Optimal Size Parameters Research Articles

Optimal reliability, production lot size and safety stock in an imperfect production system

This paper is concerned with the joint determination of optimal production lot size, safety stock and reliability parameter under the realistic assumptions that the production facility is subject to random breakdown of machinery system and also to change in the variable reliability parameter. Reliability of a machinery system is a decision variable that can be increased by more investment in production technology. In this model, preventive and corrective maintenance, safety stock for repair times and shortages are adopted to generalise the model. Except machinery breakdown, the manufacturing system may shift from in-control state to out-of-control state. During out-of-control state, a certain percentage of total production consists of defective items which can be reworked immediately at a cost to make as good as perfect quality items. The cost function is maximised by Khun-Tucker method. Numerical results are provided to illustrate both the study of the optimal solutions and sensitivity of different changes in key parameters.

Actin–Fascin Bundle Formation Under Pressure

Studies of the dependence of fascin:actin bundle formation on thermodynamic properties are important for understanding cell processes such as migration and differentiation. We report a novel approach utilizing an expanded equilibrium polymerization Flory–Huggins type model to model fascin:actin bundle formation under thermodynamic pressure. A free energy expression that considers both polymer solution physics and both the deactivation of fascin and propagation of fascin:actin bundles was derived for this system. Using this free energy expression, we report the composition’s dependency on pressure while varying: fascin to actin molar ratios [1,3, and 6], initial F-actin concentration [9.52 × 10−9–5.7 × 10−8 mM], specific volume, and K deact. Bundle formation was shown to increase as a function of pressure and to be limited by F-actin. Furthermore, our model was able to quantitatively predict an optimal size parameter for the deactivated fascin molecule (s F = 4645) and for the deactivation equilibrium constant (K deact = 2.66 × 108). These results present a novel approach to study fascin cross-linking of actin bundles and provide avenues for future experiments to develop a more comprehensive understanding of cell–matrix interactions.

Fe-Based Electrocatalysts for Oxygen Reduction in PEMFCs Using Ballmilled Graphite Powder as a Carbon Support

Active Fe-based electrocatalysts were prepared using ballmilled graphite powder as a carbon support. The best performing catalysts were achieved by acid-washing, iron-loading, and pyrolyzing the ballmilled graphite powders. Only of ballmilling was required to produce optimal catalytic activity. High-energy ballmilling of pristine graphite powder under nitrogen was shown to reduce crystallite size, increase nitrogen content, increase surface area, increase degree of disorder, and inevitably introduce metallic impurities. Acid-washing treatment of ballmilled graphite powders reduced, but did not completely eliminate, metallic impurities. Iron enrichment and pyrolysis of acid-washed, ballmilled graphite powder was shown to increase catalytic activity, have little effect on crystallite size, increase surface area, and decrease degree of disorder. It was found that catalytic activity increases as crystallite size decreases, degree of disorder and nitrogen content increase, and micropore specific surface area increases. Fuel cell test results have shown that the order of increasing maximum power density follows the order of increasing catalytic activity. Interestingly, the optimal crystallite size parameter and maximum activity for catalysts made with either ballmilled graphite powder or carbon black is almost the same.

Model Adjustment and Multi-Model Based Fault Diagnosis for Hydraulic Servo Axis

This paper presents a model adjustment and a multi-model based fault diagnosis approach. Both methods are based on the same idea. A physical model of the process is altered such that it mimics the behavior of the process in the presence of certain faults. A number of these modified models, each governing a different fault condition, are evaluated and the model with the smallest output error is determined. As this model is assumed to best govern the current process dynamics, it can be used to diagnose the actual state of the process. Two variations of this idea are presented, tailored specifically to online and offline operation respectively. For online applications, multiple models with fixed parameters are evaluated in parallel, whereas for offline application, an optimization approach is employed. Here, one model with several fault size parameters is regarded and the optimal fault size parameters are determined by means of an interval halving technique. Both techniques have been evaluated at a testbed and have shown very good fault detection and diagnosis capabilities.

Replica Symmetry Breaking in Renormalization: Application to the Randomly Pinned Planar Flux Array

The randomly pinned planar flux line array is supposed to show a phase transition to a vortex glass phase at low temperatures. This transition has been examined by using a mapping onto a 2D XY-model with random an\-iso\-tropy but without vortices and applying a renormalization group treatment to the replicated Hamiltonian based on the mapping to a Coulomb gas of vector charges. This renormalization group approach is extended by deriving renormalization group flow equations which take into account the possibility of a one-step replica symmetry breaking. It is shown that the renormalization group flow is unstable with respect to replica asymmetric perturbations and new fixed points with a broken replica symmetry are obtained. Approaching these fixed points the system can optimize its free energy contributions from fluctuations on large length scales; an optimal block size parameter $m$ can be found. Correlation functions for the case of a broken replica symmetry can be calculated. We obtain both correlations diverging as $\ln{r}$ and $\ln^2{r}$ depending on the choice of $m$.

Vehicle-and-trajectory optimization of nuclear electric spacecraft for lunar missions

A new combined vehicle-and-trajectory optimization problem is solved for a low-thrust nuclear-electricpropulsion spacecraft whose motion is governed by restricted three-body-problem dynamics for the Earth-moon system. The problem involves computing the optimal spacecraft sizing parameters and trajectory design variables that result in the maximum payload for a fixed-trip-time, planar transfer from circular low Earth orbit to circular low-lunar orbit. In particular, the optimal specific impulse and input power are computed. The detailed vehicleand-trajectory optimization approach is effective in solving a complex interactive problem that is important to both spacecraft and mission designers. Several numerical solutions are obtained for a wide range of trip times.

Determination of optimal lot sizing parameters and a controllable process mean for a production system

Several mathematical models have been developed separately for determining production and recycled lot quantities to minimize total production cost and the determination of optimal process mean setting to minimize total quality cost. For a single stage discrete part production system, this paper presents a mathematical model that combines these two inter-related aspects. The production process has a controllable parameter, the process mean, which determines the output lot quality. One-sided tolerance is used to decide the quality of finished goods. Bad units are reworked before they can be reprocessed with the fresh input. For such a situation, the model determines production lot size, recycling lot quantity, and a process mean while minimizing total system cost. The model has been validated using sample data from a pharmaceutical company. Results indicate that the production lot size and the recycled quantity have an inverse relationship with process mean and, a direct relationship with process variance.

Optimal inventory control in a production flow system with failures

We consider a continuous flow production process subject to failures with an intermediate buffer. Under the practical restriction to the class of (B, b) inventory control policies, we give a procedure for determining the optimal buffer size, B, and control parameter, b. We give conditions under which these parameters can be expressed in closed form and show that otherwise they can be computed as the solution of a two-dimensional nonlinear system.

ON REGIONAL OPTIMISATION OF GRID AND RELAXATION PARAMETER FOR FINITE DIFFERENCE SOLUTION OF POISSONS' EQUATION IN REVERSE BIASED PLANAR TYPE p‐n JUNCTIONS

The optimisation of grid structure and relaxation parameter is considered in this paper in connection with two‐dimensional finite difference solution of Poisson's equation for determining the field profile in a reverse biased planar type p?n junction. By dividing the planar junction into regions with rectangular and circular symmetry, regional optimisations have been carried out using small area test sites. Having obtained the optimal grid size and relaxation parameter for each region, the complete solution was obtained easily with very fast convergence. The method involved in this kind of regional optimisation is presented in detail with discussions on its comparative usefulness with other known techniques.

Two-stage selection and testing designs for comparative clinical trials

SUMMARY A two-stage design which selects the best of several experimental treatments and compares it to a standard control is proposed. The design allows early termination with acceptance of the global null hypothesis. Optimal sample size and cut-off parameters are obtained by minimizing expected total sample size for fixed significance level and power. with many other factors. Moreover, the usual error rate computations associated with comparative testing do not account for the preliminary selection process. Consequently, the overall procedure may be neither effective nor efficient for identifying an experimental treatment which is an improvement over C. In this paper we propose a new approach to the problem of identifying the best of K experimental treatments and determining whether it is superior to a control. We deal with the binomial setting where patient response may be characterized as either success or failure, with ok the success probability for Ek; k =0 corresponds to C. For ease of notation assume 01 -... OK . We propose a two-stage procedure which allows early termination with acceptance of H0: o = 01 =. .. = OK, with design parameters chosen to minimize expected total sample size. The design and accompanying generalized definitions of size a and power 1 - ,3 are given in ? 2. The algorithm used for optimization is described in ? 3. Numerical results are presented in ? 4, followed by a discussion of the relative merits of the proposed design.