Economic Design Of Control Charts Research Articles

Optimization of Design Parameters for X̄ Control Charts with Independent Multiple Assignable Causes Based on Continuous Flow Processes

The economic design of control charts depends on the process shock model distribution due to difficulties from both theoretical and practical aspects. This paper pursues to develop the economic design of [Formula: see text] control chart for monitoring continuous flow processes under Bur XII shock model. The Burr XII distribution is flexible and its hazard rate can take many forms like fixed, increasing, decreasing, single mode or even U-shaped. Continuous flow processes find applications in batch processes like filtration, chemical processing, and more. A sensitivity analysis is executed and numeric examples are given to illustrate the effects of changing the parameters of the shock model distribution on the optimum values of the economic design models as discussed in this paper.

An optimal economic design of control chart for correlated Poisson variables: The double-dimension LCP chart

This work proposes a control chart that uses a statistic that is a linear combination of Poisson variables considering the sampling methodology called Double Dimension. This proposal aims to reduce costs when the Poisson variables used in process monitoring are expensive or difficult to measure. Therefore, they are not measured every time the control is performed but only when there are indications that the process is out of control. A user-friendly program was developed to obtain the performance of this chart and estimate the parameters that optimize the out-of-control ARL (average run length) for a shift that the user wants to detect as quickly as possible, restricted to a fixed value of in-control ARL. In addition, numerical results are presented in different scenarios, which allows verifying the performance and sensitivity of the proposed methodology. The results show that implementing the double dimension methodology offers similar performance as always measuring the cheap and expensive variables but with significant sampling savings.

An Integrated Model of Maintenance Policies and Economic Design of X-bar Control Chart Under Burr XII Shock Model

The combination of different methods of maintenance and economic design of control charts has received much attention from researchers in recent years. These maintenance policies increase the reliability of a system. So far, only a small number of failure distributions, with fixed or increasing hazard rates, have been used as a shock model in the integrated model of maintenance and economic design of X-bar control chart. A proper alternative for this situation may be the Burr distribution, in which the hazard rate has general form. In this paper, for the economic design of the X-bar control chart under the Burr XII shock model, we have presented an integrated model using preventive maintenance and incomplete maintenance. The obtained integrated model has been implemented using a numerical example and its sensitivity analysis has been performed. The results show that, the use of higher maintenance levels causes further reduction of the average cost per unit time of the quality cycle. The results of sensitivity analysis also show that our proposed model is not sensitive to the misspecification of the Burr XII distribution parameters.

Robust economic design of NP-chart under different process and economic parameters scenarios

ABSTRACT Control charts are one of the most commonly used statistical process control (SPC) tools in industry or service sectors to improve quality and productivity. The control chart design of a particular process is a well-established and vibrant area of research. It considers the techniques that allow decision-makers to decide on the optimal values of the design parameters. However, these design techniques are not reliable in a dynamic production environment. In such cases, the Robust Economic Control Chart Design (RECCD) approach is more reliable because it considers all possible scenarios of model parameters. This paper aims to develop a RECCD model for np-chart design to mitigate the risks associated with the uncertainty in the economic and process parameters of the production environment. A case study from an automotive manufacturer is used, and sensitivity analysis is carried out to show the effectiveness of the RECCD technique for the np-chart design. It has been shown that the proposed approach can achieve a 45.56% reduction in the total cost compared to the traditional design.

Integration of Multivariate Loss Function Approach in the Hotelling’s Charts under Banerjee-Rahim (1988) Weibull Shock Models

A proper monitoring of stochastic systems is the control charts of statistical process control and drift in characteristics of output may be due to one or several assignable causes. Although many research works have been done on the economic design of control charts with single assignable cause, the economic statistical design of T^2 control chart under Weibull shock model with multiple assignable causes and considering multivariate Taguchi loss function has not been presented yet. Using Taguchi loss function in the concept of quality control charts with economic and economic statistical design leads to better decisions in the industry. Based on the optimization of the average cost per unit of time and taking into account the different combination values of Weibull distribution parameters, optimal design values ??of sample size, sampling interval and control limit coefficient were derived and calculated. Then the cost models under non-uniform and uniform sampling scheme were compared. The results revealed that the model under multiple assignable causes with Taguchi loss function has a lower cost than single assignable cause model and integrated model with non-uniform sampling has a lower cost than that with uniform sampling.

Economic Design of X̅ Control Chart under Double EWMA

Designing of parameters plays an important role in economic design of control charts for lowering the cost and time. Manipulating sample size (n) and sampling interval (h), the effect of double exponentially weighted moving average (DEWMA) model was studied for the Economic Design (ED) of X̅ control chart. Optimum sizes and level were obtained when the characteristics of an item possesses DEWMA model. When shifts are uncertain the optimal design for DEWMA chart should be more conservative and should be implemented for benefiting the consumers as well as producers.

Economic design of memory-type control charts: The fallacy of the formula proposed by Lorenzen and Vance (1986)

The memory-type control charts, such as EWMA and CUSUM, are powerful tools for detecting small quality changes in univariate and multivariate processes. Many papers on economic design of these control charts use the formula proposed by Lorenzen and Vance (1986) [Lorenzen, T. J., & Vance, L. C. (1986). The economic design of control charts: A unified approach. Technometrics, 28(1), 3-10, DOI: 10.2307/1269598]. This paper shows that this formula is not correct for memory-type control charts and its values can significantly deviate from the original values even if the ARL values used in this formula are accurately computed. Consequently, the use of this formula can result in charts that are not economically optimal. The formula is corrected for memory-type control charts, but unfortunately the modified formula is not a helpful tool from a computational perspective. We show that simulation-based optimization is a possible alternative method.

Constrained optimal design of Control Chart for correlated data under Weibull Shock Model with multiple assignable causes

An appropriate technique for monitoring a stochastic system is to utilize the control charts. In statistical process, control a drift in characteristics of output may be due to one or several assignable causes. In the establishment of charts in statistical process control, an assumption is made that there is no correlation within the samples. However, in practice there are many cases where the correlation does exist within the samples. It would be more appropriate to assume that each sample is a realization of a multivariate normal random vector. Although some research works have been done on the economic design of control charts with single assignable cause with correlated data, the economic statistical design of control chart under Weibull shock model with multiple assignable causes and correlated samples have not been presented yet. Based on the optimization of the average cost per unit of time and taking into account the different combination values of Weibull distribution parameters, optimal design values of sample size, sampling interval, and control limit coefficient were derived and calculated. Then the cost models under non-uniform and uniform sampling scheme were compared. The results revealed that the model under multiple assignable causes with correlated samples with non-uniform sampling has a lower cost than that with uniform sampling.

An economic statistical design of the Poisson EWMA control charts for monitoring nonconformities

ABSTRACTAn economic statistical model of the exponentially weighted moving average (EWMA) control chart for the average number of nonconformities in the sample is proposed. The statistical and economic performance of proposed design are evaluated using the average run length (ARL) and the hourly expected cost, respectively. A Markov chain approach is applied to derive expressions for ARL. The cost model is established based on the general cost function given in Lorenzen and Vance [The economic design of control charts: a unified approach. Technometrics. 1986;28:3–11]. An example is provided to illustrate the application of the proposed model. A sensitivity analysis is also carried out to investigate the effects of model parameters on the solution of the economic statistical design by using the design of experiments (DOE) technique.

Effect of Linex loss function on the VSIX̄ control chart

ABSTRACTThe concept of loss function has been combined, with a numerous statistical decision models which require quality cost estimation. Moreover, estimation of the costs of non-conforming product is one of the most important inputs in economic design of control charts. Therefore, on the basis of new Markov chain approach, this paper focused on extending control chart with variable sampling interval by considering the Linex and Taguchi loss functions. This study mainly differs from the others conducted in the field. In that a new approach is offered to achieve closed form of some statistical criteria. Using numerical example, we show that not only the control chart based on the Linex loss function can be more efficient than the control chart based on the Taguchi loss function in terms of the expected cost per hour, but also the percentage improvement in compared to is higher.

Statistically constrained economic design of control chart with Weibull in-control time for processes subject to multiple assignable causes

PurposeThe 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 control chart under a Weibull shock model with multiple assignable causes.Design/methodology/approachThe 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.FindingsNumerical 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.Practical implicationsThis 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.Originality/valueThe 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.

A generalized version of Ben-Daya-Rahim (2000) and Rahim-Banerjee (1993) cost models in economic design of X-control charts for systems with early replacement and preventive maintenance under decreasing integrated hazard

A remarkable deal of recent research in process management is devoted to combining the maintenance policies with statistical process control models such as optimal design of control charts. To optimize the design parameters (the sample size, the sampling intervals, the control limits coefficient, the maintenance level and the truncated time), Rahim and Banerjee and Ben-Daya and Rahim generalized cost models simplified the joint models of maintenance and economic design of control charts by assuming constant integrated hazard over sampling intervals. As an alternative to the constant approach, a decreasing integrated hazard procedure is applied in this paper for determining the inspection intervals as a conservative strategy along with increase in overall cost. A numerical study based on the -control chart with normal quality characteristic distribution and Weibull () shock model is provided to investigate the performance of this approach in comparison with the traditional one.

A joint determination of production cycle length, maintenance policy, and control chart parameters considering time value of money under stochastic shift size

Statistical process monitoring, maintenance policy, and production cycle length usually have been investigated separately while they are three dependent aspects in the industrial systems. Moreover, most of the papers that integrated simultaneously these aspects, suffer from three major drawbacks as follows: (1) Optimizing the production cost without considering the time value of money to simplify the model; (2) Considering the fixed shift size while it is a random variable in the real condition; (3) Economic design of control charts ignoring the statistical properties that lead to reduce the control chart power, extremely. To eliminate these weaknesses, this paper presents an integrated model of production cycle length, maintenance policy, and economic-statistical design considering the time value of money and the stochastic shift size. Furthermore, to maintain the reliability of the system at an acceptable level, the presented model uses non-uniform sampling. Finally, three comparative studies on the main contributions are presented to illustrate the advantages of the model and a sensitivity analysis is implemented on the several parameters to extend insights into the matter.

Joint Economic Design of CUSUM Control Chart and Age-Based Imperfect Preventive Maintenance Policy

The close relationship between statistical process control and maintenance has attracted lots of researchers to focus on the jointly economic design of control chart (a main tool of statistical process control) and preventive maintenance policy, and much progress has been made in this field. However, in the existing literatures, the X- chart is used most, and other charts are rarely considered. In this paper, the economic design of CUSUM chart and age-based imperfect preventive maintenance policy is presented. The process is considered as a multiphase system, and a recursive algorithm is used to model each phase. Besides, a sampling policy under the non-Markovian deterioration assumption is employed, and an age-based imperfect preventive maintenance policy is used. An optimization model with the objective of minimizing the expected cost per unit time is constructed to obtain the near-optimal solution of decision variables: the age of the machine for maintenance, the number of age-based maintenances, sample size, sampling intervals, and the decision interval coefficient and reference value coefficient of CUSUM chart. The solution procedure of the model is provided. Also, sensitivity analysis is performed on the decision variables for each of the various parameters.

Economic design of control charts with multiple assignable causes under Burr XII shock model

ABSTRACTThe economic 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 (Burr) distribution which is quite flexible and its hazard rate can be fixed, increasing, decreasing, single mode or even U-shaped. Yet, in Burr distribution context, only one assignable cause model were considered where more realistic approach may be to consider multiple assignable causes. Thus, in this paper, an economic design of the 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. Also, a numerical example and a sensitivity analysis for more illustration and studying the effect of changing parameters of the shock model distribution on the optimum values of proposed design models were conducted, respectively. The results indicate that when the prior distribution is of negative exponential distribution, the multiple assignable cause models under Burr XII (Burr) distribution have minimum loss-cost.

A generalized approach to economic design of control charts: A discussion on implementing

ABSTRACTDue to the importance of choosing between uniform and non uniform sampling schemes in quality control inspections, two generalized models for the economic design of control charts under both schemes are presented separately in this paper. Under uniform sampling plan, two leading models of Lorenzen and Vance (1986) and McWilliams (1989) can be obtained by applying, respectively, Exponential and Weibull in-control time distributions in the uniform generalized model. Furthermore, the generalized model of Rahim and Banerjee (1993) is achieved by using an alternative approach under arbitrary sampling interval plan. These outcomes lead us to present a comprehensive discussion on implementing the economic and economic statistical design of control charts. By imposing a new proposed restriction on the economic model, we can guarantee to have control charts whose power to report the true alarm at the end of each sampling interval is more than shift conditional probability over that interval given no shift till its start. The new restricted economic model, which we call “high-powered economic design of control charts”, can be considered as a special case of economic statistical design. The advantages of our proposed model are highlighted by some numerical examples.

Non-normality Effects on the Economic Statistical Design of $$\bar{X}$$ X ¯ Control Charts Under Burr XII Shock Models

In economic design of control charts, the distribution of quality characteristics and the distribution of failure mechanism or the shock model should be specified. The objective is then to determine three design parameters, i.e. the sample size, sampling interval and the control limits coefficient. In most of the designs and based on the central limit theorem, the sample mean distribution is considered normal where it may not be true in all cases. As economic statistical design of \(\bar{X}\) control charts for normal data with the Burr XII shock model is being under publication by the authors of the present study, non-normality case of this with non-uniform sampling scheme was developed here. The obtained design models have been implemented by a numerical example and a sensitivity analysis was conducted too. The results showed that the scale and shape parameters of the Burr shock model significantly affect the expected cost per unit time of quality cycle. Likewise, it was revealed that using the non-normal assumption caused smaller sample size, narrower control limits and lower expected cost per unit time of the quality cycle.

DE based economic control chart design and application for a typical petrochemical process

DE based economic control chart design and application for a typical petrochemical process

Cost comparisons of modifiedX̅chart for autocorrelated observations

This paper presents the economic design of modified X chart for autocorrelated data and comparison with the economic design of Shewhart’s X chart. An attempt has been made to counter autocorrelation by designing the modified X chart; as the cost of operating a process control system is an important element in the economic design of control charts. The economic designs of both modified and Shewhart X charts for autocorrelated observations are presented; using Lorenzen-Vance [1] cost model. The modified X chart is based upon sum of chi-squares and has simplicity like Shewhart X chart but more efficient than standard chart. Two sets of parameters suggested by Montgomery [2] are used to determine the optimal sampling intervals (h) and expected costs per hour. It shows that sampling interval (h) and expected cost/hour (C) depend upon various parameters of chart, used in this model. The expected costs/hour (C) for both the charts are computed for sample sizes of 2 and 4 at the various levels of correlation and process shifts in mean. It is concluded that at each level of correlation and shift in the process mean, the expected costs/hour of the modified X chart are lower than the Shewhart chart.

Economic design of control charts for monitoring batch manufacturing processes

The issue of economic design of an control chart is addressed for a batch manufacturing process, subject to Markovian failure characteristics. The objective of this design is to minimise the expected total quality cost per batch. To find the optimal sample size and control limits, a Markov chain model is formulated. There is no analytical solution to the optimisation problem, so to avoid an exhaustive search, a heuristic approach, based on a regression model with the Cobb–Douglas function, is proposed. The impact of the model parameters and their interactions on the optimal solution is explored by conducting analysis of variance on 6561 numerical examples in a factorial design. Finally, an example of a real application demonstrates the effectiveness of the proposed model and heuristic.