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This paper presents economic and economic–statistical designs of the adaptive exponentially weighted moving average (AEWMA) control chart for monitoring the process mean. It also aims to compare the effect of estimated process parameters on the economic performance of three charts, which are Shewhart, exponentially weighted moving average and AEWMA control charts with economic–statistical design.

The optimal parameters of the control charts are obtained by applying the Lorenzen and Vance’s (1986) cost function. Comparisons between the economic–statistical and economic designs of the AEWMA control chart in terms of expected cost and statistical measures are performed. Also, comparisons are made between the economic performance of the three competing charts in terms of the average expected cost and standard deviation of expected cost.

This paper concludes that taking into account the economic factors and statistical properties in designing the AEWMA control chart leads to a slight increase in cost but in return the improvement in the statistical performance is substantial. In addition, under the estimated parameters case, the comparisons reveal that from the economic point of view the AEWMA chart is the most efficient chart when detecting shifts of different sizes.

The importance of the study stems from designing the AEWMA chart from both economic and statistical points of view because it has not been tackled before. In addition, this paper contributes to the literature by studying the effect of the estimated parameters on the performance of control charts with economic–statistical design.

An economic statistical design approach takes statistical properties into account while designing control charts economically. It improves both statistical design and economic design. In this paper, we present a statistically constrained economic model for the optimal design of S control chart for controlling process variability. In the model, the process quality can be affected by an assignable cause resulting in a shift of the variance of the distribution of output when it is operating according to its capability. The parameters are obtained by minimizing a total cost function proposed by Lorenzen and Vance, which is embellished with Taguchi loss function, subject to additional statistical constraints on average run length or average time‐to‐signal (ATS). Sensitivity analysis of the minimum cost will be performed to depict the effect of the choice of ATS bounds.

The purpose of this paper is to investigate the economic‐statistical design of EWMA charts with variable sampling intervals (VSIs) under non‐normality to reduce the process production cycle cost and improve the statistical performance of control charts. The objective is to minimize the cost function by adjusting the control chart parameters which suffice for the statistical restriction.

First, using the Burr distribution to approximate various non‐normal distributions, the economic‐statistical model of the VSI EWMA charts under non‐normality can be developed. Further, the genetic algorithms will be used to search for the optimal values of parameters of the VSI EWMA charts under non‐normality. Finally, a sensitivity analysis is carried out to investigate the effect of model parameters and statistical restriction on the solution of the economic‐statistical design.

The result of sensitivity analysis shows that a large lower bound of average time to signal when the process is in control increases the control limit coefficient, no model parameter significantly affects the short sampling intervals, and so on.

The economic‐statistical design method proposed in this paper can improve the statistical performance of economic design of control charts and the general idea can be applied to other VSI control charts.

The purpose of this paper is to develop a double-objective economic statistical design (ESD) of (X ‾) control chart under Weibull failure properties with the Linex asymmetric loss function. The authors have expressed the probability of type II error (β) as the statistical objective and the expected cost as the economic objective.

The design used in this study is based on a double-objective economic statistical design of (X ‾) control chart with Weibull shock model via applying Banerjee and Rahim's model for non-uniform and uniform schemes with Linex asymmetric loss function. The results in the least average cost and β in uniform and non-uniform schemes by Linex loss function, compared with the same schemes without loss function.

Numerical results indicate that it is not possible to reduce the second type of error and costs at the same time, which means that by reducing the second type of error, the cost increases, and by reducing the cost, the second type of error increases, both of which are very important. Obtained based on the needs of the industry and which one has more priority has the right to choose. These designs define a Pareto optimal front of solutions that increase the flexibility and adaptability of the X ‾ control chart in practice. When the authors use non-uniform schemes instead of uniform schemes, the average cost per unit time decreases by an average and when the authors apply loss function, the average cost per unit time increases by an average. Also, this quantity for double-objective schemes with loss function compared to without loss function schemes in cases uniform and non-uniform increases. The reason for this result is that the model underestimated the costs before using the loss function.

This research adds to the body of knowledge related to flexibility in process quality control. This article may be of interest to quality systems experts in factories where the choice between cost reduction and statistical factor reduction can affect the production process.

The cost functions for double-objective uniform and non-uniform sampling schemes with the Weibull shock model based on the Linex loss function are presented for the first time.

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.

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 aim of this study is to present the economic‐statistical design of an EWMA control chart for monitoring the process dispersion.

The optimal economic‐statistical design of the S EWMA chart was determined for a wide benchmark of examples organized as a two level factorial design and was compared with the designs obtained for the S Shewhart chart. Both the two charts have been designed so that an equal number of false alarms (in‐control Average Run Length) is expected.

The S EWMA allows significant hourly cost savings to be achieved for the entire set of process scenarios with respect to the S Shewhart; a mean percentage cost saving of 6.77 per cent is obtained for processes characterized by a reduction in process dispersion (i.e. processes whose natural variability is reduced through an external technological intervention), whereas up to a 9.78 per cent saving is achieved for processes whose dispersion is increased by the occurrence of an undesired special cause.

The proposed S EWMA chart can be considered as an effective tool when statistical process control procedures should be implemented on a process with the aim of monitoring its data dispersion.

In literature the economic design of EWMA charts covers only the process cost evaluation when the sample mean is monitored; here, the study is extended to the sample standard deviation to investigate if the EWMA scheme still outperforms the Shewhart chart. An extensive analysis is proposed to evaluate the influence of the process operating parameters on the EWMA chart design variables.

Control charts are important tools of statistical quality control. In 1956, Duncan first proposed the economic design of x‐control charts to control normal process means and insure that the economic design control chart actually has a lower cost, compared with a Shewhart control chart. An moving average (MA) control chart is more effective than a Shewhart control chart in detecting small process shifts and is considered by some to be simpler to implement than the CUSUM. An economic design of MA control chart has also been proposed in 2005. The weaknesses to only the economic design are poor statistics because it does not consider type I or type II errors and average time to signal when selecting design parameters for control chart. This paper provides a construction of an economic‐statistical model to determine the optimal parameters of an MA control chart to improve economic design. A numerical example is employed to demonstrate the model’s working and its sensitivity analysis is also provided.

The purpose of this paper is to make economic comparison of the proposed X¯ chart with the economic and economic‐statistical design of a multivariate exponentially weighted moving average (MEWMA) control chart proposed by Linderman and Love, using Lorenzen‐Vance cost model.

The economic design of proposed X¯ chart, using Lorenzen‐Vance cost model, is discussed in the paper. It is observed that sampling interval (h) and expected cost/hour (C) depend on various parameters of the chart, used in this model. When there is any change in any parameter of the chart, obviously both sampling interval and expected cost will be different. So it is suggested that one should use Lorenzen and Vance cost model (equation 1) to compute sampling interval and expected cost/hour for the proposed X¯ chart.

The economic design of the proposed X¯ chart has been compared with the economic and economic‐statistical design of the multivariate exponentially weighted moving average (MEWMA) control chart proposed by Linderman and Love. It is found that the proposed X¯ chart performs better than MEWMA chart proposed by Linderman and Love for sample sizes of 7, 9 and 10 for first set of parameters. The proposed X¯ chart also shows lower expected cost/hour than the MEWMA chart for sample size of 2 and 3 and for shifts of 2 and 3 for the second set of parameters.

A lot of effort has been made to develop the proposed X¯ chart for monitoring the process mean. Although optimal sampling intervals are calculated only for two sets of parameters for shifts in the process average of 1, 2 and 3, it can be computed for any set of parameters using the Lorenzen‐Vance cost model.

The research findings could be applied to various manufacturing and service industries, as it is more effective than the Shewhart and EWMA charts.

The purpose of this paper is to develop an economic statistical design based on the concepts of adjusted average time to signal (AATS) and ANF for X ¯ control chart under a Weibull shock model with multiple assignable causes.

The design used in this study is based on a multiple assignable causes cost model. The new proposed cost model is compared with the same cost and time parameters and optimal design parameters under uniform and non-uniform sampling schemes.

Numerical results indicate that the cost model with non-uniform sampling cost has a lower cost than that with uniform sampling. By using sensitivity analysis, the effect of changing fixed and variable parameters of time, cost and Weibull distribution parameters on the optimum values of design parameters and loss cost is examined and discussed.

This research adds to the body of knowledge relating to the quality control of process monitoring systems. This paper may be of particular interest to practitioners of quality systems in factories where multiple assignable causes affect the production process.

The cost functions for uniform and non-uniform sampling schemes are presented based on multiple assignable causes with AATS and ANF concepts for the first time.