WIP control at end of line of semiconductor industry using CONWIP

Advancement of technology and trends in globalization has resulted in higher customer demands and expectations. Manufacturers now offer mass customization to stay competitive. In the semiconductor industry, where product mix and volume are high, production is further complicated by the different process routes and processing times for different product families. Coupled with rapid changeovers of products, it is essential to keep the work in process (WIP) low in order to reduce the inventory level on the shop floor. Constant W1P (CONWIP) is a production control strategy applicable in many manufacturing environment that use cards to control W1P level. This research was conducted in a semiconductor manufacturing company facing difficulty in reducing the variation in WIP on the shopfloor. The objectives of this research are to design and develop simulation models for single loop CONWIP, multi loop CONW1P, hybrid CONW1P, single loop CONWlP and multi loop CONWIP with buffer size optimization based on the environment in the case company. With the developed models, the maximum throughput (TH) and minimum W1P were determined. Discrete event simulation models were developed using the Witness Software for processes at the End of Line (EOL) production in the company. Experiments were conducted using these models to compare the current system with the single loop, multi loop, and hybrid CONWIP control mechanisms. ln addition, buffer optimization incorporating single loop and multi loop control were also examined. Performance parameters of TH and WIP level were compared in all experiments. The results show that CONWTP production control is more effective in reducing WlP level compared to the current system. Secondly, the single loop CONWIP showed the least number of cards in the system. However, hybrid CONWIP is more robust and provides a better control mechanism compared to the single and multi loop system. Buffer optimization control can further reduce the number of cards in the single and multi loop control. The developed simulation models are useful to determine the number of cards in the system and buffer size for each process. With these models, the production personnel can monitor and control the WJP dynamically to meet current demands and utilize the shopfloor space for more productive purposes

Geometric Distance Between Positive Definite Matrices of Different Dimensions

We show how the Riemannian distance on n++, the cone of n×n real symmetric or complex Hermitian positive definite matrices, may be used to naturally define a distance between two such matrices of different dimensions. Given that n++ also parameterizes n-dimensional ellipsoids, and inner products on ℝn, n×n covariance matrices of nondegenerate probability distributions, this gives us a natural way to define a geometric distance between a pair of such objects of different dimensions.ER

Inverting a complex matrix

We analyze a complex matrix inversion algorithm proposed by Frobenius, which we call the Frobenius inversion. We show that the Frobenius inversion uses the least number of real matrix multiplications and inversions among all complex matrix inversion algorithms. We also analyze numerical properties of the Frobenius inversion. We prove that the Frobenius inversion runs faster than the widely used method based on LU decomposition if and only if the ratio of the running time of the real matrix inversion to that of the real matrix multiplication is greater than $5/4$. We corroborate this theoretical result by numerical experiments. Moreover, we apply the Frobenius inversion to matrix sign function, Sylvester equation, and polar decomposition. In each of these examples, the Frobenius inversion is more efficient than inversion via LU-decomposition