Int J Performability Eng ›› 2018, Vol. 14 ›› Issue (12): 2971-2982.doi: 10.23940/ijpe.18.12.p7.29712982
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Senyang Bai(), Zhijun Cheng, Qian Zhao, Xiang Jia, and Hang Yao
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Bai Senyang
E-mail:1196860424@qq.com
Senyang Bai, Zhijun Cheng, Qian Zhao, Xiang Jia, and Hang Yao. A Sequential Inspection Model based on Risk Quantitative Constraint and Component Importance [J]. Int J Performability Eng, 2018, 14(12): 2971-2982.
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Nomenclature"
${{R}^{*}}$ | The constraint value of system reliability | ${{\theta }_{k}}$ | The model parameter$(a_{0k}^{(i+1)},D_{0k}^{(i+1)},Q_{k}^{(i+1)},({{\sigma }^{2}})_{k}^{(i+1)})$ |
${{r}^{*}}$ | The constraint value of components reliability | $\Delta {{t}_{ik}}$ | Inspection interval |
${{I}_{i}}$ | Importance of the components | ${{t}_{ik}}$ | Time of kth inspection after ith maintenance |
$\Delta {{r}_{i}}$ | The reliability of each component which need to be improved | ${{x}_{ik}}$ | Degradation data of kth inspection after ith maintenance |
$\mu $ | Drift coefficient | ${{x}_{i(0:k)}}$ | Set of degradation data after ith maintenance |
$\sigma $ | Diffusion coefficient | ${{l}_{k}}$ | The remaining life of the product at the time ${{t}_{k}}$ |
$w$ | Failure threshold | ${{f}_{{{L}_{k}}|{{X}_{0:k}}}}({{l}_{k}}|{{X}_{0:k}})$ | The PDF of the remaining life for the product |
$a$ | The mean of $\mu $ | ${{R}_{S}}(t|{{x}_{k}})$ | Real-time reliability of the product at time$t$ |
${{D}_{k|k}}$ | The updated variance of$\mu $ | ${{R}_{S}}({{l}_{ik}}|{{X}_{0:k}})$ | Real-time reliability of the remaining life for the product |
Table 1
The calculation results of sequential inspection interval (${{r}^{*}}=0.903$)"
The serial number | ${{t}_{ik}}/h$ | ${{x}_{ik}}/({}^\circ /h)$ | ${{a}_{ik}}$ | ${{D}_{ik}}$ | ${{Q}_{ik}}$ | ${{({{\sigma }^{2}})}_{ik}}$ | $\Delta {{\hat{t}}_{ik}}/h$ | Remarks |
---|---|---|---|---|---|---|---|---|
The initial state (${{t}_{0}}=0$) | 0.00000 | 0.00000 | 0.04426 | 0.00017 | 0.00737 | 0.00053 | 4.71120 | The degradation data exceeds the failure threshold 0.6 $({}^\circ /h)$ at the sixth inspection, which needs to be replaced. |
${{t}_{01}}$ | 4.7112 | 0.19203 | 0.04419 | 0.00016 | 0.00028 | 0.00083 | 4.71120 | |
${{t}_{02}}$ | 9.4224 | 0.35605 | 0.04273 | 0.00012 | 0.00015 | 0.00059 | 3.80590 | |
${{t}_{03}}$ | 13.2283 | 0.27352 | 0.04106 | 0.00008 | 0.00100 | 0.00434 | 3.38730 | |
${{t}_{04}}$ | 16.6156 | 0.31776 | 0.04068 | 0.00007 | 0.00068 | 0.00356 | 3.01020 | |
${{t}_{05}}$ | 19.6258 | 0.30006 | 0.04012 | 0.00007 | 0.00050 | 0.00285 | 3.58900 | |
${{t}_{06}}$ | 23.2148 | 1.84797 | —— | —— | —— | —— | —— | |
Replace as new (${{t}_{1}}$) | 23.2148 | 0.00000 | 0.04012 | 0.00007 | 0.00050 | 0.00285 | 8.75680 | The degradation data exceeds the failure threshold at the fifth inspection, which needs to be replaced. |
${{t}_{11}}$ | 31.9716 | 0.28173 | 0.03950 | 0.00006 | 0.00024 | 0.00104 | 5.26090 | |
${{t}_{12}}$ | 37.2325 | 0.19451 | 0.03773 | 0.00005 | 0.00101 | 0.00657 | 4.05290 | |
${{t}_{13}}$ | 41.2854 | 0.31754 | 0.03721 | 0.00005 | 0.00068 | 0.00546 | 2.60630 | |
${{t}_{14}}$ | 43.8917 | 0.49501 | 0.03660 | 0.00005 | 0.00052 | 0.00515 | 0.54880 | |
${{t}_{15}}$ | 44.4405 | 0.62656 | —— | —— | —— | —— | —— | |
Replace as new (${{t}_{2}}$) | 44.4405 | 0.00000 | 0.03660 | 0.00005 | 0.00052 | 0.00515 | 7.92460 | The degradation data exceeds the failure threshold at the fourth inspection, which needs to be replaced. |
${{t}_{21}}$ | 52.3651 | 0.20505 | 0.03616 | 0.00005 | 0.00032 | 0.00122 | 6.86210 | |
${{t}_{22}}$ | 59.2272 | 0.20363 | 0.03453 | 0.00004 | 0.00031 | 0.00273 | 5.85850 | |
${{t}_{23}}$ | 65.0857 | 0.49155 | 0.03359 | 0.00004 | 0.00025 | 0.00410 | 0.69760 | |
${{t}_{24}}$ | 65.7833 | 0.66387 | —— | —— | —— | —— | ||
… | … | ... | … | … | … | ... |
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