Application of the Weibull distribution for the optimization of maintenance policies of an electronic railway signaling system

The random age replacement policies discussed in literatures are helpful to complete the nonstopping works with random working cycles, however, maintenance policies are more easily performed at periodic times in real applications. For such a viewpoint, this paper proposes that age replacement policies are planned at periodic times while considering the random working cycles. Using the modeling approaches of replacement first and last policies, we discuss two models such that the unit is replaced at periodic times [Formula: see text] and working cycles [Formula: see text], whichever occurs first and whichever occurs last. The expected cost rate models are obtained and their optimal solutions for [Formula: see text] and [Formula: see text] are discussed. The comparisons between the policies of [Formula: see text] and [Formula: see text], and replacement first and last are made from the point of cost. Numerical examples are illustrated when the failure time has a Weibull distribution.

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Comparison between maintenance policies based on q-Weibull and Weibull models

International Journal of Quality & Reliability Management ◽

10.1108/ijqrm-09-2019-0283 ◽

2021 ◽

Vol ahead-of-print (ahead-of-print) ◽

Author(s):

Edilson Machado de Assis ◽

Celso Luiz Santiago Figueirôa Filho ◽

Gabriel Costa Lima ◽

Gisele Maria de Oliveira Salles ◽

Ailton Pinto

Keyword(s):

Weibull Distribution ◽

Preventive Maintenance ◽

Weibull Model ◽

Computational Effort ◽

Numerical Comparison ◽

Content Type ◽

Optimal Interval ◽

Maintenance Cycle ◽

Weibull Models ◽

Maintenance Policies

PurposeThe purpose of this article is to compare maintenance policies based on Weibull and q-Weibull models.Design/methodology/approachThis paper uses analytical developments, several figures and tables for graphical and numerical comparison. Previously published hydropower equipment data are used as examples.FindingsModels 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 implicationsThe 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/valueExpressions 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.

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Periodic and sequential preventive maintenance policies

Journal of Applied Probability ◽

10.2307/3214197 ◽

1986 ◽

Vol 23 (2) ◽

pp. 536-542 ◽

Cited By ~ 109

Author(s):

Toshio Nakagawa

Keyword(s):

Weibull Distribution ◽

Preventive Maintenance ◽

Minimal Repair ◽

Expected Cost ◽

Optimal Policies ◽

Failure Distribution ◽

Maintenance Policies

This paper considers periodic and sequential preventive maintenance (PM) policies for the system with minimal repair at failure: the PM is done (i) at periodic times kx and (ii) at constant intervals xk (k = 1, 2, ···, N). The system has a different failure distribution between PM'S and is replaced at the Nth PM. The optimal policies which minimize the expected cost rates are discussed. The optimal x and N of periodic PM and {xk} of sequential PM are easily computed in a Weibull distribution case.

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Periodic and sequential preventive maintenance policies

Journal of Applied Probability ◽

10.1017/s0021900200029843 ◽

1986 ◽

Vol 23 (02) ◽

pp. 536-542 ◽

Cited By ~ 32

Author(s):

Toshio Nakagawa

Keyword(s):

Weibull Distribution ◽

Preventive Maintenance ◽

Minimal Repair ◽

Expected Cost ◽

Optimal Policies ◽

Failure Distribution ◽

Maintenance Policies

This paper considers periodic and sequential preventive maintenance (PM) policies for the system with minimal repair at failure: the PM is done (i) at periodic timeskxand (ii) at constant intervalsxk(k= 1, 2, ···, N). The system has a different failure distribution between PM'S and is replaced at the Nth PM. The optimal policies which minimize the expected cost rates are discussed. The optimalxand N of periodic PM and {xk} of sequential PM are easily computed in a Weibull distribution case.

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Brownian motion with quadratic killing and some implications

Journal of Applied Probability ◽

10.1017/s0021900200116079 ◽

1986 ◽

Vol 23 (04) ◽

pp. 893-903 ◽

Cited By ~ 2

Author(s):

Michael L. Wenocur

Keyword(s):

Brownian Motion ◽

Weibull Distribution ◽

Special Function ◽

Function Theory ◽

Killing Rate

Brownian motion subject to a quadratic killing rate and its connection with the Weibull distribution is analyzed. The distribution obtained for the process killing time significantly generalizes the Weibull. The derivation involves the use of the Karhunen–Loève expansion for Brownian motion, special function theory, and the calculus of residues.

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