A Modified \u3cem\u3eX̄\u3c/em\u3e Control Chart for Samples Drawn from Finite Populations

The X̄ chart works well under the assumption of random sampling from infinite populations. However, many process monitoring scenarios may consist of random sampling from finite populations. A modified X̄ chart is proposed in this article to solve the problems encountered by the standard X̄ chart when samples are drawn from finite populations

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

Characterisation and optimal design of a new double sampling c chart

[EN] This paper proposes a new double sampling scheme for c control chart (DS-c), which was designed to improve the performance of c chart or to reduce the inspection cost. The mathematical expression required to do an exact evaluation of ARL and ASN is deduced. Further, a bi-objective genetic algorithm is implemented to obtain the optimal design of the DS-c scheme. This optimisation is aimed to simultaneously minimising the error probability type II and the ASN, guaranteeing a desired level for the error probability type I. A performance comparison between the double sampling (DS), fixed parameters (FP), variable simple size (VSS) and exponential weighted moving average (EWMA) schemes for the c chart is carried out. The comparison shows that with the implementation of DS-c scheme is obtained a significant reduction of the out of control ARL with a lower ASN respect to FP and a better ARL profile than VSS and EWMA.Campuzano, MJ.; Carrión García, A.; Mosquera, J. (2019). Characterisation and optimal design of a new double sampling c chart. European J of Industrial Engineering. 13(6):775-793. https://doi.org/10.1504/EJIE.2019.104312S77579313

An Assorted Design for Joint Monitoring of Process Parameters: An Efficient Approach for Fuel Consumption

Due to high fuel consumption, we face the problem of not only the increased cost, but it also affects greenhouse gas emission. This paper presents an assorted approach for monitoring fuel consumption in trucks with the objective to minimize fuel consumption. We propose a control charting structure for joint monitoring of mean and dispersion parameters based on the well-known max approach. The proposed joint assorted chart is evaluated through various performance measures such as average run length, extra quadratic loss, performance comparison index, and relative average run length. The comparison of the proposed chart is carried out with existing control charts, including a combination of X and S, the maximum exponentially weighted moving average (Max-EWMA), combined mixed exponentially weighted moving average-cumulative sum (CMEC), maximum double exponentially weighted average (MDEWMA), and combined mixed double EWMA-CUSUM (CMDEC) charts. The implementation of the proposed chart is presented using real data regarding the monitoring of fuel consumption in trucks. The outcomes revealed that the joint assorted chart is very efficient to detect different kinds of shifts in process behaviors and has superior performance than its competitor charts.Deanship of Scientific Research, King Saud University, King Fahd University of Petroleum and MineralsScopu

STATISTICAL PROPERTIES AND SENSITIVITY OF A NEW ADAPTIVE SAMPLING METHOD FOR QUALITY CONTROL

We present a new adaptive sampling method for statistical quality control. In this method, called LSI (Laplace sampling intervals), we use the probability distribution function of the Laplace standard distribution to obtain the sampling instants, depending on a k parameter that allows control of sampling costs. Several algebraic expressions concerning the statistical properties of the LSI method are presented. We compare the LSI method with fixed sampling intervals (FSI) and variable sampling intervals (VSI) methods using a Shewhart X-bar control chart and evaluate the sensitivity of these sampling methods when the lower sampling interval is truncated. The results obtained show that the new method is a viable alternative in various critical contexts and situations

Th e Non-Central Chi-Square Chart with Double Sampling

In this article, we consider a non-central chi-square chart with double sampling (DS χ2 chart) to control the process mean and variance. As in the case of Shewhart control charts, samples of fi xed size are taken from the process at regular time intervals; however, the sampling is performed in two stages. Let X be the process quality variable being measured. During the fi rst stage, one item of the sample is inspected; if its X value is close to the target value of the process mean, then the sampling is interrupted. Otherwise, the sampling goes on to the second stage, where the remaining items are inspected and a non-central chi-square statistic, say T, is computed taking into account all n items of the sample, that is, their X values. A signal is triggered when the sample point given by the T value falls above the upper control limit of the proposed chart. The DS χ2 chart performs better than the joint X and R charts, except when there is a large change in the process mean. Furthermore, if the DS χ2 chart is used for monitoring diameters, volumes, weights, etc., then the employment of appropriate devices, such as go-no-go gauges can reduce the effort to decide if the sampling should go to the second stage or not

Adaptive EWMA Control Charts with a Time Varying Smoothing Parameter

It is known that time-weighted charts like EWMA or CUSUM are designed to be optimal to detect a specific shift. If they are designed to detect, for instance, a very small shift, they can be inefficient to detect moderate or large shifts. In the literature, several alternatives have been proposed to circumvent this limitation, like the use of control charts with variable parameters or adaptive control charts. This paper has as main goal to propose some adaptive EWMA control charts (AEWMA) based on the assessment of a potential misadjustment, which is translated into a time-varying smoothing parameter. The resulting control charts can be seen as a smooth combination between Shewhart and EWMA control charts that can be efficient for a wide range of shifts. Markov chain procedures are established to analyze and design the proposed charts. Comparisons with other adaptive and traditional control charts show the advantages of the proposals.Acknowledgements: financial support from the Spanish Ministry of Education and Science, research project ECO2012-38442

An Analysis of Shewhart Quality Control Charts to Monitor Both the Mean and Variability

When monitoring the mean of a continuous quality measure it is often recommended a separate chart be used to monitor the variability. These charts are traditionally designed separately. This project considers them together as a combined charting procedure and gives recommendations for their design. This is based on an average run length (ARL) analysis. The run length distribution is determined using two methods both based on a Markov chain approach

New Univariate Synthetic Double Sampling X And Multivariate Synthetic Double Sampling T2 Control Charts

This thesis proposes a univariate synthetic double sampling X control chart to monitor the mean of a univariate process and a multivariate synthetic double sampling 2 T control chart for monitoring the mean vector of a multivariate process. The proposed univariate chart integrates the conforming run length (CRL) chart and the double sampling (DS) X chart, while the proposed multivariate chart combines the CRL chart and the DS 2 T chart. Both the proposed univariate and multivariate charts are superior to their basic counterparts, namely the synthetic X and DS X charts for the univariate case, and the synthetic 2 T and DS 2 T charts for the multivariate case