This work identifies a link between quality control scheme and the learning effect caused by the quality improvement program. The reduction rate of process standard deviation may be large during the initial stage of the quality improvement program, and influences the construction of control chart. Simulation is used to evaluate the performance of the control charts. The EWMA mean control chart with consideration of learning curve performs best. The Shewhart mean control chart without learning curve consideration has almost no detection ability when the shift magnitude of the process mean is small.

Almost all of the existing two-dimensional block-based medial axis transform (2D_BB_MAT) parallel algorithm are devised for solving the 2D_BB_MAT problem only and are very difficult to extend to a solution of the 3D_BB_MAT problem in parallel. In this paper, we propose efficient O(1) time algorithms for solving the hD_BB_MAT problems, where h is 2 or 3, on the linear array with a reconfigurable pipelined bus system (LARPBS) model. The proposed 2D_BB_MAT algorithm can easily extend to a solution of the 3D_BB_MAT problem in parallel by reducing the hD_BB_MAT problems to the forward chessboard distance transform problems. To the best of our knowledge, the proposed algorithms are the most efficient O(1) time algorithms compared with all the previously published algorithms known.

In this paper, we present a constant time algorithm for solving three dimensional block-based medial axis transform (3D BB-MAT, for short) on the array with reconfigurable optical buses (AROB). The main contribution of this work is to exploit the dominance counting method for solving the 3D BB-MAT that was never done previously in the literature. With the advantages of both optical transmission and electronic computation on the AROB model, the constant algorithm is proposed for the medial axis transform of a 3D N x N x N binary image on a 4D AROB using N^4 processors. To the best of our knowledge, this presented result of the dominance counting technique for medial axis transform of block-based is the best O(1) time algorithm known.

Many parallel algorithms have been proposed for computing the two-dimensional block-based medial axis transform (2D/spl I.bar/BB/spl I.bar/MAT). Unfortunately, almost all of them are dedicated for solving 2D/spl I.bar/BB/spl I.bar/MAT problem and are very difficult to be extended for solving the 3D/spl I.bar/BB/spl I.bar/MAT problem. In this paper, an O(1) time algorithm for solving the 2D/spl I.bar/BB/spl I.bar/MAT of a binary image P of size N /spl times/ N on an LARPBS is first developed. The running time of this algorithm has a smaller constant factor compared with those of all the other previous proposed O(1) time algorithms. Then this algorithm is extended for computing the 3D/spl I.bar/BB/spl I.bar/MAT of a binary image V of size N /spl times/ N /spl times/ N in O(1) time on an LARPBS. The running time of this algorithm has a small constant factor also. To the best of our knowledge, this is the first parallel algorithm proposed for solving the 3D/spl I.bar/BB/spl I.bar/MAT problem known.

We present two O(1)-time algorithms for solving the 2D all nearest neighbor (2D/spl I.bar/ANN) problem, the 2D closest pair (2D/spl I.bar/CP) problem, the 3D all nearest neighbor (3D/spl I.bar/ANN) problem and the 3D-closest pair (3D/spl I.bar/CP) problem of n points on the linear array with a reconfigurable pipelined bus system (LARPBS) from the computational geometry perspective. The first O(1) time algorithm, which invokes the ANN properties (introduced in this paper) only once, can solve the 2D/spl I.bar/ANN and 2D/spl I.bar/CP problems of n points on an LARPBS of size 1/2n/sup 5/3+c/, and the 3D/spl I.bar/ANN and 3D/spl I.bar/CP problems pf n points on an LARPBS of size 1/2n/sup 7/4+c/, where 0 < /spl epsi/ = 1/2/sup c+1/-1 /spl Lt/ 1, c is a constant and positive integer. The second O(1) time algorithm, which recursively invokes the ANN properties k times, can solve the kD/spl I.bar/ANN, and kD/spl I.bar/CP problems of n points on an LARPBS of size 1/2n/sup 3/2+c/, where k = 2 or 3, 0 < /spl epsi/ = 1/2/sup n+1/-1 /spl Lt/ 1, and c is a constant and positive integer. To the best of our knowledge, all results derived above are the best O(1) time ANN algorithms known.

In this paper, we present algorithms for computing the Euclidean distance transform (EDT) of a binary image on the array with reconfigurable optical buses (AROB). First, we develop a parallel algorithm termed as Algorithm Expander which can be implemented in O(1) time on an AROB with N x Ndelta processors, where delta = 1/k, k is a constant and a positive integer. Algorithm Expander is designed to compute a higher dimensional EDT based on the computed lower dimensional EDT. It functions as a general EDT expander for us to expand EDT from a lower dimension to a higher dimension. We then develop parallel algorithms for the two-dimensional (2-D)_EDT of a binary image array of size N x N in O(1) time on an AROB with N x N x Ndelta processors and for the three-dimensional (3-D)_EDT of a binary image of size N x N x N in O(1) time on an AROB with N x N x N x Ndelta processors. To the best of our knowledge, all results derived above are the best O(1) time algorithms known. We then extend it to compute the nD_EDT of a binary image of size Nn in O(n) time on an AROB with Nn+delta processors. We also apply our parallel EDT algorithms to build Voronoi diagram and Voronoi polyhetra (polygons), to find all maximal empty spheres and the largest empty sphere, and to compute the medial axis transform. All of these applications can be solved in the same time complexity on an AROB with the same number of processors as needed for solving the EDT problems in the same dimensions.

We develop a parallel algorithm for the 2D Euclidean distance transform (2D/spl I.bar/EDT, for short) of a binary image of size N /spl times/ N in O(1) time using N/sup 2+/spl delta/+/spl epsi// CRCW processors and a parallel algorithm for the 3D Euclidean distance transform (3D/spl I.bar/EDT, for short) of a binary image of size N /spl times/ N /spl times/ N in O(1) time using N/sup 3+/spl delta/+/spl epsi// CRCW processors, where /spl delta/=1/, /spl epsi/=1/(2/sup c+1/-1), h, and are constants and positive integers. Our 2D/spl I.bar/EDT (3D/spl I.bar/EDT) parallel algorithm can be used to build up Voronoi diagram and Voronoi polygons (polyhedra) in a 2D (3D) binary image also. All of these parallel algorithms can be performed in O(1) time using N/sup 2+/spl delta/+/spl epsi// (N/sup 3+/spl delta/+/spl epsi//) CRCW processors. To the best of our knowledge, all results derived above are the best O(1) time algorithms known.