The Economic Design of | barX Charts used to Maintain Current Control of a Process

Duncan, Acheson J.

doi:10.2307/2281343

Cited by 410 publications

(293 citation statements)

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“…Cost model is an extension of Duncan (1956) model which was employed in a univariate case. First, we make a number of assumptions as follows:…”

Section: Proposed Cost Modelmentioning

confidence: 99%

“…Duncan (1956) offered an economic model incorporated the most important relevant cost items associated with sampling and control charts. Through minimization of the proposed cost model, the optimum economical design parameters of control chart were presented.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we propose a novel economic design of T 2 control chart based on the extension of Duncan's (1956) cost model. By using a genetic algorithm, the optimal design parameters of the relevant cost model besides the sensitivity analysis is proposed through an illustrative example.…”

Section: Introductionmentioning

confidence: 99%

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Economic design of Hotelling’s T2 control chart on the presence of fixed sampling rate and exponentially assignable causes

Bahiraee

Raissi

2014

J Ind Eng Int

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Control charts are extensively used in manufacturing contexts to monitor production processes. This article illustrates economical design of a variable sample size and control limit Hotelling's T 2 control chart based on a novel cost model when occurrence times of the assignable causes are exponentially distributed. The proposed nonlinear cost model is an extension of Duncan's (J Am Stat Assoc 51: [228][229][230][231][232][233][234][235][236][237][238][239][240][241][242] 1956) model which was employed for univariate cases. Applying genetic algorithm to find optimum parameter values and using an L 33 orthogonal array in sensitivity analysis on the model parameters is investigated through a numerical example to illustrate the effectiveness of the proposed approach.

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“…Cost model is an extension of Duncan (1956) model which was employed in a univariate case. First, we make a number of assumptions as follows:…”

Section: Proposed Cost Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Economic design of Hotelling’s T2 control chart on the presence of fixed sampling rate and exponentially assignable causes

Bahiraee

Raissi

2014

J Ind Eng Int

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“…REMARK 1: The expressions for the operating characteristics reduce to the classical ones in the absence of exogenous opportunities as lim µ→0 [7,9]. REMARK 2: So far, we have assumed that the opportunities are of a single kind.…”

Section: Single Machine: Operating Characteristicsmentioning

confidence: 99%

“…Such opportunities have been considered for determining new policies in the maintenance literature after the seminal work by Dekker and Dijkstra [6]; but they have not received any attention in the vast quality control literature. Quality control charts have been developed from three perspectives: a purely statistical approach where the power of the test for detecting an assignable cause and value for Type I error are set to their predetermined values [15,19], a purely economic approach where the objective is minimization of the expected total costs of sampling, poor quality and downtime [7,16,18], and a mixed approach called semi-economic design [22]. For comprehensive surveys and reviews of this extensive literature, we refer the reader to Refs.…”

Section: Introductionmentioning

confidence: 99%

Quality control chart design under Jidoka

Berk

Toy

2009

Naval Research Logistics

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Abstract:We consider design of control charts in the presence of machine stoppages that are exogenously imposed (as under jidoka practices). Each stoppage creates an opportunity for inspection/repair at reduced cost. We first model a single machine facing opportunities arriving according to a Poisson process, develop the expressions for its operating characteristics and construct the optimization problem for economic design of a control chart. We, then, consider the multiple machine setting where individual machine stoppages may create inspection/repair opportunities for other machines. We develop exact expressions for the cases when all machines are either opportunity-takers or not. On the basis of an approximation for the all-taker case, we then propose an approximate model for the mixed case. In a numerical study, we examine the opportunity taking behavior of machines in both single and multiple machine settings and the impact of such practices on the design of anX− Q C chart. Our findings indicate that incorporating inspection/repair opportunities into QC chart design may provide considerable cost savings.

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Economic design of ?? andR charts under Weibull shock models

Costa

Rahim

2000

Qual. Reliab. Engng. Int.

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This paper considers the problem of a continuous production process where both the mean and variance are simultaneously monitored by an X̄ and R chart respectively, and generalizes the model of Costa (IIE Transactions 1993; 25(6):27–33). The product variable quality characteristic is assumed to be normally distributed and the process is subject to two independent assignable causes (such as tool wear‐out, overheating or vibration). One cause changes the process mean and the other changes the process variance. However, the occurrence of one kind of assignable cause does not preclude the occurrence of the other. It is also assumed that the occurrence times of the assignable causes are described by Weibull distributions with increasing failure rates. A cost model is developed and a non‐uniform sampling interval scheme is adopted. A two‐step search procedure is employed to determine the optimal design parameters. The relative contribution of the paper over the results obtained by Costa is addressed. A sensitivity analysis of the model is conducted and the cost savings associated with the use of non‐uniform sampling intervals instead of constant sampling intervals are evaluated. The economic design model is then extended to an economic–statistical design model for achieving desired levels of statistical performance while minimizing the expected cost. Performances of purely economic design and economic–statistical design are compared. Copyright © 2000 John Wiley & Sons, Ltd.

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The Economic Design of | barX Charts used to Maintain Current Control of a Process

Cited by 410 publications

References 0 publications

Economic design of Hotelling’s T2 control chart on the presence of fixed sampling rate and exponentially assignable causes

Economic design of Hotelling’s T2 control chart on the presence of fixed sampling rate and exponentially assignable causes

Quality control chart design under Jidoka

Economic design of ?? andR charts under Weibull shock models

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