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|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
|Keywords: ||Failure rate;q-Weibull model;Reliability;Parameter q;Reliability management;Distribution curves;Distribution functions;Bathtub curve|
|Issue Date: ||2013|
|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.|
|Description: ||Texto completo: acesso restrito. p. 720-736|
|Appears in Collections:||Artigos Publicados em Periódicos (PEI)|
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