Non-parametric accelerated life testing estimation for fuzzy life times under fuzzy stress levels

Muhammad Shafiq; Syed Habib Shah; Mohammad Abiad; Qamruz Zaman; Muhammad Shafiq; Syed Habib Shah; Mohammad Abiad; Qamruz Zaman

doi:10.3934/math.2023739

AIMS Mathematics

2023, Volume 8, Issue 6: 14475-14484. doi: 10.3934/math.2023739

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Non-parametric accelerated life testing estimation for fuzzy life times under fuzzy stress levels

1.
Institute of Numerical Sciences, Kohat University of Science & Technology, KP, Pakistan
2.
College of Business Administration, American University of the Middle East, Kuwait
3.
Department of Statistics, University of Peshawar

Received: 29 December 2022 Revised: 14 March 2023 Accepted: 22 March 2023 Published: 19 April 2023
MSC : 62N05, 94D05

Uncompleted developments in the fields of measurement sciences are categorically agreed on the fact that measurements obtained from continuous phenomena cannot be measured precisely. Therefore, these measurements cannot be considered precise numbers but are nonprecise or fuzzy. For this purpose, it is compulsion of the time that such estimators need to be developed to cover both the uncertainties. The classical accelerated life testing (ALT) approaches are based on precise life times and precise stress levels, but in fact, these are not precise numbers but fuzzy. In this study, the nonparametric procedure of ALT is generalized in such a manner that in addition to random variation, fuzziness of the lifetime observations and stress levels are integrated in the developed estimators. The developed generalized nonparametric estimators for accelerated life time analysis utilize all the obtainable information that is present in the form of fuzziness in single observations and random variation among the observations to make suitable inferences. On the other hand, classical estimators only deal with random variation, which is a strong reason to conclude that the developed estimators should be preferred over classical estimators.
- accelerated life time,
- characterizing function,
- fuzzy life time,
- non-precise
Citation: Muhammad Shafiq, Syed Habib Shah, Mohammad Abiad, Qamruz Zaman. Non-parametric accelerated life testing estimation for fuzzy life times under fuzzy stress levels[J]. AIMS Mathematics, 2023, 8(6): 14475-14484. doi: 10.3934/math.2023739

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Abstract

Uncompleted developments in the fields of measurement sciences are categorically agreed on the fact that measurements obtained from continuous phenomena cannot be measured precisely. Therefore, these measurements cannot be considered precise numbers but are nonprecise or fuzzy. For this purpose, it is compulsion of the time that such estimators need to be developed to cover both the uncertainties. The classical accelerated life testing (ALT) approaches are based on precise life times and precise stress levels, but in fact, these are not precise numbers but fuzzy. In this study, the nonparametric procedure of ALT is generalized in such a manner that in addition to random variation, fuzziness of the lifetime observations and stress levels are integrated in the developed estimators. The developed generalized nonparametric estimators for accelerated life time analysis utilize all the obtainable information that is present in the form of fuzziness in single observations and random variation among the observations to make suitable inferences. On the other hand, classical estimators only deal with random variation, which is a strong reason to conclude that the developed estimators should be preferred over classical estimators.

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