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Register a new userOptimal Replacement Policy under Cumulative Damage Model and Strength Degradation with Applications
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Prajamitra Bhuyan Dr.
Publication date
2019
fields
Mathematical Statistics
and research's language is
English
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In many real-life scenarios, system failure depends on dynamic stress-strength interference, where strength degrades and stress accumulates concurrently over time. In this paper, we consider the problem of finding an optimal replacement strategy that balances the cost of replacement with the cost of failure and results in a minimum expected cost per unit time under cumulative damage model with strength degradation. The existing recommendations are applicable only under restricted distributional assumptions and/or with fixed strength. As theoretical evaluation of the expected cost per unit time turns out to be very complicated, a simulation-based algorithm is proposed to evaluate the expected cost rate and find the optimal replacement strategy. The proposed method is easy to implement having wider domain of application. For illustration, the proposed method is applied to real case studies on mailbox and cell-phone battery experiments.
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Identifying the most deprived regions of any country or city is key if policy makers are to design successful interventions. However, locating areas with the greatest need is often surprisingly challenging in developing countries. Due to the logistical challenges of traditional household surveying, official statistics can be slow to be updated; estimates that exist can be coarse, a consequence of prohibitive costs and poor infrastructures; and mass urbanisation can render manually surveyed figures rapidly out-of-date. Comparative judgement models, such as the Bradley--Terry model, offer a promising solution. Leveraging local knowledge, elicited via comparisons of different areas affluence, such models can both simplify logistics and circumvent biases inherent to house-hold surveys. Yet widespread adoption remains limited, due to the large amount of data existing approaches still require. We address this via development of a novel Bayesian Spatial Bradley--Terry model, which substantially decreases the amount of data comparisons required for effective inference. This model integrates a network representation of the city or country, along with assumptions of spatial smoothness that allow deprivation in one area to be informed by neighbouring areas. We demonstrate the practical effectiveness of this method, through a novel comparative judgement data set collected in Dar es Salaam, Tanzania.
Functional Magnetic Resonance Imaging (fMRI) maps cerebral activation in response to stimuli but this activation is often difficult to detect, especially in low-signal contexts and single-subject studies. Accurate activation detection can be guided by the fact that very few voxels are, in reality, truly activated and that activated voxels are spatially localized, but it is challenging to incorporate both these facts. We provide a computationally feasible and methodologically sound model-based approach, implemented in the R package MixfMRI, that bounds the a priori expected proportion of activated voxels while also incorporating spatial context. Results on simulation experiments for different levels of activation detection difficulty are uniformly encouraging. The value of the methodology in low-signal and single-subject fMRI studies is illustrated on a sports imagination experiment. Concurrently, we also extend the potential use of fMRI as a clinical tool to, for example, detect awareness and improve treatment in individual patients in persistent vegetative state, such as traumatic brain injury survivors.
This paper introduces the R package slm which stands for Stationary Linear Models. The package contains a set of statistical procedures for linear regression in the general context where the error process is strictly stationary with short memory. We work in the setting of Hannan (1973), who proved the asymptotic normality of the (normalized) least squares estimators (LSE) under very mild conditions on the error process. We propose different ways to estimate the asymptotic covariance matrix of the LSE, and then to correct the type I error rates of the usual tests on the parameters (as well as confidence intervals). The procedures are evaluated through different sets of simulations, and two examples of real datasets are studied.
Accelerated degradation tests are used to provide accurate estimation of lifetime characteristics of highly reliable products within a relatively short testing time. Data from particular tests at high levels of stress (e.g., temperature, voltage, or vibration) are extrapolated, through a physically meaningful statistical model, to attain estimates of lifetime quantiles at normal use conditions. The gamma process is a natural model for estimating the degradation increments over certain degradation paths, which exhibit a monotone and strictly increasing degradation pattern. In this work, we derive first an algorithm-based optimal design for a repeated measures degradation test with single failure mode that corresponds to a single response component. The univariate degradation process is expressed using a gamma model where a generalized linear model is introduced to facilitate the derivation of an optimal design. Consequently, we extend the univariate model and characterize optimal designs for accelerated degradation tests with bivariate degradation processes. The first bivariate model includes two gamma processes as marginal degradation models. The second bivariate models is expressed by a gamma process along with a mixed effects linear model. We derive optimal designs for minimizing the asymptotic variance for estimating some quantile of the failure time distribution at the normal use conditions. Sensitivity analysis is conducted to study the behavior of the resulting optimal designs under misspecifications of adopted nominal values.
Under-representation of certain populations, based on gender, race/ethnicity, and age, in data collection for predictive modeling may yield less-accurate predictions for the under-represented groups. Recently, this issue of fairness in predictions has attracted significant attention, as data-driven models are increasingly utilized to perform crucial decision-making tasks. Methods to achieve fairness in the machine learning literature typically build a single prediction model subject to some fairness criteria in a manner that encourages fair prediction performances for all groups. These approaches have two major limitations: i) fairness is often achieved by compromising accuracy for some groups; ii) the underlying relationship between dependent and independent variables may not be the same across groups. We propose a Joint Fairness Model (JFM) approach for binary outcomes that estimates group-specific classifiers using a joint modeling objective function that incorporates fairness criteria for prediction. We introduce an Accelerated Smoothing Proximal Gradient Algorithm to solve the convex objective function, and demonstrate the properties of the proposed JFM estimates. Next, we presented the key asymptotic properties for the JFM parameter estimates. We examined the efficacy of the JFM approach in achieving prediction performances and parities, in comparison with the Single Fairness Model, group-separate model, and group-ignorant model through extensive simulations. Finally, we demonstrated the utility of the JFM method in the motivating example to obtain fair risk predictions for under-represented older patients diagnosed with coronavirus disease 2019 (COVID-19).
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