arXiv subjects

Kiran Prajapat

Publications and source records attributed to Kiran Prajapat.

4 recordsLinked to original sources

arXiv2026

Robust inference for cyclic-stress accelerated life tests under interval monitoring with lognormal lifetimes

Highly reliable products are often tested under accelerated conditions to provoke failures within a feasible timeframe. For products whose service life involves repeated alternation between two stress levels, such as automotive air-conditioners, batteries, and aerospace components, cyclic-stress accelerated life testing (CyALT) provides a more realistic loading profile than conventional accelerated tests. In practice, failures are often recorded only at scheduled inspection times, leading to interval-censored counts rather than exact lifetimes. Moreover, traditional maximum likelihood estimation is sensitive to data contamination, which is a genuine concern in small-sample industrial experiments. This paper develops robust inferential procedures for CyALT models with lognormal lifetimes under interval monitoring. Robust estimators are obtained by minimizing a weighted density power divergence (WDPD), leading to the weighted minimum density power divergence estimator (WMDPDE). We establish the asymptotic distribution of the WMDPDE, derive influence function expressions to characterize the robustness, and present asymptotic and bootstrap confidence intervals for important lifetime characteristics. A simulation study confirms that the WMDPDE provides substantial protection against outliers while retaining high efficiency under clean data. The methodology is illustrated through the analysis of an air-conditioner reliability dataset, demonstrating the practical advantages of robust inference in the CyALT framework.

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arXiv2026

A Finite Mixture Failure-rate based Heterogeneous Step-stress Accelerated Life Testing (h-SSALT) Model

Traditional step-stress accelerated life testing models assume that test units originate from a homogeneous population. Recently, Lu and Kateri (2025) proposed a heterogeneous cumulative exposure based SSALT model to account for the inhomogeneous aging patterns among test units belonging to the same production batch. This paper introduces an alternative yet flexible failure-rate based heterogeneous simple SSALT (h-SSALT) model with Weibull-distributed Type-II censored failure times, allowing heterogeneity to emerge at the second stress level through a finite mixture of m latent subgroups, each characterized by its own failure behavior. The expectation-maximization algorithm is developed for maximum likelihood estimation of the model parameters, exploiting the incomplete data structure arising from both unknown group membership and Type-II censoring. Interval estimation is performed using the missing information identity of Louis (1982) with transformation-based confidence intervals respecting parameter constraints. An extensive simulation study evaluates the finite-sample performance of the proposed estimators and demonstrates, through a quantile-based comparison, that ignoring population heterogeneity leads to systematic bias in lifetime predictions across the entire quantile range, with the most severe consequences at early failure quantiles of direct relevance to warranty period design. A special case comparison confirms that the proposed Weibull failure-rate based formulation reduces to the existing model of Lu and Kateri (2025) when the shape parameter equals unity, validating the proposed framework as a proper generalization. The practical application of the model is further illustrated through simulated and real data analysis examples.

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arXiv2026

Exact Bayesian Planning for Simple Step-Stress Accelerated Life Testing with Competing Risks

We propose a Bayesian framework for planning simple step-stress accelerated life tests when items are subject to two independent competing failure modes We assume that the competing risks are independent, with lifetimes following Weibull distributions, and adopt the cumulative exposure model with a log-linear stress-life relationship to connect failure time distributions across stress levels. The optimality criterion is the preposterior variance of the $p$-th quantile of the lifetime distribution at use stress, evaluated without reliance on asymptotic approximations, making the methodology valid regardless of sample size. Building on the idea of quantile-based reparametrisation used in single-mode ALT \citep{zhang2006bayesian}, we extend this approach to the competing risks setting by reparametrising the model parameters for each failure mode to physically interpretable and approximately independent quantities, making it possible to elicit priors directly from engineering knowledge of device behaviour. Posterior inference is carried out using the No-U-Turn Sampler implemented in Stan, and the optimal design is located via Monte Carlo simulation over a grid of candidate designs. The methodology is illustrated on a real step-stress dataset for a solar lighting device subject to capacitor and controller failure modes. A comprehensive sensitivity analysis with respect to the quantile probability, the lower stress level, the prior hyperparameter specification, and the sample size shows that the optimal stress-change time is moderately sensitive to these inputs while the optimal lower stress level consistently favours operation close to use conditions, a finding that holds across all prior specifications considered.

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arXiv2024

Estimation Method under Three-Parameter Generalized Exponential Model: Consistency, Uniqueness and its Applications

In numerous instances, the generalized exponential distribution can be used as an alternative to the most widely used non-regular family of distributions: Weibull, gamma, lognormal with three-parameters when analyzing lifetime or any skewed continuous data. A non-regular family is a class of probability distributions that do not satisfy the regularity conditions typically assumed in classical statistical inference. Some key features of such family of distributions are: support of its probability density function depends on one its parameters; its likelihood function may not be bounded for a certain range of parameter space, hence maximum likelihood estimators do not exist; the likelihood function even may not be differentiable or integrable as needed, hence Fisher Information may not exist or be infinite. Moreover, standard results like MLE existence, consistency, asymptotic normality may fail. Therefore, specialized or robust inferential techniques are needed. This article offers a consistent method for estimating the parameters of a three-parameter generalized exponential distribution that sidesteps the issue of an unbounded likelihood function. The method is hinged on a maximum likelihood estimation of shape and scale parameters that uses a location-invariant statistic. Important estimator properties, such as uniqueness and consistency, are demonstrated for the first time under this approach. In addition, quantile estimates for the assumed distribution are provided. We present a Monte Carlo simulation study along with comparisons to a number of well-known estimation techniques in terms of bias and root mean square error. For illustrative purposes, a real dataset from reliability engineering, has been analyzed and the goodness of fit along with the bootstrap confidence intervals are compared with existing traditional methods.

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