Reliability Analysis of the CNC System Based on Field Failure Data in Operating Environments

Dazhang You, Hoang Pham

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14 Scopus citations


Reliability is a measure of how well a product will perform under a certain set of conditions for a specified amount of time especially in the field environments. In this paper, a reliability study of a computer numerical control (CNC) system is described. For this analysis, field failure data from a shop manufacturing factory collected over the course of a year on approximately 20 CNC machine tools during their operating period were analyzed. Based on the field failure data, the two-parameter exponential distribution was found to be applicable to describe the time between failures of the CNC system from among many distributions including Weibull, gamma, two-parameter exponential, normal, and logistic using the chi-squared test. In this paper, we discuss the reliability estimation of the CNC system based on the collected field failure data from a manufacturing factory using the maximum likelihood estimate (MLE) and uniform minimum variance estimate (UMVUE) methods. We also discuss the confidence intervals of the mean residual lifetime and reliability function. The result shows that the UMVUE method can provide much better and more accurate results in estimating the reliability of the CNC system than the MLE. This finding, on the one hand, seems to be obvious because the UMVUE is not only an unbiased estimator but also sufficient statistic with the smallest variance; on the other hand, it is not straightforward to obtain the UMVUE of any complex function, which is the reliability function in this case. This is a very important finding and is very encouraging because it indicates that the reliability analysis of the CNC system based on the UMVUE can be more than compensated by the ability of the complexity of parameter estimation method to better evaluate and predict the reliability of the CNC system. Hence, we believe that it is worth the effort to derive those parameter functions using UMVUE method.

Original languageEnglish (US)
Pages (from-to)1955-1963
Number of pages9
JournalQuality and Reliability Engineering International
Issue number5
StatePublished - Jul 1 2016

All Science Journal Classification (ASJC) codes

  • Safety, Risk, Reliability and Quality
  • Management Science and Operations Research


  • CNC system
  • maximum likelihood estimate (MLE)
  • operating environment
  • reliability estimate
  • uniform minimum variance unbiased estimate (UMVUE)

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