arXiv subjects

Rathin Das

Publications and source records attributed to Rathin Das.

8 recordsLinked to original sources

arXiv2026

Optimal Design for Generalized Progressive Hybrid Censored Data via Constrained, Unconstrained, Compound, and Minimax Optimization

This paper studies the optimal design of Type-I generalized progressive hybrid censoring schemes for life-testing experiments. The design problem involves simultaneously determining the inspection time, the guaranteed number of failures, and the progressive censoring scheme. First we develop a cost-constrained optimization framework for determining the optimal censoring scheme. Structural properties of the A-optimality criterion and the experimental cost with respect to the inspection time and the guaranteed number of failures are established. It reveals that they are conflicting behaviors which enables to develop an efficient search algorithm that substantially reduces the computational burden. Building on these theoretical results, a multi-objective optimization model is proposed to simultaneously minimize A-optimality criterion and the experimental cost. A Variable Neighborhood Search (VNS) algorithm is proposed to efficiently determine the optimal progressive removal vector by exploring the feasible design space while avoiding exhaustive enumeration. The resulting compromise designs simultaneously improve estimation precision and reduce experimental cost. In addition, the Shannon differential entropy of the observed lifetime distribution is derived and employed as a complementary information-theoretic measure for evaluating the selected censoring schemes. Numerical studies show that entropy-optimal designs generally differ from A-optimal designs, indicating that Shannon entropy characterizes uncertainty in the observed data rather than estimation precision. The proposed methodology provides an efficient computational framework for optimal life-test design and offers a foundation for future multi-objective optimization incorporating statistical efficiency, experimental cost, and information-theoretic uncertainty.

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arXiv2025

Bayesian reliability acceptance sampling plans for competing risks data under interval censoring

We obtain a reliability acceptance sampling plan for independent competing risk data under interval censoring schemes using the Bayesian approach. At first, the Bayesian reliability acceptance sampling plan is obtained where the decision criteria of accepting a lot is pre-fixed. For large samples, computing Bayes risk is computationally intensive. Therefore, an approximate Bayes risk is obtained using the asymptotic properties of the maximum likelihood estimators. Lastly, the Bayesian reliability acceptance sampling plan is obtained, where the decision function is arbitrary. The manufacturer can derive an optimal decision function by minimizing the Bayes risk among all decision functions. This optimal decision function is known as Bayes decision function. The optimal sampling plan is obtained by minimizing the Bayes risk. The algorithms are provided for the computation of optimum Bayesian reliability acceptance sampling plan. Numerical results are provided and comparisons between the Bayesian reliability acceptance sampling plans are carried out.

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arXiv2025

Bayesian Optimum Warranty Region for Right Censored Two Dimensional Dependent Data

Warranty policies play a crucial role in balancing customer satisfaction and cost of the manufacturer. Traditional one-dimensional warranty frameworks, based solely on either age or usage, often fail to capture the joint effect of product life factors. This article investigates two-dimensional warranty policies by combining Free Replacement Warranty, Pro-Rata Warranty, and Combination FRW-PRW Warranty schemes across both age and usage scales. A dissatisfaction cost function is proposed alongside the economic benefit and warranty cost functions, and the expected utility framework is employed to derive optimal warranty parameters. The expectation is taken with respect to the posterior predictive distribution of product lifetime and usage data, ensuring a data-driven approach. Finally, the methodology is validated using an open-source dataset, and a new two-dimensional starter motor dataset is introduced to demonstrate the practical advantages of adopting two-dimensional warranty policies.

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arXiv2025

Bayesian reliability acceptance sampling plan sampling plans under adaptive accelerated type-II censored competing risk data

In recent times, products have become increasingly complex and highly reliable, so failures typically occur after long periods of operation under normal conditions and may arise from multiple causes. This paper employs simple step-stress partial accelerated life testing (SSSPALT) within the competing risks framework to determine the Bayesian reliability acceptance sampling plan (BRASP) under type-II censoring. Elevating the stress during the life test incurs an additional cost that increases the cost of the life test. In this context, an adaptive scenario is also considered in that sampling plan. The adaptive scenario is as follows: the stress is increased after a certain time if the number of failures up to that point is less than a pre-specified number of failures. The Bayes decision function and Bayes risk are derived for the general loss function. An optimal BRASP under that adaptive SSSPALT is obtained for the quadratic loss function by minimizing Bayes risk. An algorithm is provided to determine the optimal proposed BRASP. Further, comparative studies are conducted between the proposed BRASP, the conventional non-accelerated BRASP, and the conventional accelerated BRASP under type-II censoring to evaluate the effectiveness of the proposed approach. Finally, the methodology is illustrated using real data.

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arXiv2025

Determination of Optimum Warranty Region for Two Dimensional Dependent Data

This paper presents a method for determining the optimal two-dimensional warranty region for age and mileage scales across all possible combinations of free replacement warranty (FRW), prorata warranty (PRW), and FRW-PRW combined policies. The operational time or lifetime and usage of the products are modeled using a bivariate Gumbel copula with Weibull as the marginal distribution. The optimal warranty region is derived by maximizing an expected utility function, which incorporates two cost components: the economic benefit function and the warranty cost function, specifically constructed for the two-dimensional warranty scenario. To obtain the optimal warranty region, a real-world dataset of traction motors, including age and mileage information, is analyzed. The results show that considering a two-dimensional warranty cost function yields the highest utility compared to all other scenarios.

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arXiv2025

Reliability Acceptance Sampling Plans under Progressive Type-I Interval Censoring Schemes in Presence of Dependent Competing Risks

We discuss the development of reliability acceptance sampling plans under progressive Type-I interval censoring schemes in the presence of competing causes of failure. We consider a general framework to accommodate the presence of independent or dependent competing risks and derive the expression for the Fisher information matrix under this framework. We also discuss the asymptotic properties of the maximum likelihood estimators, which are essential in obtaining the sampling plans. Subsequently, we specialize in a frailty model, which allows us to accommodate the dependence among the potential causes of failure. The frailty model provides an independent competing risks model as a limiting case. We then present the traditional sampling plans for both independent and dependent competing risks models using producer and consumer risks. We also consider the design of optimal PIC-I schemes in this context and use a c optimal design criterion, which helps us to obtain more useful reliability acceptance sampling plans in the presence of budgetary constraints. We conduct a comprehensive numerical experiment to examine the impact of the level of dependence among the potential failure times on the resulting sampling plans. We demonstrate an application of the developed methodology using a real-life example and perform a simulation study to study the finite sample properties of the developed sampling plans. The methodology developed in this article has the potential to improve the design of optimal censoring schemes in the presence of competing risks while taking into account budgetary constraints.

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arXiv2024

Bayesian reliability acceptance sampling plans under adaptive simple step stress partial accelerated life test

In the traditional simple step-stress partial accelerated life test (SSSPALT), the items are put on normal operating conditions up to a certain time and after that the stress is increased to get the failure time information early. However, when the stress increases, an additional cost is incorporated that increases the cost of the life test. In this context, an adaptive SSSPALT is considered where the stress is increased after a certain time if the number of failures up to that point is less than a pre-specified number of failures. We consider determination of Bayesian reliability acceptance sampling plans (BSP) through adaptive SSSALT conducted under Type I censoring. The BSP under adaptive SSSPALT is called BSPAA. The Bayes decision function and Bayes risk are obtained for the general loss function. Optimal BSPAAs are obtained for the quadratic loss function by minimizing Bayes risk. An algorithm is provided for computation of optimum BSPAA. Comparisons between the proposed BSPAA and the conventional BSP through non-accelerated life test (CBSP) and conventional BSP through SSSPALT (CBSPA) are carried out.

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arXiv2024

Bayesian reliability acceptance sampling plan with optional warranty under hybrid censoring

This work considers design of Bayesian reliability acceptance sampling plan (RASP) under hybrid censored life test for the products sold under optional warranty. The consumer and manufacturer agree on a common lifetime distribution of the product. However, they differ in the assessment of the prior distributions because of the adversarial nature of the consumer and manufacturer. The consumer takes decision based on his/her utility and prior belief without warranty offer by the manufacturer. If the decision is rejection, manufacturer provides warranty offer to the consumer. If the consumer rejects the lot with a warranty, the manufacturer conducts life test under hybrid censoring scheme (HCS) and provide lifetime information to the consumer. The consumer updates his/her belief based on lifetime information provided by the manufacturer. The consumer then takes decision of acceptance or rejection of lot based on updated belief. Task of the manufacturer is to determine the optimal life testing plan.

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