Abstract

Under limited resources, the widely used Vtq-optimal test plan determines the

sample size, termination time, and number of measurements by minimizing the approximate variances of the estimated q-quantile, tq, for highly reliable products. This

approach is economically efficient when the Vtq-optimal test plan simultaneously satisfies another optimality criterion through an appropriate choice of q. Therefore, we

theoretically study a bi-optimal quantile-based test plan based on a Wiener process,

which achieves 100% efficiency for two optimality criteria. The necessary and sufficient conditions for its existence and uniqueness are derived, which can then be

used to determine the optimal test configuration for accelerated degradation tests.

Two numerical examples are presented to illustrate the practical applicability of the

proposed bi-optimal quantile-based test plan.

Key words and phrases: Cost-constrained optimization, D-optimal frequency, Inverse Gaussian distribu- tion, Monotonicity, Signal-to-noise ratio *Corresponding author email: chienyu@stat.sinica.edu.tw Ya-Shan Cheng, ORCID ID: 0009-0003-0681-0864 Chien-Yu Peng, ORCID ID: 0000-0002-0400-5015 1 Introduction Rapid advances in technology have greatly improved product quality across industries, which has led manufacturers to place a growing emphasis on the development of high- reliability products to maintain competitiveness. Ensuring long-term product quality is crucial for customer satisfaction and plays an important role in building and sustaining a company’s reputation

Information

Preprint No.SS-2025-0285
Manuscript IDSS-2025-0285
Complete AuthorsYa-Shan Cheng, Chien-Yu Peng
Corresponding AuthorsChien-Yu Peng
Emailschienyu@stat.sinica.edu.tw

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