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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 419280, 8 pages
Research Article

Parameter Estimation of a Delay Time Model of Wearing Parts Based on Objective Data

1School of Mechatronic Engineering, Southwest Petroleum University, Chengdu 610500, China
2Safety, Environment, Quality Supervision & Testing Research Institute, CCDE, Guanghan 618000, China
3School of Science, Southwest Petroleum University, Chengdu 610500, China

Received 10 June 2014; Revised 22 September 2014; Accepted 27 October 2014

Academic Editor: Wenbin Wang

Copyright © 2015 Y. Tang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The wearing parts of a system have a very high failure frequency, making it necessary to carry out continual functional inspections and maintenance to protect the system from unscheduled downtime. This allows for the collection of a large amount of maintenance data. Taking the unique characteristics of the wearing parts into consideration, we establish their respective delay time models in ideal inspection cases and nonideal inspection cases. The model parameters are estimated entirely using the collected maintenance data. Then, a likelihood function of all renewal events is derived based on their occurring probability functions, and the model parameters are calculated with the maximum likelihood function method, which is solved by the CRM. Finally, using two wearing parts from the oil and gas drilling industry as examples—the filter element and the blowout preventer rubber core—the parameters of the distribution function of the initial failure time and the delay time for each example are estimated, and their distribution functions are obtained. Such parameter estimation based on objective data will contribute to the optimization of the reasonable function inspection interval and will also provide some theoretical models to support the integrity management of equipment or systems.