A Mathematical Model for the Optimal Robust Design of Cause Selecting Control Charts

2022 ◽  
Vol 16 (2) ◽  
pp. 1
Author(s):  
SALIH OSMAN Duffuaa ◽  
Ahmed M. Ghaithan ◽  
Ahmed M. Attia
Keyword(s):  
Mathematical Model ◽  
Robust Design ◽  
Control Charts

Analytical Robust Design of a Gear Milling Machine Headstock

2010 ◽  
Vol 37-38 ◽  
pp. 162-165 ◽  
Author(s):  
Yong Liang Chen ◽  
Shuang Liu ◽  
Han Tao Wang ◽  
Pei Hua Gu
Keyword(s):  
Mathematical Model ◽  
Sensitivity Analysis ◽  
Robust Design ◽  
Optimization Model ◽  
Functional Performance ◽  
Geometric Design ◽  
Design Parameters ◽  
Milling Machine ◽  
Robust Analysis ◽  
Rayleigh Method

Headstock is a key component of gear milling machine. The dynamic functional performance of the headstock is usually influenced by uncertainties of both geometric and non-geometric design parameters. A new mathematical model to represent relationships among first frequency and design parameters of the headstock were derived with Rayleigh method. Then, a larger-the-better and smaller-the-better robust analysis and optimization model was developed. The sensitivity analysis results show that height of the headstock makes a great impact on the first frequency. Through robust optimizations, the first frequency is scaled up by 3.35 percent while minimizing the variance of the first frequency.

scholarly journals Robust Design of S-Shaped Box Beams Subjected to Compressive Load

2010 ◽  
Vol 2010 ◽  
pp. 1-18 ◽  
Author(s):  
A. Khakhali ◽  
A. Darvizeh ◽  
A. Masoumi ◽  
N. Nariman-Zadeh ◽  
A. Shiri
Keyword(s):  
Mathematical Model ◽  
Robust Design ◽  
Compressive Load ◽  
Vehicle Body ◽  
Simplified Model ◽  
Geometrical Parameters ◽  
Automotive Components ◽  
Decision Variables ◽  
Crushing Force ◽  
Box Beams

In order to design the automotive components considering probabilistic uncertainties in the decision variables, it is desired to perform a robust design process. The peak crushing force of the energy absorber components is one of the important objectives of the design of such components. In this paper, at first, the peak crushing force of the S-shaped box beams, as a highly simplified model of front member of a vehicle body, is extracted mathematically. Using such obtained mathematical model and Monte Carlo simulation, genetic algorithm is then used for the robust design of the S-shaped box beams having probabilistic uncertainties in material and geometrical parameters. In this way the variance-per-mean ratio of the peak crushing force () is considered as the objective function. It is shown that some interesting relationships as useful robust design principles involved in the performance of the S-shaped box beams can be discovered by the robust design of the obtained mathematical model.

Fuzzy Robust Design of Cycloid Pin Wheel Reducer Based on Genetic Algorithms

2013 ◽  
Vol 325-326 ◽  
pp. 319-324 ◽  
Author(s):  
Jian Bin Wang ◽  
Ji Shu Yin ◽  
Chao Yu
Keyword(s):  
Mathematical Model ◽  
Genetic Algorithms ◽  
Optimal Design ◽  
Robust Design ◽  
Correlation Functions ◽  
High Efficiency ◽  
Optimal Methods ◽  
Robust Optimal Design

Fuzzy robust design will be applied to optimal design of cycloid pin wheel reducer, and it is established that fuzzy robust optimal design mathematical model of cycloid pin wheel reducer in order to achieve the goal of the small size and high efficiency. Genetic algorithms correlation functions in MATLAB is used to solve the model, and optimal methods and calculation examples is given.

Robust Design of 4-Position Motion Generation and Application on Front End Loader

2012 ◽  
Vol 220-223 ◽  
pp. 736-739
Author(s):  
Wei Xiang Qian
Keyword(s):  
Mathematical Model ◽  
Optimum Design ◽  
Robust Design ◽  
Design Approach ◽  
Engineering Practice ◽  
Motion Generation ◽  
Robust Solution ◽  
Kinematic Accuracy ◽  
Front End ◽  
The Mathematical Model

A robust design approach of 4-position motion generation is presented, and it is applied in the design of front end loader. The mathematical model of optimum design based upon the engineering requirements has been established, by which feasible robust solution regions adhering to conventional constraints and kinematic accuracy requirements can be visually represented. It guides designers to synthesize robust mechanisms that ensure every design condition. The example of front end loader demonstrates that the process of searching the optimal robust mechanism is more intuitive, highly accessible and easy to be applied in engineering practice.

Kinematic Analysis on Running Clearance in a Trochoidal-Type Machine

1995 ◽  
Author(s):  
John B. Shung ◽  
Yi Zhang
Keyword(s):  
Mathematical Model ◽  
Optimal Design ◽  
Robust Design ◽  
Upper Bound ◽  
Kinematic Analysis ◽  
Design Parameters ◽  
Mean Values ◽  
Type Machine ◽  
The Mean ◽  
Design Optimum

Abstract A methodology to design tight running clearance between rotor and chamber in a trochoidal-type machine is presented. A mathematical model to describe the running clearance is developed. Only kinematic design parameters are considered. The effect of the mean values and tolerances of the design parameters on the running clearance is studied by applying robust design. Mean values of design parameters which provide running clearance to be less sensitive to the tolerances are obtained. The effect of the upper bound of the running clearance on the tolerance is also studied by applying the probabilistic optimal design. Optimum tolerances which minimize a cost function are obtained. Therefore, one can apply this methodology to design running clearance by choosing appropriate mean values and tolerances of the design parameters.

Vergleichende Qualitätsmessungen Teil 2: Regelkarten

Pflege ◽  
2013 ◽  
Vol 26 (2) ◽  
pp. 119-127 ◽  
Author(s):  
Jan Kottner ◽  
Armin Hauss
Keyword(s):  
Control Charts ◽  
Common Cause

Vergleichende Qualitätsmessungen und Beurteilungen spielen in der Pflege eine zunehmend wichtige Rolle. Qualitätskennzahlen sind von systematischen und zufälligen Fehlern beeinflusst. Eine Möglichkeit, mit zufälliger Variation in Kennzahlenvergleichen adäquat umzugehen, bietet die Theorie der Statistischen Prozesskontrolle (SPC). Im vorliegenden Beitrag werden Regelkarten (control charts) als Werkzeuge der SPC vorgestellt. Es handelt sich dabei um grafische Darstellungen von Qualitätskennzahlen im zeitlichen Verlauf. Attributive Merkmale können mithilfe von p-, u- und c-Regelkarten dargestellt werden. Es gibt eine Reihe von Regeln, mit denen spezielle Variationen (special cause variation) innerhalb des betrachteten Prozesses identifiziert werden können. Finden sich im Diagramm keine Hinweise auf nichtzufällige Variationen, geht man davon aus, dass sich der Prozess innerhalb «statistischer Kontrolle» befindet (common cause variation). Eine Abweichung eines Datenpunktes um mehr als drei Standardabweichungen vom Mittelwert aller vorliegenden Datenpunkte gilt als stärkstes Signal nicht zufallsbedingter Variation. Im Qualitätsmanagementkontext sind Regelkarten für die dynamische Messung von Prozessen und Ergebnissen und deren Beurteilungen traditionellen Mittelwerts- und Streuungsvergleichen überlegen.

Mathematical model of hit phenomena and its application to movie advertisement

2008 ◽  
Author(s):  
Ishii Akira ◽  
Yoshida Narihiko ◽  
Hayashi Takafumi ◽  
Umemura Sanae ◽  
Nakagawa Takeshi
Keyword(s):  
Mathematical Model
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