In this paper, we propose modeling for a single repairable system with a hierarchical structure under the assumption that the failures follow a nonhomogeneous Poisson process (which corresponds to minimal repair action) with a power-law intensity function. The properties of the new model are discussed in detail. The parameter estimators are obtained using the maximum likelihood method. A corrective approach is used to remove bias with order O(n −1), and the respective exact confidence intervals are proposed. A simulation study is conducted to show that our estimators are bias-free. The proposed modeling is illustrated via a toy example on a butterfly valve system, an example of an early-stage real project related to the traction system of an in-pipe robot, and also a real example on a blowout preventer system.

The use of transcranial Electrical Stimulation (tES) in the modulation of cognitive brain functions to improve neuropsychiatric conditions has extensively increased over the decades. tES techniques have also raised new challenges associated with study design, stimulation protocol, functional specificity, and dose-response relationship. In this paper, we addressed challenges through the emerging methodology to investigate the dose-response relationship of High Definition-transcranial Direct Current Stimulation (HD tDCS), identifying the role of negative valence in tinnitus perception. In light of the neurofunctional testable framework and tES application, hypotheses were formulated to measure clinical and surrogate endpoints. We posited that conscious pairing adequately pleasant stimuli with tinnitus perception results in correction of the loudness misperception and would be reinforced by concurrent active HD-tDCS on the left Dorsolateral Prefrontal Cortex (dlPFC). The dose-response relationship between HD-tDCS specificity and the loudness perception is also modeled. We conducted a double-blind, randomized crossover pilot study with six recruited tinnitus patients. Accrued data was utilized to design a well-controlled adaptive seamless Bayesian dose-response study. The sample size (n = 47, for 90% power and 95% confidence) and optimum interims were anticipated for adaptive decision-making about efficacy, safety, and single session dose parameters. Furthermore, preliminary pilot study results were sufficient to show a significant difference (90% power, 99% confidence) within the longitudinally detected self-report tinnitus loudness between before and under positive emotion induction. This study demonstrated a research methodology used to improve emotion regulation in tinnitus patients. In the projected method, positive emotion induction is essential for promoting functional targeting under HD-tDCS anatomical specificity to indicate the efficacy and facilitate the dose-finding process. The continuous updating of prior knowledge about efficacy and dose during the exploratory stage adapts the anticipated dose-response model. Consequently, the effective dose range to make superiority neuromodulation in correcting loudness misperception of tinnitus will be redefined. Highly effective dose adapts the study to a standard randomized trial and transforms it into the confirmatory stage in which active HD-tDCS protocol is compared with a sham trial (placebo-like). Establishing the HD-tDCS intervention protocols relying on this novel method provides reliable evidence for regulatory agencies to approve or reject the efficacy and safety. Furthermore, this paper supports a technical report for designing multimodality data-driven complementary investigations in emotion regulation, including EEG-driven neuro markers, Stroop-driven attention biases, and neuroimaging-driven brain network dynamics.

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In this paper, our proposal consists of incorporating frailty into a statistical methodology for modeling time-to-event data, based on non-proportional hazards regression model. Specifically, we use the generalized time-dependent logistic (GTDL) model with a frailty term introduced in the hazard function to control for unobservable heterogeneity among the sampling units. We also add a regression in the parameter that measures the effect of time, since it can directly reflect the influence of covariates on the effect of time-to-failure. The practical relevance of the proposed model is illustrated in a real problem based on a data set for downhole safety valves (DHSVs) used in offshore oil and gas production wells. The reliability estimation of DHSVs can be used, among others, to predict the blowout occurrence, assess the workover demand and aid decision-making actions.INDEX TERMS Downhole safety valve, frailty model, generalized time-dependent logistic, hydrogen sulfide concentration, non-proportional hazard.

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