Economic Statistical Design of X̄ Control Charts for Systems With Weibull in-Control Times

Zhang, Guoqiang; Berardi, Victor L.

doi:10.1016/s0360-8352(96)00314-2

Cited by 58 publications

(21 citation statements)

References 13 publications

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“…If the constraints alone are used in determining design parameters, without considering the cost objectives, they become statistical designs. Zhang and Berardi (1997) showed that economic statistical designs are generally more costly than economic designs due to the additional constraints. However, the tight limits on the statistical properties of the control charts may lead to low process variability that enhances output quality which leads to a reduction in the cost of comebacks and rewards.…”

Section: Design Of Thex-control Chart -A Unified Approachmentioning

confidence: 99%

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: Design Of Thex-control Chart -A Unified Approachmentioning

confidence: 99%

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

Deventer

Manna

2009

ORiON

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“…Al-oraini and Rahim (2003) also concluded in the same way. Zhang and Berardi (1997), Chou et al (2000), Chen and Cheng (2007) and Yeh and Chen (2010) have also worked on this type of design of x control chart. Alkhedher and Darwish (2013), Sing et al (2014), Hashemi et al (2014) have also reported optimisation procedures in various applications.…”

Section: Introductionmentioning

confidence: 99%

Economic design of moving average control chart for non-normally distributed data: a comparative study

Patil¹,

Shirke

2017

IJOR

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An economic cost function for moving average control chart under non-normal quality characteristic is obtained using continuous and ceased production modes. This cost function can be used to obtain optimal design parameters which minimise the loss cost per hour of the production. Burr distribution has been used to transform the non-normal data to normal. Sensitivity analysis of the economic design is also discussed. The ceased process is observed to be dominant with significant saving in the cost over the continuous process.

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“…Furthermore, Shewhart proposed a so-called heuristic design approach for determining the values of three parameters of a control chart in 1939 (Chou et al, 2000). However, this approach may lack the performance that a manager desires to find process shifts promptly, correctly and economically (Zhang and Berardi, 1997).…”

Section: Introductionmentioning

confidence: 99%

“…In general, economic statistical designs are more costly than economic designs due to the added statistical constraints (ie, minimum value of power and maximum value of Type I error). However, the tight limits on the statistical properties of control charts can result in low process variability which enhances output quality (Zhang and Berardi, 1997). McWilliams (1994) presented the economic statistical design of x-bar control charts.…”

Section: Introductionmentioning

confidence: 99%

Economic statistical design for x-bar control charts under non-normal distributed data with Weibull in-control time

Chen

Yeh

2011

Journal of the Operational Research Society

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This paper proposes an approach which simultaneously considers the properties of cost and quality based on the Burr distribution to determine three parameters (including sample size, sampling interval between successive samples, and the control limits) when an x-bar chart monitors a manufacturing process with Weibull failure characteristic and non-normal data. Also, the cost model of Banerjee and Rahim (1988) is used as the objective function, and the probability density function of the Burr distribution is applied to derive the statistical constraints of economic statistical design of the x-bar control charts for non-normal data. The example of Banerjee and Rahim (1988) is adopted to indicate the solution procedure and sensitivity analyses. Meanwhile, the design parameters of the x-bar control charts can be obtained through the grid search method. The results show that an increase of skewness coefficient ( 3 ) results in a slight decrease for sample size (n), but is robust to the control limit width (L). Also, an increase of kurtosis coefficient ( 4 ) leads to a wider control limit width.

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Economic Statistical Design of X̄ Control Charts for Systems With Weibull in-Control Times

Cited by 58 publications

References 13 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

Economic design of moving average control chart for non-normally distributed data: a comparative study

Economic statistical design for x-bar control charts under non-normal distributed data with Weibull in-control time

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