An information entropy-based risk (IER) index of mining safety using clustering and statistical methods

The U.S. mining industry has made progress in reducing accidents and injuries, but interpreting safety data remains difficult due to changes in workforce size and productivity. The Mine Safety and Health Administration (MSHA) uses tools like the pattern of violation (POV) and significant & substantial (S&S) calculator to monitor safety, though these have limitations. To address this, we developed an information entropy-based risk (IER) index that combines various safety metrics, including citations, penalties and injuries. Using data from 2011 to 2020, the IER index was validated with statistical methods and clustering algorithms to ensure it accurately reflects risk levels. The analysis showed clear differences in risk across mining sites, proving the index’s usefulness. The IER index was then applied to a coal mine to demonstrate its effectiveness. This new tool can help mining companies better assess their safety risks and take action to improve workplace safety. Introduction Mining plays a crucial role in industries like steel production, power generation and electronics, but it is one of the most hazardous professions. Workers are exposed to risks like dust inhalation, roof collapses, explosions and rockslides. Although the U.S. mining industry has seen safety improvements, with a decline in fatal injury rates, it remains more dangerous than many other industries. Tools like the POV and S&S calculator, implemented by MSHA, help monitor mining safety, but they have limitations. The POV provides only a binary outcome, and the S&S calculator focuses on a limited number of parameters. To address these gaps, we proposed a new IER index.The IER index uses multiple safety indicators, such as citations and injuries, to assess mining risk more comprehensively. By applying information entropy, the index optimizes the weight of each indicator. This allows mining companies to better track safety performance, identify trends in risk levels and implement targeted improvements, providing a more balanced and reliable assessment than existing tools. Materials and methods In this study, data from the MSHA open data portal were used, specifically focusing on violation, inspection, production and accident data sets from underground U.S. mines between 2011 and 2020. These data sets provided critical information, including citations, orders, significant and substantial (S&S) violations, penalties and inspection hours. Accident data were categorized into incidents resulting in no lost-time injuries (NLT) and lost-time injuries (LT), which were further classified into nonfatal days-lost injuries (NFDL) and no-days-lost injuries (NDL). Seven key risk indices were developed: S&S citations per 100 inspection hours (SS/100 IH), orders per 100 inspection hours (O/100 IH), citations per 100 inspection hours (C/100 IH), penalty per 100 inspection hours (P/100 IH), no-days-lost incidence rate (NDL IR), nonfatal days-lost incidence rate (NFDL IR) and the severity measure (SM).The IER index was calculated by assigning weights to these risk indicators using the information entropy method, which objectively determines weight based on the variance of each index. The BIRCH clustering algorithm was used to validate the IER index. Statistical analyses, including multivariate analysis of variance (MANOVA) and post-hoc tests, were performed to assess the statistical significance of clustering results. Fig. 1 Box plots of all seven indices for underground mines in 2012. Results Table 1 provides descriptive statistics for these seven indices from underground mines in 2012. The wide range of index values and skewed distributions (with the median lower than the mean) indicated the need for normalization before calculating the IER index. The normalized data confirmed the uniform distribution of risk values across the data set. Figure 1 presents the box plots for these indices, illustrating the distribution and dispersion. The SM showed the highest variability, while the C/100 IH had the lowest.Table 2 presents the descriptive statistics for the IER and equal weights risk (EWR) index values for underground mines in 2012. The IER values range from 1.08E-04 to 0.47, with a skewed distribution and a long tail at higher values. Although the IER could theoretically reach 1, it peaks at 0.47. In contrast, the EWR index, which assigns equal weight to all seven indices, shows a smaller long tail and fails to capture the variability of the data, leading to higher errors. This limitation is supported by research experiments [1]. The IER index was validated through the BIRCH clustering algorithm, which effectively grouped mines based on risk. Silhouette analysis determined the optimal number of clusters (three in 2012), confirming distinct risk groups. MANOVA results indicated statistically significant differences between clusters, supported by p-values less than 0.05. The ANOVA test showed that at least one cluster’s mean risk value differed significantly from others, as confirmed by post-hoc analysis. Fig. 2 Risk index and associated extreme outlier value (EOV) and outlier value (OV) values from 2006 to 2011 for the Upper Big Branch coal mine: (a) IER and (b) EWR (see full paper for the EOV and OV threshold calculations). Case study A case study was conducted on the Upper Big Branch Mine, which experienced a catastrophic explosion in 2010. The IER index and EWR index were applied to assess its safety from 2006 to 2011 (Fig. 2). The IER showed a steady increase in risk leading up to the disaster, surpassing the outlier threshold in 2009. In contrast, the EWR failed to capture this rising risk effectively. This demonstrates the superior performance of the IER in identifying high-risk scenarios compared to traditional methods. Conclusions The IER index provides a comprehensive approach to assessing mine safety by integrating multiple risk indicators. It effectively captures variability across different factors and offers a more accurate reflection of mining risks compared to traditional methods like the EWR index. The IER index was validated using clustering algorithms and statistical methods, showing a clear differentiation of risk levels. Its application to the Upper Big Branch Mine highlights its practical use in identifying rising safety risks. Future work should focus on incorporating additional indicators, such as fatalities, into the IER model for a more complete assessment. Additionally, developing a forecasting tool to predict future risks could enhance proactive safety management. Improved thresholding methods for categorizing risk levels are also needed to provide clearer guidance for mine operators in mitigating safety hazards. Selected reference DelSole T, Yang X, Tippett MK (2013) Is unequal weighting significantly better than equal weighting for multi-model forecasting? Q J R Meteorol Soc 139(670):176–183

An information entropy-based risk (IER) index of mining safety using clustering and statistical methods

Authored by: Dharmasai Eshwar, Snehamoy Chatterjee, Rennie Kaunda, Hugh Miller and Aref Majdara

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