Asynchronous Stochastic Learning Curves for Production Simulation
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Solution Overview
Problem
Large-scale engineer-to-order production systems, such as those producing complex products like commercial airplanes, face challenges in predicting component providers' ability to meet deadlines due to dynamic and unequally distributed lead times and improvement rates, especially when components are sourced from various parties worldwide.
Innovation Solution
The use of asynchronous stochastic learning curves for arithmetic modeling allows for the simulation and analysis of production systems, enabling the assignment of learning curve parameters to each component and simulating production cycles to analyze the ability of multiple providers to meet common deadlines, thereby improving the understanding and integration of mass customization production systems.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional production modeling methods are used, then the system is simpler to implement, but the ability to accurately predict component providers' ability to meet deadlines deteriorates due to dynamic and unequally distributed lead times and improvement rates
Solution Approach 1:
The patent applies parameter changes by transforming static production models into dynamic stochastic models that incorporate time-varying parameters. Specifically, lead times and improvement rates are modeled as stochastic processes that change over time, allowing the system to capture the dynamic nature of production systems while maintaining mathematical tractability through defined probability distributions and update rules.
Solution Approach 2:
The patent implements dynamics by introducing time-dependent stochastic processes for lead times and improvement rates. Rather than using fixed parameters, the model allows these parameters to evolve dynamically according to specified probability distributions, enabling accurate prediction of component delivery timelines in changing production environments while managing complexity through structured stochastic modeling approaches.
2Reliability
If asynchronous stochastic learning curves are implemented for each component, then the statistical analysis capability improves, but the computational complexity and data processing requirements worsen
Solution Approach 1:
The patent applies segmentation by dividing the overall production system into independent component models, each with its own asynchronous stochastic learning curve. This allows statistical analysis to be performed on individual components separately, reducing the computational burden compared to analyzing the entire system as a single complex unit, while still capturing the collective behavior through integration of component-level predictions.
3Adaptability or versatility
If distributed component providers are integrated into the production system, then the system's adaptability and resource availability improve, but the difficulty of coordinating deadlines and managing lead times worsens
Solution Approach 1:
The patent implements universality by creating a standardized stochastic modeling framework that can be applied uniformly across distributed component providers regardless of their specific characteristics. This universal model structure enables different providers to be integrated into the same production system with consistent coordination rules, managing complexity through standardization while maintaining adaptability to individual provider capabilities through parameter customization.
Data Source
AI summary
Systems and methods for arithmetic modeling of large scale engineer-to-order production systems using asynchronous stochastic learning curve are disclosed. In one embodiment, a method for simulating a production system configured to produce a product includes, for a plurality of components, assigning learning curve parameters for an asynchronous stochastic learning curve associated with each component. Master schedule data for manufacturing a plurality of the product are received, and production of the plurality of components a plurality of cycles corresponding to the plurality of the product is simulated. The results of the simulated productions are output for analysis. In a further aspect, the product is an aircraft, and the components are aircraft components.