Economic design of an X chart for short-run production

The aim of this paper is to present an economical design of an X chart for a short-run production. The process mean starts equal to mu(0) (in-control, State I) and in a random time it shifts to mu(1) > mu(0) (out-of-control, State II). The monitoring procedure consists of inspecting a single item at every m produced ones. If the measurement of the quality characteristic does not meet the control limits, the process is stopped, adjusted, and additional (r - 1) items are inspected retrospectively. The probabilistic model was developed considering only shifts in the process mean. A direct search technique is applied to find the optimum parameters which minimizes the expected cost function. Numerical examples illustrate the proposed procedure. (C) 2009 Elsevier B.V. All rights reserved.

Economic design of (X)over-bar and R charts under Weibull shock models

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Economic design of two-stage (X)over-bar charts: the Markov chain approach

When the (X) over bar chart is in use, samples are regularly taken from the process, and their means are plotted on the chart. In some cases, it is too expensive to obtain the X values, but not the values of a correlated variable Y. This paper presents a model for the economic design of a two-stage control chart, that is. a control chart based on both performance (X) and surrogate (Y) variables. The process is monitored by the surrogate variable until it signals an out-of-control behavior, and then a switch is made to the (X) over bar chart. The (X) over bar chart is built with central, warning. and action regions. If an X sample mean falls in the central region, the process surveillance returns to the (Y) over bar chart. Otherwise. The process remains under the (X) over bar chart's surveillance until an (X) over bar sample mean falls outside the control limits. The search for an assignable cause is undertaken when the performance variable signals an out-of-control behavior. In this way, the two variables, are used in an alternating fashion. The assumption of an exponential distribution to describe the length of time the process remains in control allows the application of the Markov chain approach for developing the cost function. A study is performed to examine the economic advantages of using performance and surrogate variables. (C) 2003 Elsevier B.V. All rights reserved.

Economic design of (X)over-bar charts with variable parameters: the Markov chain approach

This paper presents an economic design of (X) over bar control charts with variable sample sizes, variable sampling intervals, and variable control limits. The sample size n, the sampling interval h, and the control limit coefficient k vary between minimum and maximum values, tightening or relaxing the control. The control is relaxed when an (X) over bar value falls close to the target and is tightened when an (X) over bar value falls far from the target. A cost model is constructed that involves the cost of false alarms, the cost of finding and eliminating the assignable cause, the cost associated with production in an out-of-control state, and the cost of sampling and testing. The assumption of an exponential distribution to describe the length of time the process remains in control allows the application of the Markov chain approach for developing the cost function. A comprehensive study is performed to examine the economic advantages of varying the (X) over bar chart parameters.

Economic design of a Vp X̄ chart

We develop an economic model for X̄ control charts having all design parameters varying in an adaptive way, that is, in real time considering current sample information. In the proposed model, each of the design parameters can assume two values as a function of the most recent process information. The cost function is derived and it provides a device for optimal selection of the design parameters. Through a numerical example one can foresee the savings that the developed model possibly provides. © 2001 Elsevier Science B.V. All rights reserved.

Economic design of Shewhart control charts for monitoring autocorrelated data with skip sampling strategies

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Joint economic design of X̄ and R control charts for processes subject to two independent assignable causes

A model for the joint economic design of X̄ and R control charts is developed. This model assumes that the process is subject to two assignable causes. One assignable cause shifts the process mean; the other shifts the process variance. The occurrence of the assignable cause of one kind does not block the occurrence of the assignable cause of another kind. Consequently, a second process parameter can go out-of-control after the first process parameter has gone out-of-control. A numerical study of the cost surface to the model considered has revealed that it is convex, at least in the interest region.

Economic-statistical design of the (X)over-bar chart used to control a wandering process mean using genetic algorithm

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Constrained optimization model for the design of an adaptive (X)over-bar chart

An economic-statistical model is developed for variable parameters (VP) (X) over bar charts in which all design parameters vary adaptively, that is, each of the design parameters (sample size, sampling interval and control-limit width) vary as a function of the most recent process information. The cost function due to controlling the process quality through a VP (X) over bar chart is derived. During the optimization of the cost function, constraints are imposed on the expected times to signal when the process is in and out of control. In this way, required statistical properties can be assured. Through a numerical example, the proposed economic-statistical design approach for VP (X) over bar charts is compared to the economic design for VP (X) over bar charts and to the economic-statistical and economic designs for fixed parameters (FP) (X) over bar charts in terms of the operating cost and the expected times to signal. From this example, it is possible to assess the benefits provided by the proposed model. Varying some input parameters, their effect on the optimal cost and on the optimal values of the design parameters was analysed.

Joint conomic design of (x)over-bar and R charts under Weibull shock models

This paper deals with the joint economic design of (x) over bar and R charts when the occurrence times of assignable causes follow Weibull distributions with increasing failure rates. The 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. A cost model is developed and a non-uniform sampling interval scheme is adopted. A two-step search procedure is employed to determine the optimum design parameters. Finally, 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.

Joint conomic design of x̄ and R charts under Weibull shock models

This paper deals with the joint economic design of x̄ and R charts when the occurrence times of assignable causes follow Weibull distributions with increasing failure rates. The 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. A cost model is developed and a non-uniform sampling interval scheme is adopted. A two-step search procedure is employed to determine the optimum design parameters. Finally, 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.

Rigorous design of distillation columns using surrogate models based on Kriging interpolation

The economic design of a distillation column or distillation sequences is a challenging problem that has been addressed by superstructure approaches. However, these methods have not been widely used because they lead to mixed-integer nonlinear programs that are hard to solve, and require complex initialization procedures. In this article, we propose to address this challenging problem by substituting the distillation columns by Kriging-based surrogate models generated via state of the art distillation models. We study different columns with increasing difficulty, and show that it is possible to get accurate Kriging-based surrogate models. The optimization strategy ensures that convergence to a local optimum is guaranteed for numerical noise-free models. For distillation columns (slightly noisy systems), Karush–Kuhn–Tucker optimality conditions cannot be tested directly on the actual model, but still we can guarantee a local minimum in a trust region of the surrogate model that contains the actual local minimum.

Efficiency, costs and trade-offs in marine reserve system design

With marine biodiversity conservation the primary goal for reserve planning initiatives, a site's conservation potential is typically evaluated on the basis of the biological and physical features it contains. By comparison, socio-economic information is seldom a formal consideration of the reserve system design problem and generally limited to an assessment of threats, vulnerability or compatibility with surrounding uses. This is perhaps surprising given broad recognition that the success of reserve establishment is highly dependent on widespread stakeholder and community support. Using information on the spatial distribution and intensity of commercial rock lobster catch in South Australia, we demonstrate the capacity of mathematical reserve selection procedures to integrate socio-economic and biophysical information for marine reserve system design. Analyses of trade-offs highlight the opportunities to design representative, efficient and practical marine reserve systems that minimise potential loss to commercial users. We found that the objective of minimising the areal extent of the reserve system was barely compromised by incorporating economic design constraints. With a small increase in area (< 3%) and boundary length (< 10%), the economic impact of marine reserves on the commercial rock lobster fishery was reduced by more than a third. We considered also how a reserve planner might prioritise conservation areas using information on a planning units selection frequency. We found that selection frequencies alone were not a reliable guide for the selection of marine reserve systems, but could be used with approaches such as summed irreplaceability to direct conservation effort for efficient marine reserve design.

Effects of the preventive and corrective adjustments in economical designs for online process control for attributes with misclassification errors

The procedure for online process control by attributes consists of inspecting a single item at every m produced items. It is decided on the basis of the inspection result whether the process is in-control (the conforming fraction is stable) or out-of-control (the conforming fraction is decreased, for example). Most articles about online process control have cited the stoppage of the production process for an adjustment when the inspected item is non-conforming (then the production is restarted in-control, here denominated as corrective adjustment). Moreover, the articles related to this subject do not present semi-economical designs (which may yield high quantities of non-conforming items), as they do not include a policy of preventive adjustments (in such case no item is inspected), which can be more economical, mainly if the inspected item can be misclassified. In this article, the possibility of preventive or corrective adjustments in the process is decided at every m produced item. If a preventive adjustment is decided upon, then no item is inspected. On the contrary, the m-th item is inspected; if it conforms, the production goes on, otherwise, an adjustment takes place and the process restarts in-control. This approach is economically feasible for some practical situations and the parameters of the proposed procedure are determined minimizing an average cost function subject to some statistical restrictions (for example, to assure a minimal levelfixed in advanceof conforming items in the production process). Numerical examples illustrate the proposal.

Tuulivoimapuiston keskijänniteverkon teknistaloudellinen optimointi

Euroopan Unionin asettamat tavoitteet uusiutuvien energialähteiden lisäämiselle sähköntuotannossa ovat johtamassa tuulivoimalla tuotetun sähkön merkittävään kasvamiseen. Suomeenkin suunnitellaan suuria, useista kymmenistä tuulivoimaloista koostuvia tuulivoimapuistoja niin maalle kuin merelle. Tuulivoimapuiston suunnittelu on kokonaisuudessaan pitkä prosessi, johon sisältyy sähköteknisen suunnittelun lisäksi myös ympäristövaikutusten arviointiohjelma ja erinäiset lupa-asiat. Tämän diplomityön tavoitteena on kehittää menetelmiä, joiden avulla suurten tuulivoimapuistojen keskijänniteverkon teknistaloudellinen suunnittelu helpottuisi. Tuulivoimapuiston keskijänniteverkon parhaan teknistaloudellisen ratkaisun löytyminen riippuu useista muuttujista. Työssä kehitettiin laskentamallipohja, jonka avulla voidaan helposti ja nopeasti tarkastella erilaisten ratkaisuiden vaikutusta kokonaisuuteen. Tavoite on optimoida teknistaloudellisessa mielessä koko tuulivoimapuiston sisäinen keskijänniteverkko. Kehitettyä laskentamallipohjaa hyödynnettiin esimerkkiprojektina olleen tuulivoimapuiston keskijänniteverkon suunnittelussa. Mallin avulla voidaan laskea nopeasti verkon kustannukset koko pitoajalta. Kustannuslaskelmissa otetaan huomioon investointi-, häviö- ja keskeytyskustannukset.