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Accelerated life models when the stress is not constant. (English) Zbl 0760.62091

The author introduces the idea of a “relation functional” to conceptualize the notion of accelerated life test models in a unified framework. Two models are considered, which are shown to include the so called power rule, Arrhenius and the Eyring laws as well as the models of Miner, Sediakins and Stepanova-Peses as special cases. A statistical test for the ADD (additive accumulated damage) model is considered.

MSC:

62N05 Reliability and life testing
90B25 Reliability, availability, maintenance, inspection in operations research
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References:

[1] V. Bagdonavičius: Testing hypothesis of the linear accumulation of damages. Teor. Veroyatnost. i Primenen. 23 (1978), 2, 403 - 408. · Zbl 0399.62099
[2] R. L. Schmoyer: An exact distribution-free analysis for accelerated life testing at several levels of a single stress. Technometrics 28 (1986), 1, 165-175. · Zbl 0588.62177 · doi:10.2307/1270453
[3] J. Sethuraman, N. D. Singpurwalla: Testing of hypothesis for distributions in accelerated life tests. J. Amer. Statist. Assoc. 77 (1982), 1, 204-208.
[4] M. Shaked, N. D. Singpurwalla: Nonparametric estimation and goodness-of-fit testing of hypothesis for distributions in accelerated life testing. IEEE Trans, on Reliability 3 (1982), 1,69-74. · Zbl 0489.62084
[5] I. Ushakov: Reliability of Technical Systems (in Russian). Radio and Communications, Moscow 1983.
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