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The purpose of this paper is to present an economic–statistical design (ESD) for the Bayesian X‾ control chart based on predictive distribution with two types of informative and noninformative prior distributions.

The design used in this study is based on determining the control chart of the predictive distribution and then its ESD. The new proposed cost model is presented by considering the conjugate and Jeffrey's prior distribution in calculating the expected total cycle time and expected cost per cycle, and finally, the optimal design parameters and related costs are compared with the fixed ratio sampling (FRS) mode.

Numerical results show decreases in costs in this Bayesian approach with both Jeffrey's and conjugate prior distribution compared to the FRS mode. This result shows that the Bayesian approach which is based on predictive density works better than the classical approach. Also, for the Bayesian approach, however, there is no significant difference between the results of using Jeffrey's and conjugate prior distributions. Using sensitivity analysis, the effect of cost parameters and shock model parameters and deviation from the mean on the optimal values of design parameters and related costs have been investigated and discussed.

This research adds to the body of knowledge related to quality control of process monitoring systems. This paper may be of particular interest to quality system practitioners for whom the effect of the prior distribution of parameters on the quality characteristic distribution is important.

economic statistical design (ESD) of Bayesian control charts based on predictive distribution is presented for the first time.

The search of the optimal economic design of the Bayesian adaptive control charts for finite production runs can be a long and tedious procedure due to the intrinsic structure of the optimization problem, which requires a dynamic programming approach to select the best decision at each sampling epoch during the production horizon of the process. This paper aims to propose a new efficient procedure implementing a genetic algorithm neighbourhood search scheme embedded within the dynamic programming procedure with the aim of reducing the computational burden and achieving significant cost savings in the chart implementation.

The efficiency of the developed procedure has been verified through a comparison with another existing exhaustive approach working exclusively on one‐sided X¯ Bayesian control charts; then, it has been extended to the design of two‐sided Bayesian control charts.

The proposed procedure implementing the genetic algorithm neighbourhood search is very fast and efficient in detecting optimal solutions: it allows significant quality control cost savings to be achieved during the Bayesian charts implementation thanks to the possibility of investigating larger spaces of decisions than the existing optimization procedures.

With reference to discrete part manufacturing, where the assumption of finite production runs is often realistic, the design and implementation of adaptive Bayesian control charts by means of the proposed procedure allows significant cost savings to be achieved with respect to the fixed parameters Shewhart charts.

The exhaustive optimization procedure cannot be executed in a reasonable computational time when the space of decisions to select Bayesian chart design parameters significantly enlarges, which is the case of two‐sided control charts. The paper documents the proposed procedure which overcomes this problem and allows the two‐sided Bayesian chart to be designed and proposed as an efficient means to monitor short production runs.

Bayesian networks (BNs) are implemented for monitoring a process via statistical process control (SPC) where attribute data are available on output from the system. The paper aims to discuss this issue.

The BN provides a graphical and numerical tool to help a manager understand the effect of sample observations on the probability that the process is out-of-control and requires investigation. The parameters for the BN SPC model are statistically designed to minimize the out-of-control average run length (ARL) of the process at a specified in-control ARL and sample size.

The BN model outperforms adaptive np control charts in all experiments, except for some cases where only a large change in the proportion of sample defects is relevant. The BN is particularly useful when small sample sizes are available and when managers need to detect small changes in the proportion of defects produced by the process.

The BN model is statistically designed and parameters are chosen to minimize out-of-control ARL. Future advancements will address the economic design of BNs for SPC with attribute data.

The BNs allow qualitative knowledge to be combined with sample data, and the average percentage of defects can be modeled as a continuous random variable. The framework of the BN easily permits classification of the system operation into two or more states, so diagnostic analysis can be performed simultaneously with statistical inference.

Discusses the problem of the joint determination of the parameters for X and R control charts. A simple heuristic, called a power approximation, is presented. The power approximation is based on three regression equations which are used to estimate the sample size and the control limits for the X chart and the R chart. Thereafter, some developments and discussion about the proposed power approximation are presented and the method’s performance is tested and assessed using a set of problems previously studied in various scientific publications, and also using a specific set of data from a previously published study.

This chapter proposes semiparametric estimation of the relationship between growth rate of GDP per capita, growth rates of physical and human capital, labor as well as other covariates and common trends for a panel of 23 OECD countries observed over the period 1971–2015. The observed differentiated behaviors by country reveal strong heterogeneity. This is the motivation behind using a mixed fixed- and random coefficients model to estimate this relationship. In particular, this chapter uses a semiparametric specification with random intercepts and slopes coefficients. Motivated by Lee and Wand (2016), the authors estimate a mean field variational Bayes semiparametric model with random coefficients for this panel of countries. Results reveal nonparametric specifications for the common trends. The use of this flexible methodology may enrich the empirical growth literature underlining a large diversity of responses across variables and countries.

The purpose of this paper is to develop a cost model by the variable sampling interval and optimization of the average cost per unit of time. The paper considers an economic–statistical design of the X̅ control charts under the Burr shock model and multiple assignable causes were considered and compared with three types of prior distribution for the mean shift parameter.

The design of the modified X̅ chart is based on the two new concepts of adjusted average time to signal and average number of false alarms for X̅ control chart under Burr XII shock model with multiple assignable causes.

The cost model was examined through a numerical example, with the same cost and time parameters, so the optimal of design parameters were obtained under uniform and non-uniform sampling schemes. Furthermore, a sensitivity analysis was conducted in a way that the variability of loss cost and design parameters was evaluated supporting the changes of cost, time and Burr XII distribution parameters.

The economic–statistical model scheme of X̅ chart was developed for the Burr XII distributed with multiple assignable causes. The correlated data are among the assumptions to be examined. Moreover, the optimal schemes for the economic-statistic chart can be expanded for correlated observation and continuous process.

The economic–statistical design of control charts depends on the process shock model distribution and due to difficulties from both theoretical and practical aspects; one of the proper alternatives may be the Burr XII distribution which is quite flexible. Yet, in Burr distribution context, only one assignable cause model was considered where more realistic approach may be to consider multiple assignable causes.

This study presents an advanced theoretical model for cost model that improved the shock model that presented in the literature. The study obviously indicates important evidence to justify the implementation of cost models in a real-life industry.

Explains that the shifts of a process may be classified into a set of modes (or classifications), each of which is incurred by an assignable cause. Presents an algorithm to determine the process shift mode and estimate the run length when an out‐of‐control status is signalled by the x‐ or s chart in statistical process control. The information regarding the process shift mode and run length is very useful for diagnosing the assignable cause correctly and promptly. The algorithm includes two stages. First, the process shift modes are established using the sample data acquired during an explorative run. Afterwards, whenever an out‐of‐control case is detected, Bayes’ rule is employed to determine the active process shift mode and estimate the run length. In simulation tests, the proposed algorithm attains a fairly high probability (around 0.85) of correctly determining the active process shift mode and estimating the run length.

The purpose of this paper is to develop an extensive economic production quantity (EPQ) model on the basis of previous research. Considering an imperfect three‐state production process, this paper makes contributions to an integrated model combining conceptions of quality loss and design of control chart based on EPQ model. The objective is to minimize the total production cost with the determination of EPQ and design parameters of control chart subjected to quality loss and other process costs.

In this paper, imperfect process is defined as a three‐state process, and the quality cost corresponding to each state contributes to the eventual total expected cost formulation. Control chart is used to monitor the shift from the target value within whole process and its control limits are set to be related to the quality cost.

The proposed integrated model conforms more closely to the real situation of production process considering the process shift as a random variable.

Numerical computation and sensitivity analysis through a case study are presented to demonstrate the applications of the model.

Few research efforts investigate an integrated model considering EPQ, control chart and quality loss simultaneously. In particular, compared with the former researches, the process shift, due to which the quality cost incurs, is considered as a random variable in this paper.

Quality control charts are statistical process control tools aimed at monitoring a (manufacturing) process to detect any deviations from normal operation and to aid in process diagnosis and correction. The information presented on the chart is a key to the successful implementation of a quality process correction system. Pattern recognition methodology has been pursued to identify unnatural behaviour on quality control charts. This approach provides the ability to utilize patterning information of the chart and to track back the root causes of process deviation, thus facilitating process diagnosis and maintenance. Presents analysis and development of a statistical pattern recognition system for the explicit identification of unnatural patterns on control charts. Develops a set of statistical pattern recognizers based on the likelihood ratio approach and on correlation analysis. Designs and implements a training algorithm to maximize the probability of identifying unnatural patterns, and presents a classification procedure for real‐time operation. Demonstrates the system performance using a set of newly defined measures, and obtained results based on extensive experiments illustrate the power and usefulness of the statistical approach for automating unnatural pattern detection on control charts.

The purpose of this paper is to study the effect of correlation on the performance of CUSUM and EWMA charts. The performance of the CUSUM and EWMA charts is measured in terms of average run lengths (ARLs) for the positively correlated data. The ARLs at various set of parameters of the CUSUM and EWMA charts are computed, using MATLAB. The behavior of the CUSUM and EWMA chart at the various shifts in the process mean is studied, analyzed and compared at different levels of correlation (Φ). The optimum schemes for both the charts are suggested for various levels of correlation (Φ).

Positively correlated observations having normal distribution are generated with the help of the MATLAB. Performance of both the charts in terms of ARLs is measured and compared at various levels of correlation (Φ). The optimal schemes of charts which give the desired in‐control ARLs are suggested for various levels of correlation (Φ).

For each level of correlation (Φ) various schemes of both the charts are suggested. Moreover those suggested schemes which give quick response to the shifts in the process mean is termed as optimal scheme. It is concluded that CUSUM schemes are preferred as compared to the EWMA schemes for quicker response. The optimal schemes of CUSUM and EWMA chart are also compared with the EWMAST chart suggested by Winkel and Zhang (2004).

Both the schemes are optimized by assuming the autocorrelated numbers to be normally distributed. But this assumption may also be relaxed to design these schemes for autocorrelated data. Moreover sample size of four is taken while developing these schemes; various other schemes can also be developed for different sample sizes. Control charts for attribute type of data can also be developed for different level of correlation (Φ).

For a specific control chart, if the in‐control ARL of the process outputs of any industry is in accordance with the simulated in‐control ARL. It means the process outputs must have same level of correlation (Φ) corresponding to the simulated in‐control ARL and the suggested optimal schemes, corresponding to that level of correlation (Φ), must be adopted to avoid the false alarm rate. 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. Thus false alarms generated, will be minimum for the suggested schemes at different level of correlation (Φ).

If the optimal CUSUM schemes are employed in process/service industry, there will be a considerable amount of saving in time and money expended in search of causes behind frequent false alarms. 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.

The research findings could be applied to various manufacturing industries as well as service industries where the data is positively correlated and normally distributed.