terms of its average time to signal in the case where the process parameters are known and in the case where these parameters are estimated. We also provide new chart constants taking into account the number of phase I samples. Copyright © 2011 John Wiley & Sons, Ltd.     

A new nonparametric double exponentially weighted moving average control chart

There are many practical situations where the underlying distribution of the quality characteristic either deviates from normality or it is unknown. In such cases, practitioners often make use of the nonparametric control charts. In this paper, a new nonparametric double exponentially weighted moving average control chart on the basis of the signed-rank statistic is proposed for monitoring the process location. Monte Carlo simulations are carried out to obtain the run length characteristics of the proposed chart. The performance comparison of the proposed chart with the existing parametric and nonparametric control charts is made by using various performance metrics of the run length distribution. The comparison showed the superiority of the suggested chart over its existing parametric and nonparametric counterparts. An illustrative example for the practical implementation of the proposed chart is also provided by using the industrial data set.     

Adaptive multivariate double sampling and variable sampling interval Hotelling's T2 charts

In this article, two adaptive multivariate charts, which combine the double sampling (DS) and variable sampling interval (VSI) features, called the adaptive multivariate double sampling variable sampling interval T² (AMDSVSI T²) and the adaptive multivariate double sampling variable sampling interval combined T² (AMDSVSIC T²) charts, are proposed. The real purpose of using the proposed charts is to provide flexibility by enabling the sampling interval length of the DS T² chart to be varied so that the chart's sensitivity can be enhanced. The fundamental difference between the two proposed charts is that when a second sample is taken, the AMDSVSI T² chart uses the information of the combined sample mean vectors while the AMDSVSIC T² chart uses the information of the combined T² statistics, in deciding about the process status. This research is motivated by existing combined DS and VSI charts in the literature, which show convincing performance improvement over the standard DS chart. Consequently, it is believed that adopting this existing approach in the multivariate case will enable superior multivariate DS charts to be proposed. Numerical results show that the proposed charts outperform the existing standard T² and other adaptive multivariate charts, in detecting shifts in the mean vector, for the zero‐state and steady‐state cases. The performances of both charts when the shift sizes in the mean vector are unknown are also measured. The application of the AMDSVSI T² chart is illustrated with an example.     

An efficient double exponentially weighted moving average Benjamini‐Hochberg control chart to control false discovery rate

A control chart based on double exponentially weighted moving average and Benjamini‐Hochberg multiple testing procedure is proposed that controls the false discovery rate (FDR). The proposed control chart is based on probabilities (or P values) to accept or reject the null hypothesis of the underlying process is in control. To make a decision, instead of using only the current probability, previous “m” probabilities are considered. The performance of the control chart is evaluated in terms of average run length (ARL) using Monte Carlo simulations. Procedure for estimation of parameters used in the control chart is also discussed. The proposed control chart is compared with previous control charts and found to be more efficient in controlling the false discovery rate.