Abstract: In the field of computer-based data processing, data sorting is an important issue. Among various sorting methods, Quick Sort is generally used. However, there is a problem that using Quick Sort makes sort time longer if the data to be sorted is already partially or fully in order. The invention solves the above-mentioned problem and makes the complexity of the sorting lower than or at least equal to that of Quick Sort. Thus, it provides a faster sorting method than Quick Sort does.

Abstract: Example embodiments of the present invention relate to a multivariate modeling method, a method of fabricating semiconductors using a semiconductor fabricating facility and a multivariate model creating apparatus. Other example embodiments of the present invention relate to a method and apparatus for modeling multivariate parameters having constants and the same pattern and a semiconductor fabricating method of detecting whether a semiconductor fabricating facility is operating normally using the multivariate modeling method. In a multivariate modeling method according to example embodiments of the present invention, data of parameters are selected during a modeling period. Averages and standard deviations of the data of the parameters may be calculated. It may be determined whether the data of the parameters contain non-random data. If the data of the parameters do not contain non-random data, the data may be normalized using the averages and standard deviations of the data of the parameters.

Abstract: An apparatus for controlling a semiconductor manufacturing process includes, a filter which receives from semiconductor processing devices first process parameters for processing a wafer and measured data obtained by measuring the wafer, and removes noise from the first process parameters and the measured data, a model generating unit which receives the first process parameters and the measured data from the filter and generates process models for predicting results of processing the wafer, a model selecting unit which selects a process model suitable for processing the wafer from a plurality of the process models stored in the model generating unit according to a received request, a process predicting unit which receives second process parameters for processing the wafer from the semiconductor processing devices, requests and receives the process model to and from the model selecting unit, and predicts a result of processing the wafer using the received process model, and a process controlling unit which rec