Statistical analysis for masked hybrid system lifetime data in step-stress partially accelerated life test with progressive hybrid censoring.

Xiaolin Shi,Yanchao Liu,Yimin Shi,Tao Lu

doi:10.1371/journal.pone.0186417

Xiaolin Shi, Yanchao Liu + Show 2 more

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https://doi.org/10.1371/journal.pone.0186417

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Abstract

In this paper, we investigate a step-stress partially accelerated lifetime test for the four-component hybrid systems with Type-II progressive hybrid censoring scheme while the life time of system component follows exponential failure rate. In many cases, the exact component causing the system failure cannot be identified and the cause of failure is masked. Based on Type-II progressively hybrid censored and masked data, the maximum likelihood estimations for unknown parameters and acceleration factor are obtained. In addition, approximate confidence interval and bootstrap confidence interval are presented by using the asymptotic distributions of the maximum likelihood estimations for unknown parameters and bootstrap method, respectively. Finally, the proposed method is illustrated through the simulation studies.

Highlights

The failure data from multi-component systems plays an important role in system reliability analysis
Due to lack of proper diagnostic equipment or cost and time constraints, the exact component causing the system failure is not identified, and the failure cause is isolated to a subset of the system components
F"1ðtÞ 1⁄4 expðÀ 2lðet À 1ÞÞ1⁄22 À expðÀ 2lðet À 1ÞÞ; t > 0; l > 0: The reliability function of system at accelerated stress level is F"2ðtÞ 1⁄4 expðÀ 2lðeðtþaðtÀ tÞÞ À 1ÞÞ1⁄22 À expðÀ 2lðeðtþaðtÀ tÞÞ À 1ÞÞ; t > 0; l > 0: Based on Type-II progressively hybrid censoring (PHC) sample, the likelihood function for the hybrid systems (a) is given by

Summary

Introduction

The failure data from multi-component systems plays an important role in system reliability analysis. Based on Type-I censoring scheme, reliability analysis for a series system in SSPALT was studied in [12], where the components lifetime follows Weibull distributions. Wang et al [11] studied parameter inference on the independent component hybrid system with masked data, where the component’s failure rate was considered as a constant or a linear function.

Results

Conclusion