A dynamic span model and associated control strategy for roll-transport systems used for sheet materials (Part II)

In this study, we propose a mathematical model that simulates the tension occurring at stands between rolls in a roll-transport system, and then we propose a method to estimate tension. The model is a lumped parameter system described by an ordinary differential equation (ODE). The ODE is derived on the basis of the tension of the stages between drive rolls on the stands. To build a realistic system, we utilized an estimation theory, which is the Kalman filter theory in a control theory. As a result, the proposed system is highly feasible

CHARACTERISTIC SIMILARITY OF PRODUCTION KEY ELEMENTS GREATLY AFFECTING PROFIT OF A PRODUCTIVE BUSINESS

In this study, we illustrate that the lead time, inventory, and rate of return deviation time series for production processes exhibit similar power-law distribution characteristics by analyzing the actual data. Lead time and inventory are considered to be autonomous distributed systems involving multiple oscillators, and the Kuramoto model is used to represent the synchronization phenomena. As an evidence for the existence of power-law characteristics, we depict that their behaviors demonstrate uctuations and on-off intermittency that can be represented using Langevin dynamics. Finally, we verify that all the three parameters depict power-law distributions using actual data

AN OPTIMAL PRODUCTION CAPACITY CONTROL INCLUDING OUTSIDE SUPPLIERS

This study is part of an ongoing report on an analysis of production processes using a lead-time function. We present a strategy for determining the optimal production capacity using a quadratic form evaluation function in the production process. A mathematical model of production process is introduced by a stochastic differential equations with a lognormal type. In general, a production capacity is proportional to the rate of return. To determine the optimal production capacity, we calculated the optimal solution by introducing the Hamilton-Jacobi-Bellman equation. We determine the optimum parameters of the quadratic form evaluation function on the basis of the optimal capacity solution. We reported that an optimal production capacity is highly dependent on a volatility in workers. Further, we present the actual throughput data for a production flow process with high productivity (using a synchronous method) and in the absence of a production flow process (using an asynchronous method). The production efficiency of the synchronous process becomes clear from the actual data. For further verification, we confirmed the benefit of using the synchronization process to attempt to perform dynamic simulation

ANALYSIS OF BUSINESS LOSS AND SYSTEM RISK CAUSED BY NONSTANDARD AND EXCESSIVE QUALITY

The loss function by Professor G.Taguchi is defined by the quality as "losses to be given to society after shipment, but excluding losses due to the function itself". Furthermore, he proposed an evaluation with a loss function that approximates that the loss is proportional to the square of the deviation from the target, and it was economically reasonable that the quality control using the standard deviation and the least squares method are appropriate. The probability distribution of the quality of main manufacturing parts (hybrid integrated chips) used in products is assumed to be a normal distribution. The distribution function gives the probability density function of the quality measurements for the individual products, and we here introduce a major loss function in quality engineering. Generally, the shipping-side standard and the receiving-side standard differ; therefore, the underquality and overquality are analyzed. The loss cost significantly fluctuates because of product quality problems, process lead time, and so forth, thereby affecting the profit risk. These system risks can be mathematically analyzed. We report calculation results for process risk probability based on actual data

Optimal Servo Design for distributed parameter system defined by a bilinear partial differential equation

We propose a mathematical model described in a bilinear partial differential equation of nonlinear coupled with state variable and control variable in this study. Furthermore, we propose the optimal servo system design of the stochastic model considering the disturbance. The general mixing reaction system is described in a bilinear partial differential equation.The complete mixing reaction system is assumed to maintain a space uniformly, we construct a bilinear model lumped parameter system. The target model is linearized by using a exact linear theory, we present a design proposal on the optimal servo system considering a disturbance into the system

PROFIT AND LOSS ANALYSIS ON A PRODUCTION BUSINESS USING LEADTIME FUNCTION

We propose a profit and loss analysis on the outlet side of a production flow processes using a lead time function. This is the ongoing study, which analyzes a production process by using a lead time function. With respect to a production business, we need to secure operating revenue as a production company. To analyze the profit and loss on a production business, we introduce a system for the evaluation of revenue under the conditions of borrowing and capital repayments. We use the actual data obtained from a production flow process for evaluation of the break even point. With regard to a value after a repayment, whether the value is changed or not in the case where a guaranty by a company president is required is reported. In addition, how a value of manufacturing equipment (remaining value) changes after a repayment of a loan relative to a repayment period is reported. Finally, a degree (sensitivity) of influence of parameters, an initial plan money amount, a repaid money amount and a repayment period, on a remaining value and a result of risk analysis is also reported

Mathematical Model of Plant Leaf Area Growth

In this paper, we introduce a mathematical model of plant growth, from the seedling to shipping of the adult plant. Our model has three parts. The first analyzes plant growth, the second models the fertilizer supply system, and the third identifies an optimal control strategy by matching the control system to the growth density. The mathematical model was defined using bilinear partial differential equations, but these were replaced by a strictly linear model

PROCESS-DELAY MODEL ESTIMATION AND RISK-AVOIDANCE

We propose the production process with time delay as the Ornstein-Uhlenbeck (OU) process in finance theory, which is a mathematical model of a mass-production process with a production delay. We also estimate the expected value and variance of the throughput of the whole period by utilizing Kalman flter theory, which is used for state estimation in control theory under the incomplete information is available for the whole period of the manufacturing process. Further, we propose an empirical equation,which represents a product value at the exit of the production process. For the theoretical verifcation, we present a numerical simulation

MATHEMATICAL MODELING AND POTENTIAL FUNCTION OF A PRODUCTION SYSTEM CONSIDERING THE STOCHASTIC RESONANCE

Why does stochastic resonance occur in production system? There is the motivation of this paper. The noises regard as the probability element that the worker affects the process progress, or the supply chain has an impact in the process. The probability element represents a working ability to have a probability distribution. The stochastic resonance represents the relationship between the volatility of the working ability as the noise intensity and the throughput. We construct a mathematical model utilizing a Langevin-type equation for propagation of throughput under a stochastic resonance. We also deeply analyze the fluctuation of production processes. The model includes the supply chain to be produced in collaboration with external companies. A flow-shop-type production method, which generally constitutes a line, is utilized in this paper. The mathematical model ultimately becomes a diffusion-type equation. Moreover, with respect to fluctuation, we report that a diffusion coefficient results in a synchronous status. The validation of evaluation based on the data throughput of the production process is presented. The synchronous process is shown to be a much better method. For further verification, we confirm the benefit of using the synchronous process for performing dynamic simulations