Economic design of control charts using the Taguchi loss function

Alexander, Suraj M.; Dillman, Matthew A.; Usher, John S.; Damodaran, Biju

doi:10.1016/0360-8352(94)00219-d

Cited by 53 publications

(31 citation statements)

References 10 publications

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“…The optimal control limit k and sampling interval h are computed for several values of n. The values of the cost function together with the associated in-control and out-of-control average run lengths are shown in Table 1. This is the same approach used by Alexander et al (1995), Linderman and Love (2000b), and Montgomery (2001). Using the output, Table 1 reveals that the optimal design has n = 12, k = 2.6, h = 1.9 hours, with a minimum cost of approximately R14.84 per hour.…”

Section: The Optimal Economic Designmentioning

confidence: 99%

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An easy and low cost option for economic statistical process control using Excel

Deventer

Manna

2009

ORiON

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In this paper, a user-friendly, Excel program is developed to search for the optimal values of the parameters in minimizing the total cost function in both economic and economic statistical designs of theX-control chart. Two assumptions are considered in the development and use of the economic or economic statistical models. These assumptions are potentially critical. It is assumed that the time between process shifts can be modelled by means of the exponential distribution. It is further assumed that there is only one assignable cause. Based on these assumptions, economic or economic statistical models are derived using a total cost function per unit time as proposed by a unified approach. In this approach the relationship between the three-control chart parameters as well as the three types of costs are expressed in the total cost function. The optimal parameters are usually obtained by the minimization of the expected total cost per unit time. Nevertheless, few practitioners have tried to optimize the design of theirX-control charts. One reason for this is that the cost models and their associated optimization techniques are often too complex and difficult for practitioners to understand and apply. Therefore, a user-friendly Excel program has been developed in this paper and the numerical examples illustrated are executed on this program. The optimization procedure is easy-to-use, easy-to-understand, and easy-to-access. Moreover, and not least important, it is a low cost option unlike previous approaches which can be found in expensive software packages only. The results and the execution times of all numerical examples show that our optimization procedure using Excel is accurate and efficient.

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Section: The Optimal Economic Designmentioning

confidence: 99%

“…Table 1 (in the main text) shows only the basic results, i.e. the optimum result for each value of n ranging over the interval [1,25] in steps of 1, but some calculation steps have been left out.…”

Section: Appendixmentioning

confidence: 99%

An easy and low cost option for economic statistical process control using Excel

Deventer

Manna

2009

ORiON

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“…Additionally, several researchers have applied the Taguchi loss function approach in the economic design of X control charts (see, e.g., references [16][17][18][19][20][21]). Deming [22] believed that the Taguchi loss function in which there is a minimum loss at the nominal value and an everincreasing loss with the departure either way from the nominal value is a better description of the world.…”

Section: Introductionmentioning

confidence: 99%

Multi-objective economic statistical design of X-bar control chart considering Taguchi loss function

Safaei

Kazemzadeh

Niaki

2011

Int J Adv Manuf Technol

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Shewhart charts are the most popular control charts that can be used to monitor variable quality characteristics in a production process. In this paper, a multi-objective model of the economic statistical design of the X-bar control chart is first proposed by incorporating the Taguchi loss function and the intangible external costs. The model minimizes the mean hourly loss cost while minimizing out-of-control average run length and maintaining reasonable in-control average run length. A multiobjective evolutionary algorithm, namely NSGA-II, is then developed and used to obtain the Pareto optimal solution of the model. Some sensitivity analyses are next performed to investigate the effect of parameter estimation on the chart performances. Finally, a comparison study with a traditional economic design model reveals that the proposed multiple objective design of the X-bar control chart offers a better approach and more practical outcomes for the practitioners.

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“…To illustrate the numerical methods procedure, consider an example employed by Chou, et al (2000), which corresponds to the first row of Table 1 (Alexander, et al, 1995).…”

Section: A Numerical Example For An Exact Solutionmentioning

confidence: 99%

“…A cost model is employed to assist in the selection of these parameters (Duncan 1956, Alexander, et al 1995, Chou, et al 2000. (A summary of notations adopted, which closely follows that of Chou, et al (2000), is listed in the Appendix.)…”

Section: Introductionmentioning

confidence: 99%

An Approximate Approach to the Economic Design of <em>x̅</em> Charts By Considering the Cost of Quality

Cox

2013

J. Mod. App. Stat. Meth.

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Economic design of control charts using the Taguchi loss function

Cited by 53 publications

References 10 publications

An easy and low cost option for economic statistical process control using Excel

An easy and low cost option for economic statistical process control using Excel

Multi-objective economic statistical design of X-bar control chart considering Taguchi loss function

An Approximate Approach to the Economic Design of <em>x̅</em> Charts By Considering the Cost of Quality

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