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a b s t r a c tThe delay time model (DTM) is widely used to model the two-stage failure process and is helpful for developing cost-effective inspection/maintenance plans. Imperfect maintenance is common in practice, but seldom considered in DTM. An improved DTM with imperfect maintenance at inspection has been developed based on the assumption of imperfect inspection maintenance and perfect failure maintenance. The model of the long-run availability for the improved DTM is established. Parameters estimation method and the test for goodness of fit method are given. Numerical simulations are performed to study the influence of imperfect maintenance on the long-run availability and to validate the credibility of the parameters estimation method. The results show that imperfect maintenance will decrease the long-run availability. The existence of the optimal inspection interval regarding the maximum long-run availability is tightly related to the improvement factor, which denotes the maintenance effect. The parameters estimation method proves credible. The maximum likelihood estimations of the reliability parameters can be easily achieved by the Genetic Algorithms (GAs) searching tool.

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BackgroundGlioblastoma (GBM) isa lethal type of primary brain tumor with a median survival less than 15 months.Despiting the recent improvements of comprehensive strategies,the outcomes for GBM patients remain dismal.Accumulating evidence indicates that rapid acquired chemoresistance is the major cause ofGBM recurrence thus leads to worse clinical outcomes. Therefore, developing novel biomarkers and therapeutic targets for chemoresistant GBM is crucial for long-term cures. MethodsTranscriptomic profiles of glioblastoma were downloaded from gene expression omnibus (GEO) and TCGA database. Differentially expressed genes were analyzed and candidate gene PLK2 was selected for subsequent validation. Clinical samples and corresponding data were collected from our center and measured using immunohistochemistry analysis. Lentiviral transduction and in vivo xenograft transplantation were used to validate the bioinformatic findings. GSEA analyses were conducted to identify potential signaling pathways related to PLK2 expression and further confirmed by in vitro mechanistic assays. ResultsIn this study, we identified PLK2 as an extremely suppressed kinase-encoding gene in GBM samples, particularly in therapy resistant GBM. Additionally, reduced PLK2 expression implied poor prognosis and TMZ resistance in GBM patients. Functionally, up-regulated PLK2 attenuated cell proliferation, immigration, invasion, and tumorigenesis of GBM cells. Besides, exogenous overexpression of PLK2 reduced acquired TMZ resistance of GBM cells. Furthermore, bioinformatics analysis indicated that PLK2 was negatively correlated with Notch signaling pathway in GBM. Mechanically, loss of PLK2 activated Notch pathway through negative transcriptional regulation of HES1 and degradation of Notch1.ConclusionLoss of PLK2 enhances aggressive biological behavior of GBM through activation of Notch signaling, indicating that PLK2 could be a prognostic biomarker and potential therapeutic target for chemoresistant GBM.