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Computational Testing Procedure for the Overall Lifetime Performance Index of Multi-Component Exponentially Distributed Products
by Shu-Fei Wu *ORCID andChia-Chi Hsu
Department of Statistics and Data Science, Tamkang University, New Taipei City 251301, Taiwan
*
Author to whom correspondence should be addressed.
Stats 2025, 8(4), 104; https://doi.org/10.3390/stats8040104
Submission received: 7 September 2025 / Revised: 15 October 2025 / Accepted: 23 October 2025 / Published: 2 November 2025
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Abstract
In addition to products with a single component, this study examines products composed of multiple components whose lifetimes follow a one-parameter exponential distribution. An overall lifetime performance index is developed to assess products under the progressive type I interval censoring scheme. This study establishes the relationship between the overall and individual lifetime performance indices and derives the corresponding maximum likelihood estimators along with their asymptotic distributions. Based on the asymptotic distributions, the lower confidence bounds for all indices are also established. Furthermore, a hypothesis testing procedure is formulated to evaluate whether the overall lifetime performance index achieves the specified target level, utilizing the maximum likelihood estimator as the test statistic under a progressive type I interval censored sample. Moreover, a power analysis is carried out, and two numerical examples are presented to demonstrate the practical implementation for the overall lifetime performance index. This research can be applied to the fields of life testing and reliability analysis.
