Application of three-parameter Weibull mixture model for reliability assessment of NC machine tools: a case study
23 Sep 2011-Vol. 225, Iss: 11, pp 2718-2726
TL;DR: The results show that the mixture model of three-parameter Weibull distribution, with advantages over other WeibULL models, is suitable for modelling failure data of multiple NC machine tools with multiple failure modes and causes.
Abstract: To analyse the reliability of numerical control (NC) machine tools, a three-parameter Weibull mixture model is proposed in this case study. Negative log-likelihood function is used as an optimal objective instead of solving complex system of equations; the problem of parameter estimation of mixture model is solved by a non-linear programming method. A comprehensive criteria, which include Akaike information criterion, Bayesian information criterion, and root mean squared error, is presented for selecting the number of components of mixture model. The field failure data of three NC machine tools are analysed and the results of reliability assessment, such as the reliability, maintainability, availability, etc., are all presented. The results show that the mixture model of three-parameter Weibull distribution, with advantages over other Weibull models, is suitable for modelling failure data of multiple NC machine tools with multiple failure modes and causes.
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TL;DR: In this article, the main analysis methods and modeling techniques used in reliability assessment of numerical control (NC) machine tools are illustrated with brief case studies and the reliabilities of typical subsystems of NC machine tools were discussed.
Abstract: Numerical control (NC) machine tools are the fundamental equipment of the machinery industry. The reliability of NC machine tools directly influences the processing quality, productivity, and efficiency. This paper reviews the latest developments in the reliability analysis of NC machine tools. The main analysis methods and modeling techniques used in reliability assessment of NC machine tools are illustrated with brief case studies. The reliabilities of typical subsystems of NC machine tools are discussed. In addition, several important key problems and issues remain to be addressed about the reliability analysis of NC machine tools and opportunities for further research are identified.
25 citations
TL;DR: Compared with the long-term machining to load the feeding system in traditional reliability tests of machine tools, the proposed MLD provides an efficient method to simulate the loading condition of the system with reduced testing costs.
Abstract: Reliability of machine tools is critical to high- efficiency manufacturing, and the failure data of feeding systems are requisite to analyze the reliability. This paper presents a multiaxis loading device (MLD) to simulate loading condition of an operating feeding system of a machine tool in a real machining process; this could cause breakdowns of the system and collect failure data. The MLD was developed based on a six-degree-of-freedom (6-DOF) parallel mechanism, and its prototype was presented. Its kinematics was analyzed, and dynamic equations were established based on the principle of virtual work. A fuzzy proportional-integral-derivative controller was designed to build an explicit force control system, whose proportional and integral gain can be adjusted according to the errors between reference and actual forces; and a force and a velocity feedforward were integrated to improve the performance of the control system. Loading experiments were conducted on an experimental platform to validate the loading capacity of the MLD; the spindle of the platform was set to be stationary and driven to perform feeding motions with different dimensions. Results of the experiment with the stationary spindle indicate that the MLD can simultaneously provide a 3-DOF force and a 3-DOF moment with acceptable errors. Experiments with moving spindle illustrate that the MLD accomplished tracking a spindle that is executing a 3-DOF trajectory-unknown feeding motion and adding 3-DOF forces on the feeding system through the spindle. The actual output multiaxis forces have little hysteresis and errors less than 10%. Compared with the long-term machining to load the feeding system in traditional reliability tests of machine tools, the proposed MLD provides an efficient method to simulate the loading condition of the system with reduced testing costs.
16 citations
Cites background from "Application of three-parameter Weib..."
...These failure records, provided by users of CNC machine tools after a certain period of operation, are essential information to analyze the reliability of machine tools [6]–[8]....
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12 citations
01 Dec 2015
TL;DR: This paper presents a mathematical model based on continuous time Markov chain for performing availability and reliability analysis of a repairable system consisting of n components and describes a methodology for identifying a critical componentbased on continuous-time MarkovChain state probabilities of an n-component repairable and non-repairable system.
Abstract: This paper presents a mathematical model based on continuous time Markov chain for performing availability and reliability analysis of a repairable system consisting of n components. It also describes a methodology for identifying a critical component based on continuous-time Markov chain state probabilities of an n-component repairable and non-repairable system. As an illustration, a 3-component repairable system has been modelled. A case study of conventional lathe machine has been presented to solve for state probabilities and analysed to find reliability indices, MTTF, MTBF, MTTR and Availability to provide insights and guidance on improving upon the reliability and maintainability.
10 citations
Cites methods from "Application of three-parameter Weib..."
...Various methods are available in the literature for or for two-parameter and three-parameter Weibull model [8]....
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TL;DR: In this paper, the authors proposed a way of improving the efficiency of drilling operation and to reduce the drilling cost by determining the reliabilities of the tri-cone roller bits.
Abstract: Tri-cone roller bits are mostly used for drilling blast holes in surface mines. One way of improving the efficiency of drilling operation and to reduce drilling cost is to determine the rel...
9 citations
Cites methods from "Application of three-parameter Weib..."
...In 3P Weibull distribution, maximum likelihood estimation (MLE) method is used to determine shape parameter (beta), scale parameter (eta) and location parameter (gamma) parameter for reliability analysis [29,30]....
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References
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TL;DR: The first € price and the £ and $ price are net prices, subject to local VAT, and the €(D) includes 7% for Germany, the€(A) includes 10% for Austria.
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357 citations
TL;DR: A three-parameter Weibull failure rate function is discussed for wind turbines and the parameters are estimated by maximum likelihood and least squares and shown to obtain more accuracy on reliability growth of wind turbines.
173 citations
TL;DR: In this paper, a graphical approach to decide on the appropriateness of a mixture of 2 Weibull distributions to model a given failure data set is presented, where plots are completely characterized and the parameters estimated for various cases.
Abstract: The paper presents a graphical approach to decide on the appropriateness of a mixture of 2 Weibull distributions to model a given failure data set. It involves plotting the data on Weibull paper. The plots are completely characterized and the parameters estimated for various cases. Two examples involving real data illustrate the usefulness of the approach. The results are compared with those of Jiang and Kececioglu (1992) and the errors therein are pointed out. >
115 citations