A nonparametric health index and its statistical threshold for machine condition monitoring

•Statistical modeling and statistical analysis of normalized square envelope spectrum are proposed.•A nonparametric health index and its statistical threshold are constructed for system health monitoring.•Only a normal dataset is required in the statistical modeling and analysis.•Box-Cox transformation of normalized square envelope spectrum is introduced to system health monitoring.•The parameter of Box-Cox transformation is sensitive to bearing degradation. Machine condition monitoring uses monitoring data to evaluate machine health conditions and conduct condition-based maintenance. Nowadays, kurtosis, entropy, Gini index and smoothness index are popular indices for machine condition monitoring and they fall into a unified framework. A problem is that, if monitoring data do not follow a particular assumed parametric health index, the parametric index is not fully useful for machine condition monitoring. Another problem is that parametric health indices lack their associate statistical thresholds at a significance level for machine condition monitoring. In this paper, statistical modeling and statistical analysis of normalized square envelope spectrum are proposed to construct a nonparametric health index and its associate statistical threshold at a significance level for machine condition monitoring. An illustrative bearing run-to-failure example showed that the proposed nonparametric health index and its statistical threshold can assess degradation well without needing a specific parametric form and abnormal and faulty datasets.