Double Sampling Chart Research Articles

The Modified Double Sampling Coefficient of Variation Control Chart

The concept of monitoring the coefficient of variation has gained significant interest in quality control, particularly in situations where the mean and standard deviation of a process are not constant. This study modified the procedure of the previous double sampling chart for monitoring the coefficient of variation, developed by Ng et al. in 2018. Instead of using only information from the second sample, here, information from both samples is used. The probability properties of the out-of-control signal and run length of this chart are presented. To evaluate the chart’s performance, the optimal design and a comparison with the previous double sampling control chart using average run-length criteria are described. It was found that the modified double sampling chart has better performance and is more efficient compared to the previous chart, especially when the total sample size is smaller. As a study case, the application of this chart is illustrated using real data from a molding process. This confirmed that the modified double sampling chart improved performance in detecting out-of-control signals. Thus, the modified chart is recommended to be applied in industry.

Monitoring the process mean with an ATTRIVAR chart

In this article, we propose an ATTRIVAR chart to control the process mean. With the ATTRIVAR chart, the sampling is performed in two stages, collecting attribute and variable sample data from the same sample (attribute plus variable data – ATTRIVAR). That is, if the first m items of the sample fail to pass the go gauge test, or they pass the no-go gauge test, the sampling moves on to stage two, where the quality characteristic X of the first m and the remaining n-m items of the sample is measured. Otherwise, the sampling is interrupted and the process is declared to be in control. The number of tested items, if one, or two, or as many as m, is only known after the completion of the first stage. At the second stage, the value is computed and used to decide the state of the process. It is worthwhile to stress that the go/no-go gauge test truncates the X distribution and, because of that, the mathematical development to obtain the distribution is not trivial. The ATTRIVAR chart signals faster than the Double Sampling chart and, more important than that, it is simpler to use because the go/no-go gauge test reduces the frequency with which the quality characteristic X of the sample items is measured. The ATTRIVAR chart is also faster and simpler than the mixed chart. With the mixed chart, the sampling is also performed in two stages; the difference is that all items of the sample are always submitted to the go/no-go gauge test before deciding to go to stage two, where the value is computed.

Modified Double Sampling Control Chart for Monitoring The Coefficient of Variation

Monitoring the coefficient of variation (CV) has received wide attention in quality control, mainly used when the process mean and standard deviation are not constant. This work proposes a modified Double Sampling (DS) chart for monitoring the CV, denoted DS-G chart, in order to improve the sensitivity of previous DS chart for monitoring the CV, denoted DS-γ chart. Some numerical results for statistical properties of the proposed chart and performance comparisons are provided in the form of tables. Based on the average number of observation to signal (ANOS) performance, the proposed DS-G chart outperforms the DS-γ chart.

A new double sampling control chart for monitoring an abrupt change in the process location

This paper develops a new double sampling (DS) monitoring scheme, namely, the side-sensitive DS chart, to monitor the process mean. The operational procedure is presented first followed by the exact form of the probability of the in-control process under the normality assumption. Finally, the performance of the new scheme is investigated by minimizing the out-of-control average run-length and extra quadratic loss function. It was observed that the proposed chart presents a better overall performance than the existing DS chart. An illustrative example is given to facilitate the design and implementation of the new chart.

Performance of Synthetic Double Sampling Chart with Estimated Parameters Based on Expected Average Run Length

A synthetic double sampling (SDS) chart is commonly evaluated based on the assumption that process parameters (namely, mean and standard deviation) are known. However, the process parameters are usually unknown and must be estimated from an in-control Phase-I dataset. This will lead to deterioration in the performance of a control chart. The average run length (ARL) has been implemented as the common performance measure in process monitoring of the SDS chart. Computation of ARL requires practitioners to determine shift size in advance. However, this requirement is too restricted as practitioners may not have the experience to specify the shift size in advance. Thus, the expected average run length (EARL) is introduced to assess the performance of the SDS chart when the shift size is random. In this paper, the SDS chart, with known and estimated process parameters, was evaluated based on EARL and compared with the performance measure, ARL.

The economic and economic statistical designs of synthetic double sampling chart

ABSTRACTThe purpose of this paper is to investigate the economic and economic statistical designs of the synthetic double sampling (DS) chart. The optimal design parameters for the economic design are determined such that the cost is minimized for the given cost model parameters. For the economic statistical design, the cost is minimized subject to statistical constraint. The numerical comparison demonstrates that the synthetic DS chart is economically superior to the synthetic and DS charts. A sensitivity analysis is conducted to study the effect of the cost model parameters on the solution for the economic statistical design.

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

AbstractIn 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.

A new double sampling control chart for monitoring process mean using auxiliary information

ABSTRACTStatistical quality control charts have been widely accepted as a potentially powerful process monitoring tool because of their excellent speed in tracking shifts in the underlying process parameter(s). In recent studies, auxiliary-information-based (AIB) control charts have shown superior run length performances than those constructed without using it. In this paper, a new double sampling (DS) control chart is constructed whose plotting-statistics requires information on the study variable and on any correlated auxiliary variable for efficiently monitoring the process mean, namely AIB DS chart. The AIB DS chart also encompasses the classical DS chart. We discuss in detail the construction, optimal design, run length profiles, and the performance evaluations of the proposed chart. It turns out that the AIB DS chart performs uniformly better than the DS chart when detecting different kinds of shifts in the process mean. It is also more sensitive than the classical synthetic and AIB synthetic charts when detecting a particular shift in the process mean. Moreover, with some realistic beliefs, the proposed chart outperforms the exponentially weighted moving average chart. An illustrative example is also presented to explain the working and implementation of the proposed chart.

The double sampling range chart

AbstractThe 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.

와이블 고장모형 하에서의 이중샘플링 T<sup>2</sup> 관리도의 경제적-통계적 설계 (이중샘플링 T<sup>2</sup> 관리도의 경제적-통계적 설계)

Purpose: Double sampling   chart is a useful tool for detecting a relatively small shift in process mean when the process is controlled by multiple variables. This paper finds the optimal design of the double sampling   chart in both economical and statistical sense under Weibull failure model. Methods: The expected cost function is mathematically derived using recursive equation approach. The optimal designs are found using a genetic algorithm for numerical examples and compared to those of single sampling   chart. Sensitivity analysis is performed to see the parameter effects. Results: The proposed design outperforms the optimal design of the single sampling   chart in terms of the expected cost per unit time and Type-I error rate for all the numerical examples considered. Conclusion: Double sampling   chart can be designed to satisfy both economic and statistical requirements under Weibull failure model and the resulting design is better than the single sampling counterpart.

Modified chart with optimized ARLs in autocorrelated processes

Purpose – The purpose of this paper is to counter autocorrelation by designing the chart, using warning limits. Various optimal schemes of modified chart are proposed for various sample sizes (n) at levels of correlation (Φ) of 0.00, 0.475 and 0.95. These optimal schemes of modified chart are compared with the double sampling (DS) chart, suggested by Costa and Claro (2008). Design/methodology/approach – The performance of the chart is measured in terms of the average run length (ARL) that is the average number of samples before getting an out-of-control signal. Ultimately, due to the effect of autocorrelation among the data, the performance of the chart is suspected. The ARLs at various sets of parameters of the chart are computed by simulation, using MATLAB. The suggested optimal schemes are simpler schemes with limited number of parameters and smaller sample size (n=4) and this simplicity makes them very helpful in quality control. Findings – The suggested optimal schemes of modified chart are compared with the DS chart, suggested by Costa and Claro (2008). It is concluded that the modified chart outperforms the DS chart at various levels of correlation (Φ) and shifts in the process mean. The simplicity in the design of modified chart, makes it versatile for many industries. Research limitations/implications – Both the schemes are optimized by assuming the normal distribution. But this assumption may also be relaxed to design theses schemes for autocorrelated data. The optimal schemes for chart can be developed for variable sample size and for variable sampling intervals. The optimal schemes can also be explored for cumulative sum and exponentially weighted moving average charts. Practical implications – The correlation among the process outputs of any industry can be find out and corresponding to that level of correlation the suggested control chart parameters can be applied. The understandable and robust design of modified chart makes it usable for industrial quality control. Social implications – The rejection level of products in the industries can be reduced by designing the better control chart schemes which will also reduce the loss to the society, as suggested by Taguchi (1985). Originality/value – Although it is the extension of previous work but it can be applied to various manufacturing industries as well as service industries, where the data are positively correlated and normally distributed.

Extending a double sampling control chart for non-conforming proportion in high quality processes to the case of small samples

When production processes reach high quality standards they are known as high quality processes. In this situation, the conventional p charts (based on 3-sigma limits) used for monitoring non-conforming products have serious drawbacks in detecting changes in p due to excess of false alarm risk. In a previous paper, the authors showed a new p chart that provides a large improvement over the usual p chart in these situations. In this paper, authors propose a new corrected version of a double sampling (DS) control chart for monitoring the proportion p of non-conforming presented in the literature for large samples, in order to extend its applicability to the case of small samples. This procedure offers better statistical efficiency (in terms of the average run length) than the previous p charts, without increasing the sampling. Tables are provided to aid in the choice of DS parameters. The benefits of the corrected version of a DS chart for monitoring high-quality processes are illustrated with real data.

The steady‐state behavior of the synthetic and side‐sensitive synthetic double sampling charts

The steady‐state average run length is used to measure the performance of the recently proposed synthetic double sampling chart (synthetic DS chart). The overall performance of the DS chart in signaling process mean shifts of different magnitudes does not improve when it is integrated with the conforming run length chart, except when the integrated charts are designed to offer very high protection against false alarms, and the use of large samples is prohibitive. The synthetic chart signals when a second point falls beyond the control limits, no matter whether one of them falls above the centerline and the other falls below it; with the side‐sensitive feature, the synthetic chart does not signal when they fall on opposite sides of the centerline. We also investigated the steady‐state average run length of the side‐sensitive synthetic DS chart. With the side‐sensitive feature, the overall performance of the synthetic DS chart improves, but not enough to outperform the non‐synthetic DS chart. Copyright © 2014 John Wiley & Sons, Ltd.

Statistical design of <span style="text-decoration: overline">X</span> charts for autocorrelated processes for different sample sizes

The charts for variables are widely used in industries to detect the shift in the process mean. As in actual practice, some process outputs are correlated and conventional charts may not be effective in such situation. The performance of the chart is measured in terms of the average run length (ARL) that is the average number of samples before getting an out-of-control signal. Ultimately the performance of the chart is suspected due to the effect of correlation. The ARLs at various sets of parameters of the chart are computed by simulation, using MATLAB. An attempt has been made to counter autocorrelation by designing the chart, using warning limits. Various optimal schemes of modified chart are proposed for various sample sizes (n) at the levels of correlation (Φ) of 0.00, 0.475 and 0.95. These optimal schemes of modified chart are compared with the double sampling (DS) chart, suggested by Costa and Claro (2008). It is concluded that the modified chart outperforms the DS chart at various levels of correlation (Φ) and shifts in the process mean. The simplicity in the design of modified chart makes it versatile for many industries.

Adaptive Max charts for monitoring process mean and variability

Max chart uses a single chart to control the process mean and variance. It performs with similar efficiency to joint and s charts. This study combined adaptive chart and Max chart to increase the detecting ability. A Markov chain approach was used to develop the statistical indicator and statistical design model of adaptive Max charts. This study designed adaptive Max charts to detect the mean shift and variance increase, and measured their performance for comparison with EWMA, CUSUM, and double-sampling charts. A comparison study revealed that the adaptive Max charts with variable parameter exhibited superior performance to detect the small shift than that of EWMA, CUSUM, and double sampling charts.

A synthetic double sampling control chart for the process mean

This article proposes a synthetic double sampling chart that integrates the Double Sampling (DS) chart and the conforming run length chart. The proposed procedure offers performance improvements in terms of the zero-state Average Run Length (ARL) and Average Number of Observations to Sample (ANOS). When the size of a mean shift δ (given in terms of the number of standard deviation units) is small (i.e., between 0.4 and 0.6) and the mean sample size n= 5, the proposed procedure reduces the out-of-control ARL and ANOS values by nearly half, compared with both the synthetic and DS charts. In terms of detection ability versus the Exponentially Weighted Moving Average (EWMA) chart, the synthetic DS chart is superior to the synthetic or even the DS chart, as the former outperforms the EWMA chart for a larger range of δ values compared to the latter. The proposed procedure generally outperforms the EWMA chart in the detection of a mean shift when δ is larger than 0.5 and n= 5 or 10. Although the proposed procedure is less sensitive than the EWMA chart when δ is smaller than 0.5, this may not be a setback as it is usually not desirable, from a practical viewpoint, to signal very small shifts in the process to avoid too frequent process interruptions. Instead, under such circumstances, it is better to leave the process undisturbed.

Non-normality and combined double sampling and variable sampling interval control charts

A combination of double sampling the chart and the variable sampling interval of the chart (DSVSI chart) increases the sensitivity in the small shift detection. A usual assumption of control charts is that the process observations are normally distributed. However, this assumption may not be true for some processes in the real industry. This paper presented the performance of DSVSI chart under non-normality and compared it with the Shewhart chart and the variable parameters chart. The compared results show that the DSVSI chart has the best performance in detecting small process mean shifts.

The Performance of Double Sampling Control Charts Under Non Normality

In this study, the performances of double sampling (DS) chart under non normality are presented and compared with Shewhart chart and VP chart. The comparison result shows the DS chart has performance as good as the VP chart, but it is more effective than the Shewhart chart in detecting small process mean shifts.

Double sampling control chart for a first order autoregressive process

In this paper we propose the Double Sampling control chart for monitoring processes in which the observations follow a first order autoregressive model. We consider sampling intervals that are sufficiently long to meet the rational subgroup concept. The Double Sampling chart is substantially more efficient than the Shewhart chart and the Variable Sample Size chart. To study the properties of these charts we derived closed-form expressions for the average run length (ARL) taking into account the within-subgroup correlation. Numerical results show that this correlation has a significant impact on the chart properties.

Joint statistical design of double sampling [formula omitted] and s charts

In statistical quality control, usually the mean and variance of a manufacturing process are monitored jointly by two statistical control charts, e.g., a X ¯ chart and a R chart. Because of the efficiency of double sampling (DS) X ¯ charts in detecting shifts in process mean and DS s charts in process standard deviation it seems reasonable to investigate the joint DS X ¯ and s charts for statistical quality control. In this paper, a joint DS X ¯ and s chart scheme is proposed. The statistical design of the joint DS X ¯ and s charts is defined and formulated as an optimization problem and solved using a genetic algorithm. The performance of the joint DS X ¯ and s charts is also investigated. The results of the investigation indicate that the joint DS X ¯ and s charts offer a better statistical efficiency in terms of average run length (ARL) than combined EWMA and CUSUM schemes, omnibus EWMA scheme over certain shift ranges when all schemes are optimized to detect certain shifts. In comparison with the joint standard, two-stage samplings and variable sampling size X ¯ and R charts, the joint DS charts offer a better statistical efficiency for all ranges of the shifts.