Effect of applying independence axiom of Axiomatic Design theory on performance of an Integrated Manufacturing Information System: a computer simulation modeling approach

To control manufacturing processes, integration of flows of manufacturing information is an important starting point. In this regard, an effective Integrated Manufacturing Information System (IMIS) which is capable of monitoring, analyzing, and inspecting manufacturing processes properly is critical. Often, most of difficulties in achieving an effective IMIS stem from a poor design for the system architecture. This study particularly addresses the problem of coupling in architecture of an IMIS and its effect on the system performance. This study employs “Independence Axiom” of the Axiomatic Design (AD) theory to deal with the problem and uses “times in process” and “utilized capacities of available resources” as two important criteria for evaluating the system performance. To verify the proposed methodology, a real IMIS is addressed, its stochastic behavior is simulated in Visual SLAM and AweSim (version 3.o) software environment, and the outcomes are analyzed by using logistic regression method for each level of system decomposition. Results of the analyses indicate that fulfillment of independence axiom of AD theory can significantly enhance performance of the concerned IMIS.

Probability weighting explains Independence Axiom violations of Expected Utility Theory in monkeys

Expected Utility Theory (EUT) provides axioms for maximizing utility in risky choice. The independence axiom (IA) is its most demanding axiom: preferences between two options should not change when altering both options equally by mixing them with a common gamble. We tested common consequence (CC) and common ratio (CR) violations of the IA in thousands of stochastic choice over several months using a large variety of binary option sets. Three monkeys showed few outright Preference Reversals (8%) but substantial graded Preference Changes (46%) between the initial preferred gamble and the corresponding altered gamble. Linear Discriminant Analysis (LDA) indicated that gamble probabilities predicted most Preference Changes in CC (72%) and CR (87%) tests. The Akaike Information Criterion indicated that probability weighting within Cumulative Prospect Theory (CPT) explained choices better than models using Expected Value (EV) or EUT. Fitting by utility and probability weighting functions of CPT resulted in nonlinear and non-parallel indifference curves (IC) in the Marschak-Machina triangle and suggested IA non-compliance of models using EV or EUT. Indeed, CPT models predicted Preference Changes better than EV and EUT models. Indifference points in out-of-sample tests were closer to CPT-estimated ICs than EV and EUT ICs. Finally, while the few outright Preference Reversals may reflect the long experience of our monkeys, their more graded Preference Changes corresponded to those reported for humans. In benefitting from the wide testing possibilities in monkeys, our stringent axiomatic tests contribute critical information about risky decision-making and serves as basis for investigating neuronal decision mechanisms.

Evaluation of Human Ear Anatomy and Functionality by Axiomatic Design

The design of the human ear is one of nature’s engineering marvels. This paper examines the merit of ear design using axiomatic design principles. The ear is the organ of both hearing and balance. A sensitive ear can hear frequencies ranging from 20 Hz to 20,000 Hz. The vestibular apparatus of the inner ear is responsible for the static and dynamic equilibrium of the human body. The ear is divided into the outer ear, middle ear, and inner ear, which play their respective functional roles in transforming sound energy into nerve impulses interpreted in the brain. The human ear has many modules, such as the pinna, auditory canal, eardrum, ossicles, eustachian tube, cochlea, semicircular canals, cochlear nerve, and vestibular nerve. Each of these modules has several subparts. This paper tabulates and maps the functional requirements (FRs) of these modules onto design parameters (DPs) that nature has already chosen. The “independence axiom” of the axiomatic design methodology is applied to analyze couplings and to evaluate if human ear design is a good design (i.e., uncoupled design) or a bad design (i.e., coupled design). The analysis revealed that the human ear is a perfect design because it is an uncoupled structure. It is not only a perfect design but also a low-cost design. The materials that are used to build the ear atom-by-atom are chiefly carbon, hydrogen, oxygen, calcium, and nitrogen. The material cost is very negligible, which amounts to only a few of dollars. After a person has deceased, materials in the human system are upcycled by nature. We consider space requirements, materials cost, and upcyclability as “constraints” in the axiomatic design. In terms of performance, the human ear design is very impressive and serves as an inspiration for designing products in industrial environments.

The Consumer Problem

The theory of a rational consumer characterized by an incomplete preference order is developed using distance functions and the zero-minimum (zero-maximum) principle. The essential comparative-static properties of the associated quantity-dependent and price-dependent demand structures are characterized. Utility functions are derived from distance functions for preference structures satisfying a complete ordering assumption. The Marshall-Hicks demand theory that is based on a utility-maximizing consumer is derived as a special case of rational consumer behavior. The Hicks-Allen demand decomposition is reviewed and a conjugate profit function approach to utility maximization is developed and used to discuss Revealed Preference Theory. The Chapter closes by examining the structural consequences of the independence axiom for d(x,y;g).

New Hybrid AD Methodology for Minimizing the Total Amount of Information Content: A Case Study of Rehabilitation Robot Design

Converting customer needs into specific forms and providing consumers with services are crucial in product design. Currently, conversion is no longer difficult due to the development of modern technology, and various measures can be applied for product realization, thus increasing the complexity of analysis and evaluation in the design process. The focus of the design process has thus shifted from problem solving to minimizing the total amount of information content. This paper presents a New Hybrid Axiomatic Design (AD) Methodology based on iteratively matching and merging design parameters that meet the independence axiom and attribute constraints by applying trimming technology, the ideal final results, and technology evolution theory. The proposed method minimizes the total amount of information content and improves the design quality. Finally, a case study of a rehabilitation robot design for hemiplegic patients is presented. The results indicate that the iterative matching and merging of related attributes can minimize the total amount of information content, reduce the cost, and improve design efficiency. Additionally, evolutionary technology prediction can ensure product novelty and improve market competitiveness. The methodology provides an excellent way to design a new (or improved) product.

Estimation of porosity of rocks based upon axiomatic local linear model tree (a lolimot model) approach

Shear and Compressional Wave Velocities along with other Petrophysical Logs, are considered as upmost important data for Hydrocarbon reservoirs characterization. In this study, porosity of the extracted rocks form concerned wells is interest as it can indicate the oil capacity of the wells of interest. In this study, we employ the principles of Axiomatic Design theory, specially the first (independence) axiom, to more simplify the measurement system. Also, to clarify the strength of Axiomatic Design theory in reducing the complexity of the system and optimizing the measurement system, we utilize the The Lolimot model (LOcal LInear MOdel Tree) as a model from the neural network family and apply it before and after implementing the basic logic of Axiomatic Design (AD) theory. In addition, in order to illustrate strength of the proposed method emphasizing the effectiveness of a method which benefit from both AD theory and Lolimot model together, the existing system used to measure the rock porosity is addressed and actual data related to one of wells located in southern Iran is utilized. The results of the study show that integrating the Axiomatic Design principles with the LOLIMOT method leads to the least complex and most accurate results.