scholarly journals Building Cost Function 3D Benchmarks to Improve the Economic Statistical Design ofX¯Control Charts

2014 ◽  
Vol 2014 ◽  
pp. 1-20 ◽  
Author(s):  
Santiago-Omar Caballero-Morales
Keyword(s):  
Cost Function ◽  
Control Charts ◽  
Statistical Design ◽  
Search Space ◽  
Production Costs ◽  
3D Analysis ◽  
Heuristic Methods ◽  
Nonlinear Functions ◽  
Statistical Process ◽  
The Cost

Shewhart or control charts are important Statistical Process Control (SPC) techniques used for prompt detection of failures in a manufacturing process and minimization of production costs which are modelled with nonlinear functions (cost functions). Heuristic methods have been used to find the chart’s parameters integrated within the cost function that best comply with economic and statistical restrictions. However heuristic estimation is highly dependent on the size of the search space, the set of initial solutions, and the exploration operators. In this paper the 3D analysis of the cost function is presented to more accurately identify the search space associated with each parameter ofX¯control charts and to improve estimation. The parameters estimated with this approach were more accurate than those estimated with Hooke and Jeeves (HJ) and Genetic Algorithms (GAs) under different failure distributions. The results presented in this work can be used as a benchmark to evaluate and improve the performance of other heuristic methods.

scholarly journals Economic-statistical design of variable parameters non-central chi-square control chart

Production ◽  
2011 ◽  
Vol 21 (2) ◽  
pp. 259-270 ◽  
Author(s):  
Maysa Sacramento de Magalhães ◽  
Francisco Duarte Moura Neto
Keyword(s):  
Cost Function ◽  
Production Process ◽  
Control Chart ◽  
Control Charts ◽  
Variable Parameter ◽  
Statistical Design ◽  
Optimization Techniques ◽  
Chi Square ◽  
Gradient Based ◽  
The Cost

Production processes are monitored by control charts since their inception by Shewhart (1924). This surveillance is useful in improving the production process due to increased stabilization of the process, and consequently standardization of the output. Control charts keep track of a few key quality characteristics of the outcome of the production process. This is done by means of univariate or multivariate charts. Small improvements in control chart methodology can have significant economic impact in the production process. In this investigation, we propose the monitoring of a single variable by means of a variable parameter non-central chi-square control chart. The design of the chart is accomplished by means of optimizing a cost function. We use here a simulated annealing optimization tool, due to the difficulty of classical gradient based optimization techniques to handle the optimization of the cost function. The results show some of the drawbacks of using this model.

scholarly journals Parallel sequential Monte Carlo for stochastic gradient-free nonconvex optimization

2020 ◽  
Vol 30 (6) ◽  
pp. 1645-1663
Author(s):  
Ömer Deniz Akyildiz ◽  
Dan Crisan ◽  
Joaquín Míguez
Keyword(s):  
Monte Carlo ◽  
Cost Function ◽  
Global Minimum ◽  
Sequential Monte Carlo ◽  
Convergence Rates ◽  
Optimization Problems ◽  
Search Space ◽  
Gradient Based ◽  
Multiple Minima ◽  
The Cost

Abstract We introduce and analyze a parallel sequential Monte Carlo methodology for the numerical solution of optimization problems that involve the minimization of a cost function that consists of the sum of many individual components. The proposed scheme is a stochastic zeroth-order optimization algorithm which demands only the capability to evaluate small subsets of components of the cost function. It can be depicted as a bank of samplers that generate particle approximations of several sequences of probability measures. These measures are constructed in such a way that they have associated probability density functions whose global maxima coincide with the global minima of the original cost function. The algorithm selects the best performing sampler and uses it to approximate a global minimum of the cost function. We prove analytically that the resulting estimator converges to a global minimum of the cost function almost surely and provide explicit convergence rates in terms of the number of generated Monte Carlo samples and the dimension of the search space. We show, by way of numerical examples, that the algorithm can tackle cost functions with multiple minima or with broad “flat” regions which are hard to minimize using gradient-based techniques.

A cost-scale factor relationship for topographic mapping

CISM journal ◽  
1989 ◽  
Vol 43 (4) ◽  
pp. 367-376
Author(s):  
Sylvie Laroche ◽  
Angus C. Hamilton
Keyword(s):  
Quality Control ◽  
Cost Function ◽  
Unit Cost ◽  
Scale Factor ◽  
Production Costs ◽  
Topographic Mapping ◽  
Reference Scale ◽  
Universal Relationship ◽  
The Cost

An analysis of conventional map production costs such as provided by different organizations has led to the development of a universal relationship between cost and scale factor for topographic mapping: the “Laroche-Hamilton” unit cost function. This function has been established as: Cn = Ci x EF1.4 in which Ci = Unit cost per square kilometer (currency or person-hours) for production of topographic mapping; for the 1:50 000 reference scale, Ci is $36 CDN81 Cn = unit cost per square kilometer of any larger scale EF = scale enlargement factor on a reference scale basis (e.g., if Ci is 1:50 000 and Cn is 1:10 000, then EF is 5). It is implicit in this relationship that the type of terrain, the quality control and the type of end product are all comparable. For the particular case when the scale factor is doubled, this relationship predicts that the cost will increase by a factor of 2.5.

scholarly journals A New Approach to Statistical Process Control: Identification of Outliers in Yield Maps

2018 ◽  
Vol 10 (8) ◽  
pp. 334
Author(s):  
Danilo Tedesco de Oliveira ◽  
Leonardo Bernache ◽  
Luan Pereira de Oliveira ◽  
Murilo Aparecido Voltarelli ◽  
Rouverson Pereira da Silva
Keyword(s):  
Standard Deviation ◽  
Process Control ◽  
Statistical Process Control ◽  
Precision Agriculture ◽  
Control Charts ◽  
Production Costs ◽  
Statistical Process ◽  
New Approach ◽  
Individual Control ◽  
Productivity Data

The tools of precision agriculture are of utmost importance in the Brazilian agribusiness, enabling increases in yields and reducing production costs. The use of harvest monitoring systems makes it possible due the possibility to identify pontual problems in an area, however, it becomes necessary to be working properly so it does not acquire incorrect information. Therefore, the purpose with this study was to propose a new approach to identify discrepant points in harvesting maps using statistical process control, as well as to define the best multiple of the standard deviation to identificate these points. The work was conducted during the soybean harvesting at São Geronimo farm in an area of 38 hectares in the municipality of Candido Mota, located in the the state of São Paulo. For gathering information, it was used a Stara crop monitoring system (model Topper Maps) set to record information during harvest in each three second. The productivity data were used to generate an individual control chart to identify points that were out of control so they could be removed. Two standard deviation multiples, that presented an average productivity closer to the average real productivity of the area, were selected. The multiples of the deviations that came closest were the 2σ and 3σ. Two multiples of standard deviation presented an average yield closer to the average real yield of the area. Individual control charts can be used to set control limits and identify possible discrepancies. The multiple of standard deviation 3σ presented information with greater reliability.

scholarly journals On Generating Optimal Signal Probabilities for Random Tests: A Genetic Approach

VLSI Design ◽  
1996 ◽  
Vol 4 (3) ◽  
pp. 207-215 ◽  
Author(s):  
M. Srinivas ◽  
L. M. Patnaik
Keyword(s):  
Genetic Algorithms ◽  
Cost Function ◽  
Gradient Descent ◽  
Random Search ◽  
Search Space ◽  
Optimization Techniques ◽  
Gradient Descent Methods ◽  
Test Vectors ◽  
The Cost ◽  
Optimal Signal

Genetic Algorithms are robust search and optimization techniques. A Genetic Algorithm based approach for determining the optimal input distributions for generating random test vectors is proposed in the paper. A cost function based on the COP testability measure for determining the efficacy of the input distributions is discussed. A brief overview of Genetic Algorithms (GAs) and the specific details of our implementation are described. Experimental results based on ISCAS-85 benchmark circuits are presented. The performance of our GAbased approach is compared with previous results. While the GA generates more efficient input distributions than the previous methods which are based on gradient descent search, the overheads of the GA in computing the input distributions are larger.To account for the relatively quick convergence of the gradient descent methods, we analyze the landscape of the COP-based cost function. We prove that the cost function is unimodal in the search space. This feature makes the cost function amenable to optimization by gradient-descent techniques as compared to random search methods such as Genetic Algorithms.

A Method for Inferring the Optimization Cost Function of Experimentally Observed Motor Strategies

2005 ◽  
Author(s):  
Carlo L. Bottasso ◽  
Alessandro Croce ◽  
Stefano Sartirana ◽  
Boris I. Prilutsky
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Cost Function ◽  
Motor Task ◽  
Computational Procedure ◽  
Search Space ◽  
Optimality Criteria ◽  
Cost Functions ◽  
The Cost ◽  
Motor Strategies

We propose a computational procedure for inferring the cost functions that, according to the Principle of Optimality, underlie experimentally observed motor strategies. This work tries to overcome the need to hypothesize the cost functions, extracting this non-directly observable information from experimental data. Optimality criteria of observed motor tasks are here indirectly derived using: a) a mathematical model of the bio-system; and b) a parametric mathematical model of the possible cost functions, i.e. a search space constructed in such a way as to presumably contain the unknown function that was used by the bio-system in the given motor task of interest. The cost function that best matches the experimental data is identified within the search space by solving a nested optimization problem. This problem can be recast as a non-linear programming problem and therefore solved using standard techniques. The proposed methodology is tested on representative examples.

scholarly journals Individual-versus group-optimality in the production of secreted bacterial compounds

2016 ◽  
Author(s):  
Konstanze T. Schiessl ◽  
Adin Ross-Gillespie ◽  
Daniel M. Cornforth ◽  
Michael Weigert ◽  
Colette Bigosch ◽  
...  
Keyword(s):  
Cost Function ◽  
Division Of Labor ◽  
Production Costs ◽  
Cell Level ◽  
Compound Synthesis ◽  
Unicellular Organisms ◽  
Level Of Selection ◽  
The Individual ◽  
The Cost ◽  
Evolution Of Specialization

AbstractHow unicellular organisms optimize the production of compounds is a fundamental biological question. While it is typically thought that production is optimized at the individual-cell level, secreted compounds could also allow for optimization at the group level, leading to a division of labor where a subset of cells produces and shares the compound with everyone. Using mathematical modelling, we show that the evolution of such division of labor depends on the cost function of compound production. Specifically, for any trait with saturating benefits, linear costs promote the evolution of uniform production levels across cells. Conversely, production costs that diminish with higher output levels favor the evolution of specialization – especially when compound shareability is high. When experimentally testing these predictions with pyoverdine, a secreted iron-scavenging compound produced by Pseudomonas aeruginosa, we found linear costs and, consistent with our model, detected uniform pyoverdine production levels across cells. We conclude that for shared compounds with saturating benefits, the evolution of division of labor is facilitated by a diminishing cost function. More generally, we note that shifts in the level of selection from individuals to groups do not solely require cooperation, but critically depend on mechanistic factors, including the distribution of compound synthesis costs.

scholarly journals When more competition may damage welfare with socially responsible firms

Ekonomia ◽  
2018 ◽  
Vol 23 (3) ◽  
pp. 123-134
Author(s):  
Luciano Fanti ◽  
Domenico Buccella
Keyword(s):  
Social Responsibility ◽  
Cost Function ◽  
Production Costs ◽  
Linear Quadratic ◽  
Socially Responsible ◽  
Common View ◽  
Duopoly Model ◽  
The Common ◽  
The Cost ◽  
Welfare Changes

When more competition may damage welfare with socially responsible firmsConsidering a Cournot monopoly/duopoly model with linear/quadratic production costs and Cor­porate Social Responsibility CSR activities, this note shows that, in contrast to the common view, entry may reduce social welfare. Moreover, we remark that the higherthe CSR activities are, the more likely the welfare-damaging entry effect may occur, and thesocial welfare changes following a firm’s entry crucially depend on the degree of convexity of the cost function.

scholarly journals STUBBLE DAMAGE AND UNSETTLING INDEXES FOR DIFFERENT CUTTING AND LOADING SYSTEMS

2021 ◽  
Vol 35 (4) ◽  
pp. 493-506
Author(s):  
Eduardo Prisco Angelo ◽  
Carla Segatto Strini Paixão Voltarelli ◽  
Murilo Aparecido Voltarelli ◽  
Rouverson Pereira da Silva ◽  
Cristiano Zerbato
Keyword(s):  
Quality Control ◽  
Statistical Process Control ◽  
Control Charts ◽  
Statistical Design ◽  
Statistical Process ◽  
Harvesting Time ◽  
Agricultural Mechanization ◽  
Mechanical Cutting ◽  
Sugarcane Ratoon

STUBBLE DAMAGE AND UNSETTLING INDEXES FOR DIFFERENT CUTTING AND LOADING SYSTEMS   EDUARDO PRISCO ANGELO1, CARLA SEGATTO STRINI PAIXÃO2, MURILO APARECIDO VOLTARELLI1 ROUVERSON PEREIRA DA SILVA3, CRISTIANO ZERBATO3   1 Centro de Ciências da Natureza, Universidade Federal de São Carlos, Rodovia Lauri Simões de Barros, km 12 - SP-189 - Aracaçu, 18290-000, Buri – SP, Brasil. [email protected] 2 Departamento de Engenharia, Faculdade de Engenharia de Sorocaba, Rodovia Senador José Ermírio de Moraes, 1425 - Jardim Constantino Matucci,18085-784, Sorocaba – SP, Brasil. [email protected] 3 Centro de Ciências da Natureza, Universidade Federal de São Carlos, Rodovia Lauri Simões de Barros, km 12 - SP-189 - Aracaçu, 18290-000, Buri – SP, Brasil. [email protected] 4 Departamento de Engenharia Rural, Universidade Estadual Paulista ‘Júlio de Mesquita Filho’, Via de Acesso Professor Paulo Donato Castelane S/N - Vila Industrial, 14884-900, Jaboticabal, SP, Brasil. [email protected]. 5 Departamento de Engenharia Rural, Universidade Estadual Paulista ‘Júlio de Mesquita Filho’, Via de Acesso Professor Paulo Donato Castelane S/N - Vila Industrial, 14884-900, Jaboticabal, SP, Brasil. [email protected].   ABSTRACT: Simultaneous mechanical cutting and loading of sugarcane may trample the remaining stumbles in the harvested area, thus increasing the damage and unsettling indexes of the stubs remaining in the ground after the harvest, which, in the end, can hamper sugarcane regrowth. To this end, this work aimed to evaluate how cutting and loading systems affect sugarcane ratoon using statistical process control. The experiment was conducted in an agricultural area in Frutal, MG, in June 2014. Mechanical harvesting was conducted at a 1.1 m s-1(4.0 km h-1) average working speed and 1.50m spacing. The statistical design used was completely randomized, based on the concepts of quality control, in which the data were collected during harvesting time. The study treatments were as follows, basal cut, and mechanical sets A, B, C and D according to equipment gauge width. The stubble damage and unsettling indexes were the parameters used to determine the quality of the process under study. Set D with the widest gauge is the best option for mechanical harvesting, loading and transporting sugarcane since it has significantly lower sugarcane stubble damage and unsettling indices compared to sets A, B, and C.   Keywords: agricultural mechanization, control charts, mechanical harvest, stubble trampling, variability.   RESUMO: O corte mecânico e carregamento simultâneo da cana-de-açúcar pode atropelar a palha remanescente na área colhida, aumentando os índices de danos e abalos das socas que permanecem no solo após a colheita, o que, ao final, pode dificultar a rebrota da cana-de-açúcar. Para tanto, o objetivo deste trabalho foi avaliar como os sistemas de corte e carregamento que afetam a soca de cana-de-açúcar por meio do controle estatístico do processo. O experimento foi conduzido em uma área agrícola em Frutal, MG, em junho de 2014. A colheita mecanizada foi realizada a uma velocidade média de trabalho de 1,1m s-1 (4,0 km h-1) e espaçamento de 1,50m. O delineamento estatístico utilizado foi inteiramente casualizado, em que os dados foram coletados na época da colheita. Os tratamentos estudados foram o corte basal e os conjuntos mecânicos A, B, C e D de acordo com a largura de bitola do equipamento. Dessa forma, conclui-se que o Conjunto D com a bitola mais larga é a melhor opção para colheita mecânica, carregamento e transporte da cana-de-açúcar, pois apresenta danos significativamente mais baixos à palha da cana-de-açúcar, além dos índices de abalos, quando comparados aos conjuntos A, B e C.   Palavras-chave: mecanização agrícola, cartas de controle, colheita mecanizada, pisoteio de soqueira, variabilidade.

Catalog-Based Customization

1999 ◽  
Author(s):  
Bala Chidambaram ◽  
Alice M. Agogino
Keyword(s):  
Cost Function ◽  
Cost Estimation ◽  
A Priori ◽  
Production Costs ◽  
Estimation Methods ◽  
Optimization Formulation ◽  
Catalog Design ◽  
Standard Designs ◽  
Approximate Cost ◽  
The Cost

Abstract This paper develops a new method for implementing mass-customization, namely, the customization around standard products, or catalog-based customization. The method addresses the customization requirements of a class of products that are complex in configuration, multi-functional and structurally similar. We formulate catalog-based customization as an optimization problem consistent with the manufacturer’s goal of incurring minimal costs in the redesign of existing standard components, while meeting customer specifications and satisfying design constraints. The ‘catalog-based’ nature of the formulation raises concomitant issues of cost function development and problem simplification/solution. We identify the generational structure as best suited to exploit the cost data in existing catalogs and construct a product cost function. The cost-estimation methods used by the generational structure in the construction are identified as weight-based — for modeling the material costs, and methods based on similarity principles and regression analyses — for the production costs. The optimization formulation of catalog-based customization may be simplified by an a priori identification of a standard catalog design as the customization basis. This is accomplished with function costing — a cost-estimation hypothesis that uses product functionality to develop an approximate cost-estimate. The function-costing estimate is also used to abstract features from the standard base design into the optimization formulation. The preferred solution strategy for the optimization formulation is identified as genetic algorithms. We apply the customization method developed to Brushless D.C. Permanent Magnet (BDCPM) motors and obtain optimal minimal cost custom designs (from the standard designs of a BDCPM motor family) for different sets of customer requirements.

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