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Article

Edilson M. Assis, Ernesto P. Borges, Silvio A.B. Vieira de Melo and Leizer Schnitman

The purpose of this paper is to compare four life data models, namely the exponential and the Weibull models, and their corresponding generalized versions, q-exponential…

Abstract

Purpose

The purpose of this paper is to compare four life data models, namely the exponential and the Weibull models, and their corresponding generalized versions, q-exponential and q-Weibull models, by means of one practical application.

Design/methodology/approach

Application of the models to a practical example (a welding station), with estimation of parameters by the use of the least squares method, and the Akaike Information Criterion (AIC).

Findings

The data of the example considered in this paper is divided into three regimes, decreasing, constant and increasing failure rate, and the q-Weibull model describes the bathtub curve displayed by the data with a single set of parameters.

Practical implications

The simplicity and flexibility of the q-Weibull model may be very useful for practitioners of reliability analysis, and its benefits surpasses the inconvenience of the additional parameter, as AIC shows.

Originality/value

The q-Weibull model is compared in detail with other three models, through the analysis of one example that clearly exhibits a bathtub curve, and it is shown that it can describe the whole time range with a single set of parameters.

Details

International Journal of Quality & Reliability Management, vol. 32 no. 2
Type: Research Article
ISSN: 0265-671X

Keywords

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Article

Edilson M. Assis, Ernesto P. Borges and Silvio A.B. Vieira de Melo

The purpose of this paper is to analyze mathematical aspects of the q‐Weibull model and explore the influence of the parameter q.

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.

Details

International Journal of Quality & Reliability Management, vol. 30 no. 7
Type: Research Article
ISSN: 0265-671X

Keywords

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Abstract

Purpose

The purpose of this article is to compare maintenance policies based on Weibull and q-Weibull models.

Design/methodology/approach

This paper uses analytical developments, several figures and tables for graphical and numerical comparison. Previously published hydropower equipment data are used as examples.

Findings

Models for optimal maintenance interval determination based on q-Weibull distribution were defined. Closed-form expressions were found, and this allows the application of the method with small computational effort.

Practical implications

The use of the q-Weibull model to guide the definition of maintenance strategy allows decision-making to be more consistent with sample data. The flexibility of the q-Weibull model is able to produce failure rate modeling with five different formats: decreasing, constant, increasing, unimodal and U-shaped. In this way, the maintenance strategies resulting from this model should be more assertive.

Originality/value

Expressions for determining the optimal interval of preventive maintenance were deduced from q-Weibull distribution. Expected costs per maintenance cycle of Brazilian hydropower equipment were calculated with q-Weibull and Weibull distributions. These results were compared in terms of absolute values and trends. Although a large number of works on corrective and preventive maintenance have been proposed, no applications of the q-Weibull distribution were found in literature.

Details

International Journal of Quality & Reliability Management, vol. ahead-of-print no. ahead-of-print
Type: Research Article
ISSN: 0265-671X

Keywords

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