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Statistical process monitoring in a specified period for the image data of fused deposition modeling parts with consistent layers

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Abstract

Statistical process monitoring (SPM) methods have been adopted and studied to detect variations in the fused deposition modeling (FDM) process in recent years. The FDM process that builds parts layer-by-layer is accomplished in a specified manufacturing period (number of layers) without interruption or suspension. Thus, traditional SPM methods, where the average run length is used for the calculation of the control limits and the measurement of the performance, are no longer applicable to the FDM process. In this paper, an SPM method is proposed based on the surface image data of FDM parts with consistent layers and a specified period. The probability of alarm in a specified period (PASP) and the cumulative PASP are introduced to determine the control limits and evaluate the monitoring performance. Regions of interest are determined in a fixed way to cover the sizes and locations of different defects. The statistics are calculated based on the generalized likelihood ratio. The control limit is determined based on the specified period and the nominal in-control PASP. A simulation study for different locations, sizes and magnitudes of the mean shift of defects is presented. In the case study, the proposed SPM method is applied to monitor the FDM process of a cuboid, which verifies the effectiveness of the proposed method.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (NSFC71601009).

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Authors and Affiliations

  1. School of Reliability and Systems Engineering, Beihang University, Beijing, China

    Tingting Huang, Shanggang Wang, Shunkun Yang & Wei Dai

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  1. Tingting Huang
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  2. Shanggang Wang
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  3. Shunkun Yang
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  4. Wei Dai
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Correspondence to Wei Dai.

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Appendix

Appendix

The Hotelling T2 control chart is presented as an application of PASP and a comparison with the GLR method. In the simulation study, for the determination of ROIs, the nominal image is divided into 10 × 10 blocks with equal size, and results in 100 non-overlap ROIs. The mean intensity values of ROIs are considered as the variables for the Hotelling T2 control chart. In total 1000 images are generated by adding Poisson noise to the nominal image, the sample mean vector and the variance–covariance matrix can then be calculated. As period M = 40, the nominal PASP0 is equal to 0.1025 according to the Type-I error listed in Table 3, and the upper control limit (UCL) is equal to 175 with the calculated PASP0 = 0.108 based on 1000 simulation runs. The difference between the calculated and the nominal PASP0 is 0.0055. In total 30 different conditions are considered in the simulation as the GLR method. Simulation results of cumulative PASP1 with a delay of 8 for 30 conditions are listed in Table 13, and simulation results of cumulative PASP1 for two different locations, three different sizes with a delay from 0 to 8 and a shift of − 10, − 8, − 5, − 3 and − 1 are listed in Tables 14, 15, 16, 17 and 18 as follow.

Table 13 Cumulative PASP1 with a delay of 8 for 30 conditions
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Table 14 Cumulative PASP1 with a delay from 0 to 8 and a shift of − 10
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Table 15 Cumulative PASP1 with a delay from 0 to 8 and a shift of − 8
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Table 16 Cumulative PASP1 with a delay from 0 to 8 and a shift of − 5
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Table 17 Cumulative PASP1 with a delay from 0 to 8 and a shift of − 3
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Table 18 Cumulative PASP1 with a delay from 0 to 8 and a shift of − 1
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The ROIs determined in the Hotelling T2 control chart do not have overlaps as in the GLR method to avoid too many highly correlated variables. The number of variables in the Hotelling T2 control chart is determined considering the overall efficiency of the control chart for different possible sizes of defects. For large size of defect, small number of variables is preferred as the cumulative PASP1 converges to 1 faster with the increase of the delay; for small size of defect, large number of variables is preferred as the ROIs can cover the defect area more properly without containing too many non-defect areas. Compared with the Hotelling T2 control chart, GLR method has smaller cumulative PASP1 for small delay for many cases, but cumulative PASP1 converges to 1 with the increase of delay much faster. In addition, GLR method is capable of finding the change point of the out of control condition, and detecting the location of the defect, while the Hotelling T2 control chart could not.

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Huang, T., Wang, S., Yang, S. et al. Statistical process monitoring in a specified period for the image data of fused deposition modeling parts with consistent layers. J Intell Manuf 32, 2181–2196 (2021). https://doi.org/10.1007/s10845-020-01628-4

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  • DOI: https://doi.org/10.1007/s10845-020-01628-4

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