https://repositorio.ufba.br/handle/ri/15172
metadata.dc.type: | Artigo de Periódico Artigo de Periódico |
Title: | Generalized q-Weibull model and the bathtub curve |
Other Titles: | International Journal of Quality and Reliability Management |
Authors: | Assis, Edilson Machado de Borges, Ernesto Pinheiro Melo, Silvio Alexandre Beisl Vieira de |
metadata.dc.creator: | Assis, Edilson Machado de Borges, Ernesto Pinheiro Melo, Silvio Alexandre Beisl Vieira de |
Abstract: | Purpose – The purpose of this paper is to analyze mathematical aspects of the q-Weibull model and explore the influence of the parameter q. Design/methodology/approach – The paper uses analytical developments with graph illustrations and an application to a practical example. Findings – The q-Weibull distribution function is able to reproduce the bathtub shape curve for the failure rate function with a single set of parameters. Moments of the distribution are also presented. Practical implications – The generalized q-Weibull distribution unifies various possible descriptions for the failure rate function: monotonically decreasing, monotonically increasing, unimodal and U-shaped (bathtub) curves. It recovers the usual Weibull distribution as a particular case. It represents a unification of models usually found in reliability analysis. Q-Weibull model has its inspiration in nonextensive statistics, used to describe complex systems with long-range interactions and/or long-term memory. This theoretical background may help the understanding of the underlying mechanisms for failure events in engineering problems. Originality/value – Q-Weibull model has already been introduced in the literature, but it was not realized that it is able to reproduce a bathtub curve using a unique set of parameters. The paper brings a mapping of the parameters, showing the range of the parameters that should be used for each type of curve. |
Keywords: | Failure rate q-Weibull model Reliability Parameter q Reliability management Distribution curves Distribution functions Bathtub curve |
metadata.dc.rights: | Acesso Aberto |
URI: | http://repositorio.ufba.br/ri/handle/ri/15172 |
Issue Date: | 2013 |
Appears in Collections: | Artigo Publicado em Periódico (PEI) |
File | Description | Size | Format | |
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10.1108IJQRM-Oct-2011-0143.pdf | 482,03 kB | Adobe PDF | View/Open |
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