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The problem of image segmentation can be reduced to the clustering of pixels in the intensity space. The traditional fuzzy c-means algorithm only uses pixel membership information and does not make full use of spatial information around the pixel, so it is not ideal for noise reduction. Therefore, this paper proposes a clustering algorithm based on spatial information to improve the anti-noise and accuracy of image segmentation. Firstly, the image is roughly clustered using the improved L&eacute, vy grey wolf optimization algorithm (LGWO) to obtain the initial clustering center. Secondly, the neighborhood and non-neighborhood information around the pixel is added into the target function as spatial information, the weight between the pixel information and non-neighborhood spatial information is adjusted by information entropy, and the traditional Euclidean distance is replaced by the improved distance measure. Finally, the objective function is optimized by the gradient descent method to segment the image correctly.

Starting the online monitoring of a quality characteristic by means of a control chart at the beginning of a short production run is often a challenging issue for quality practitioners: in fact, the frequent absence of preliminary information prevents from getting a precise estimate of the characteristic mean and standard deviation. Furthermore, for short runs having a finite rolling horizon, the number of inspections scheduled within the run can be too small to get sufficient samples allowing the phase I implementation of the chart to be completed. Recently, t control charts have been proposed as efficient means to overcome this problem because they do not need any phase I tentative control limits definition or preliminary process knowledge. In this paper, a variable sample size (VSS) version of the t chart is proposed. Adaptive control charts have been implemented with success in long runs: here, the performance of the variable sample size strategy is investigated for a chart used in a short run. The statistical performance of the VSS t chart is compared with the one of the fixed-parameter (FP) t chart for both scenarios of fixed and unknown shift size, with the latter situation being frequent in short-run manufacturing environments. An extensive numerical investigation reveals the potential benefits of the proposed chart. When the statistical design is optimized with respect to a fixed value of the shift size δ, the VSS t chart has a better statistical performance than the FP t chart for moderate to large values of δ. Conversely, for the unknown shift size condition, the VSS t chart always outperforms the FP t chart for in-control average sample sizes ASS0 > 7. An illustrative example shows the implementation of the VSS during the production of a finite lot of mechanical parts.