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Shovan Chowdhury

Publications and source records attributed to Shovan Chowdhury.

18 recordsLinked to original sources

Human AI Construction of Bayesian Networks for Operational Decision Support -- A Virtual Survey Approach

Bayesian Belief Networks (BBNs) are powerful tools for decision-making under uncertainty. However, building their structures and estimating parameters are difficult. Currently, researchers must choose between relying on expert judgement or using large datasets to learn the structure and parameters of the network. We propose a new methodology using Large Language Models to bridge the gap between expert opinion and data-driven learning. This approach uses a panel of AI agents to estimate probabilities based on specific personas and context. We then apply a trimmed-mean rule to remove noise from these responses. We develop a six step BBN framework and illustrate it to model customer intention to consult a doctor in an alternative healthcare system. The model reveals that while self efficacy appears to be a major factor, its actual causal impact is small. In contrast, subjective norms have a much stronger effect in modelling customers' intention. The most effective strategy is to improve both confidence and community norms simultaneously.

cs.AI

Active Redundancy Allocation Strategy at Component and System Level

Researchers and practitioners in the field of reliability engineering and optimization frequently use active redundancy techniques to intensify the performance of systems. In this article, we study allocation strategies of non-matching active redundancies (spares) in coherent systems consisting of possibly dependent and identical components for achieving better system reliability. The dependence of the components is modeled through copulas using the distortion function. Sufficient conditions are derived to establish optimal allocation strategies for two heterogeneous active redundancies at the component or system levels. Moreover, the results are true for the component lifetimes following a general family of parametric distributions. The results guarantee the likelihood ratio (reversed hazard) ordering between the coherent systems at the component level (system level) active redundancies. Some aging properties are also established in this endeavor. Several examples are provided to demonstrate the theoretical results.

stat.AP

Optimal Accelerated Life Testing Sampling Plan Design with Piecewise Linear Function based Modeling of Lifetime Characteristics

Researchers have widely used accelerated life tests to determine an optimal inspection plan for lot acceptance. All such plans are proposed by assuming a known relationship between the lifetime characteristic(s) and the accelerating stress factor(s) under a parametric framework of the product lifetime distribution. As the true relationship is rarely known in practical scenarios, the assumption itself may produce biased estimates that may lead to an inefficient sampling plan. To this endeavor, an optimal accelerating life test plan is designed under a Type-I censoring scheme with a generalized link structure similar to a spline regression, to capture the nonlinear relationship between the lifetime characteristics and the stress levels. Product lifetime is assumed to follow Weibull distribution with non-identical scale and shape parameters linked with the stress factor through a piecewise linear function. The elements of the Fisher information matrix are computed in detail to formulate the acceptability criterion for the conforming lots. The decision variables of the sampling plan including sample size, stress factors, and others are determined using a constrained aggregated cost minimization approach and variance minimization approach. A simulated case study demonstrates that the nonlinear link-based piecewise linear approximation model outperforms the linear link-based model.

stat.CO

Control Charts for Percentiles of Truncated Beta Distributed Environmental Data Using Studentized Bootstrap Method

This paper proposes a control chart for monitoring percentiles of a process that follows a truncated beta distribution, utilizing a studentized parametric bootstrap method to account for the case when in-control parameters are unknown. To evaluate the in-control performance, extensive Monte Carlo simulations are conducted across various combinations of percentiles, false alarm rates, and sample sizes, with performance measured in terms of the average run length. The out-of-control performance is thoroughly assessed by introducing shifts in the distributional parameters and comparing the proposed chart with the conventional beta-based chart. The effectiveness and practical applicability of the proposed chart is illustrated through real-world examples from environmental data.

stat.ME

Some Results on Comparisons of Random Extremes having Identical and Non-Identical Components

In this article, we revisit the paper by Kundu et al.~(2024), presenting new results and insights for both identical and non-identical independent random variables. We derive sufficient conditions for preserving the hazard rate and reversed hazard rate orderings between the random maximum and minimum order statistics, respectively. Our results show that these preservation conditions also hold for independent and identically distributed random variables. We also demonstrate that the findings in Kundu et al.~(2024) for the non-identical cases do not apply to the identical cases.

stat.AP

Stochastic Comparisons of Random Extremes from non-identical Random Variables

We propose some new results on the comparison of the minimum or maximum order statistic from a random number of non-identical random variables. Under the non-identical set-up, with certain conditions, we prove that random minimum (maximum) of one system dominates the other in hazard rate (reversed hazard rate) order. Further, we prove variation diminishing property (Karlin [8]) for all possible restrictions to derive the new results.

math.ST

Control Chart for Generalized Weibull Quantiles under Hybrid Censoring

In this article, bootstrap and Shewhart type process control monitoring schemes are proposed for the quantiles of generalized Weibull distribution under hybrid censoring. Monitoring schemes for the quantiles of Weibull, generalized exponential, Rayleigh, and Burr type $X$ distributions for type I, type II and hybrid censoring can be obtained as the special cases of the proposed schemes. The maximum likelihood estimators are derived under hybrid censoring using EM algorithm and the asymptotic properties of the estimators are discussed in order to develop the Shewhart type scheme. The in-control performance of the schemes is examined in a simulation study on the basis of the average run length for different choices of quantiles, false-alarm rates and sample sizes. Behavior of the out-of-control performance of the schemes is studied for several choices of shifts in the parameters of the chosen density function. The proposed monitoring schemes are illustrated with an example from healthcare and compared with similar schemes under type I and type II censoring. The schemes are found to detect out-of-control signals effectively in terms of frequency and speed both.

stat.ME

Evaluation of Tree Based Regression over Multiple Linear Regression for Non-normally Distributed Data in Battery Performance

Battery performance datasets are typically non-normal and multicollinear. Extrapolating such datasets for model predictions needs attention to such characteristics. This study explores the impact of data normality in building machine learning models. In this work, tree-based regression models and multiple linear regressions models are each built from a highly skewed non-normal dataset with multicollinearity and compared. Several techniques are necessary, such as data transformation, to achieve a good multiple linear regression model with this dataset; the most useful techniques are discussed. With these techniques, the best multiple linear regression model achieved an R^2 = 81.23% and exhibited no multicollinearity effect for the dataset used in this study. Tree-based models perform better on this dataset, as they are non-parametric, capable of handling complex relationships among variables and not affected by multicollinearity. We show that bagging, in the use of Random Forests, reduces overfitting. Our best tree-based model achieved accuracy of R^2 = 97.73%. This study explains why tree-based regressions promise as a machine learning model for non-normally distributed, multicollinear data.

cs.LG

Ordering properties of the smallest and largest lifetimes in Gompertz-Makeham model

The Gompertz-Makeham distribution, which is used commonly to represent lifetimes based on laws of mortality, is one of the most popular choices for mortality modelling in the field of actuarial science. This paper investigates ordering properties of the smallest and largest lifetimes arising from two sets of heterogeneous groups of insurees following respective Gompertz-Makeham distributions. Some sufficient conditions are provided in the sense of usual stochastic ordering to compare the smallest and largest lifetimes from two sets of dependent variables. Comparison results on the smallest lifetimes in the sense of hazard rate ordering and ageing faster ordering are established for two groups of heterogeneous independent lifetimes. Under similar set-up, no reversed hazard rate ordering is shown to exist between the largest lifetimes with the use of a counter-example. Finally, we present sufficient conditions to stochastically compare two sets of independent heterogeneous lifetimes under random shocks by means of usual stochastic ordering. Such comparisons for the smallest lifetimes are also carried out in terms of hazard rate ordering.

stat.AP

Ordering properties of the smallest order statistic from Weibull G random variables

In this paper we compare the minimums of two heterogeneous samples each following Weibull-G distribution under three scenarios. In the Fifirst scenario, the units of the samples are assumed to be independently distributed and the comparisons are carried out through vector majorization. The minimums of the samples are compared in the second scenario when the independent units of the samples also experience random shocks. The last scenario describes the comparison when the units have a dependent structure sharing Archimedean copula.

math.ST

Shannon's entropy and its Generalizations towards Statistics, Reliability and Information Science during 1948-2018

Starting from the pioneering works of Shannon and Weiner in 1948, a plethora of works have been reported on entropy in different directions. Entropy-related review work in the direction of statistics, reliability and information science, to the best of our knowledge, has not been reported so far. Here we have tried to collect all possible works in this direction during the period 1948-2018 so that people interested in entropy, specially the new researchers, get benefited.

stat.OT

Errors Due to Departure from Independence in Exponential Series System

In reliability and life testing when the exponentially distributed components are put in series, it is generally assumed that the lifetimes of the components are independently distributed, which leads to some errors if they are not actually independent. In this paper, we study the relative errors incurred in different reliability measures due to such assumptions when actually they follow some bivariate exponential distributions.

math.ST

Stochastic Comparisons of Lifetimes of Two Series and Parallel Systems with Location-Scale Family Distributed Components having Archimedean Copulas

In this paper, we compare the lifetimes of two series and two parallel systems stochastically where the lifetime of each component follows location-scale (LS) family of distributions. The comparison is carried out under two scenarios: one, that the components of the systems have a dependent structure sharing Archimedean copula and two, that the components are independently distributed. It is shown that the systems with components in series or parallel sharing Archimedean copula with more dispersion in the location or scale parameters results in better performance in the sense of the usual stochastic order. It is also shown that if the components are independently distributed, it is possible to obtain more generalized results as compared to the dependent set-up. The results in this paper generalizes similar results in both independent and dependent set up for exponential and Weibull distributed components.

math.ST

Ordering properties of sample minimum from Kumaraswamy-G random variables

In this paper we compare the minimums of two independent and heterogeneous samples each following Kumaraswamy-G distribution with the same and the different parent distribution functions. The comparisons are carried out with respect to usual stochastic ordering and hazard rate ordering with majorized shape parameters of the distributions. The likelihood ratio ordering between the minimum order statistics is established for heterogeneous multiple outlier Kumaraswamy-G random variables with the same parent distribution function

math.ST

Ordering Properties of Order Statistics from Heterogeneous Generalized Exponential and Gamma Populations

Let $X_1, X_2,\ldots, X_n$ (resp. $Y_1, Y_2,\ldots, Y_n$) be independent random variables such that $X_i$ (resp. $Y_i$) follows generalized exponential distribution with shape parameter $θ_i$ and scale parameter $λ_i$ (resp. $δ_i$), $i=1,2,\ldots, n$. Here it is shown that if $\left(λ_1, λ_2,\ldots,λ_n\right)$ is $p$-larger than (resp. weakly supermajorizes) $\left(δ_1,δ_2,\ldots,δ_n\right)$, then $X_{n:n}$ will be greater than $Y_{n:n}$ in usual stochastic order (resp. reversed hazard rate order). That no relation exists between $X_{n:n}$ and $Y_{n:n}$, under same condition, in terms of likelihood ratio ordering has also been shown. It is also shown that, if $Y_i$ follows generalized exponential distribution with parameters $\left(\barλ,θ_i\right)$, where $\barλ$ is the mean of all $λ_i$'s, $i=1\ldots n$, then $X_{n:n}$ is greater than $Y_{n:n}$ in likelihood ratio ordering. Some new results on majorization have been developed which fill up some gap in the theory of majorization. Some results on multiple-outlier model are also discussed. In addition to this, we compare two series systems formed by gamma components with respect to different stochastic orders.

stat.AP