An Extended Weibull Model with Variable Periodicity

A new distribution for the fluctuation of materials’ lifetime cumulative hazard rate is firstly proposed. The new distribution is extended from the Weibull distribution by adding a sine function. After that, the properties of its hazard rate function, cumulative hazard rate function, probability den...

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Bibliographic Details
Published inJournal of systems science and complexity Vol. 31; no. 3; pp. 841 - 858
Main Author Peng, Xiuyun
Format Journal Article
LanguageEnglish
Published Beijing Academy of Mathematics and Systems Science, Chinese Academy of Sciences 01.06.2018
Springer Nature B.V
Subjects
Complex Systems
Control
Control charts
Distribution functions
Economic models
Mathematics
Mathematics and Statistics
Mathematics of Computing
Operations Research/Decision Theory
Periodic variations
Probability density functions
Statistical analysis
Statistics
Systems Theory
Trigonometric functions
Weibull distribution
Sine function
Weibull distribution
Cumulative hazard rate function
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Summary:A new distribution for the fluctuation of materials’ lifetime cumulative hazard rate is firstly proposed. The new distribution is extended from the Weibull distribution by adding a sine function. After that, the properties of its hazard rate function, cumulative hazard rate function, probability density function and cumulative distribution function are studied. The analysis result shows this distribution can well model the lifetime with variable and periodic hazard rate. Finally, the new distribution is verified with two real data sets as examples to demonstrate its capability.
ISSN:1009-6124
1559-7067
DOI:10.1007/s11424-018-7046-7