Factors That Influence Failure Behaviour and Remaining Useful Life of Mining Equipment Components

3.1. Select Asset Class, Subsystem, and Components

With industry assistance, we compiled a confidential failure database. It includes data from 14 mine sites, 4 commodities, and 6 organisational entities. The largest set of data is for heavy mobile equipment, including front-end loaders (FELs), dozers, shovels, graders, scrapers, drills, and dump trucks. Some models of equipment are used across all of the different commodity groups and at many of the sites. Mobile equipment has a number of components with similar functions. An example is the hydraulic cylinders used on FELs and dozers in surface mining operations. The two classes of hydraulic cylinders of interest are the following: (1) lift cylinders used in lifting or lowering a boom to which the implement is attached and (2) tilt cylinders responsible for changing the angle of the implement.

3.2. Define Failure and Cleanse Data

For lift and tilt cylinders, events classified as failures include (1) major leaks preventing the equipment from further operation and (2) loss of function to causes other than leaks. In responding to these failure events, two assumptions are made, the first assumption is that repair restore the component to as good as new and that when a replacement cylinder is installed, a new (not refurbished) cylinder. In order to test whether the failures are independent and identically distributed, an examination of the cumulative failures versus time plots is performed. This is described in a subsequent section. Events involving these cylinders that are NOT classified as failures include (1) preventative replacement of cylinders (a suspension is recorded), (2) accidental damage (a suspension is recorded), (3) minor leaks under observation but not preventing further operation, and (4) repairs or adjustments to cylinder attachments such as mountings, pins, valves, hoses, and rods. In total, there were a total of 1342 records of interest, including 551 suspensions and 791 failure events.

3.3. Identify and Characterise the Covariates of Potential Interest

The external covariates examined in this paper include values that can be measured via analysis of data provided, or examining the conditions present at each mine site. The covariates can be broadly classified into two categories: characteristics of the mine and characteristics of the operation and maintenance of each piece of equipment. Covariates examined in this study originating from the characteristics of the mine include ore properties such as rock impact hardness number (RIHN), absolute hardness, density, abrasive index, and unconfined compressive strength, quartile indicators for concentrations of sodium, potassium and silicon compounds, and 3 ore-type indicators corresponding to each ore type. Covariates examined originating from the characteristics of the operation and maintenance include the equipment size, noncompliance to mechanical lubrication schedules, inspection intervals, and duty level of the equipment. It is important to note that this list of covariates is not a complete list of all possible covariates; however, the study was restricted to covariates whose values were directly observable via provided data or published reference material.

In instances where the exact value for that mine site was not known, a value in the middle of the range for that ore type was assumed for each group. Data were compiled (in order of preference) from the mine site's geotechnical database (where available), estimated parameters from equipment manufacturers, or commonly accepted ranges from published reference material [16].

3.4. Examine Characteristics of the Dataset

3.4.1. Examination of Weibull Parameters of Stratified Population

Table 1 shows the shape parameter (β) of the Weibull distribution for each population of FEL and dozer cylinders. It can be seen that the β values for lift cylinders for both types of equipment are similar for Fe and coal but distinctly different for Ni. For the tilt cylinders, the β values are similar for coal and nickel but slightly lower for Fe.

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Table 1:

Weibull parameters and statistics of dataset.

Type	β (Fe)	β (coal)	β (Ni)	Number of failures Fe/coal/Ni	Number of suspensions Fe/coal/Ni
FEL lift cylinders	1.36	1.4	1.95	33/50/8	41/30/14
FEL tilt cylinders	1.07	1.25	1.32	30/52/6	41/32/12
Dozer lift cylinders	1.67	1.77	1.22	42/349/26	23/242/25
Dozer tilt cylinders	1.1	1.36	1.3	40/146/12	11/58/22

Other items of note in Table 1 are the low population of failures and high ratio of suspensions to failures (2: 1) for cylinders on both FELs and dozers in nickel sulphide operations. Cylinders for FELs in haematite operations also exhibit high suspension to failure ratios with 1.36 suspensions per failure. This results in wide confidence intervals when estimating parameters; however, this is somewhat mitigated by the fact that both the combined populations as well as most populations stratified by commodity all have statistically significant numbers of failures greater than 30. An exception to this is cylinders for FELs mining for nickel sulphide for which there are sparse failure data (8 lift cylinder failures and 6 tilt cylinder failures) which are outnumbered by suspensions (14 lift cylinder suspensions and 12 tilt cylinder suspensions).

3.4.2. Verification of Independent and Identically Distributed Data

Verification that datasets are independent and identically distributed (IID) is performed by plotting plots of times between consecutive failures and cumulative failure times against failure number [17]. Identical distributions can be verified by ensuring a single linear trend in the cumulative failure times.

Figures 1 (a), 1 (b), 1 (c), and 1 (d) show the cumulative failure times between consecutive failures. There are no significant changes in slope that would indicate an increasing or decreasing hazard rate. This absence of any significant change in slope of these curves does not guarantee that repairs are as good as new, but it is indicative of an absence of factors that indicate increasing or decreasing life of subsequent failures or lack of independence of the dataset.

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Figure 1:

(a) FEL lift cylinder cumulative TTF. (b) FEL tilt cylinder cumulative TTF. (c) Dozer lift cylinder cumulative TTF. (d) Dozer tilt cylinder cumulative TTF.

3.5. Explore Effects of Covariates on Failure Behaviour

The relationships between ore characteristics and failure behaviour are explored statistically using proportional hazards modelling (PHM). For each cylinder type on each mobile equipment type, it is possible to construct a total of 15 one-covariate models (models with a single explanatory covariate) and 105 two-covariate models (models with two explanatory covariates). Due to the existence of only 3 ore types in this study, it is only possible to construct models with, at maximum, 2 covariates (corresponding to the 2 degrees of freedom available). This process was applied to both types of cylinders on each of the two types of mobile equipment leading to a total of 60 one-covariate models and 420 two-covariate models. The 480 models developed cover all possible combinations of the given covariates. All models were then tested for statistical accuracy and significance by the use of criteria in a model selection process.

The outputs from the proportional hazards model include the coefficients for each covariate, the standard error associated with each coefficient, and the baseline hazard rate. The coefficient of each covariate is proportional to the impact that covariate has on the hazard rate. Thus, positive coefficients indicate that the covariate increases the hazard rate while negative coefficients that indicate the covariate decreases the hazard rate. The baseline hazard rate can be modified by the calculated coefficients, and observed values of each covariate to obtain the modified hazard function and survival curves. A parametric fit is performed to determine the Weibull parameters for the theoretical distribution that best fits each modified survival curve. These are the predicted parameters that each PHM would predict for each commodity. The actual parameters are obtained by performing a standard Weibull analysis directly to the dataset of each commodity.

3.6. Select PHM Models Using Model Selection Criteria

In order to assess the suitability of each PHM model, we consider the following factors. The accuracy for the model is assessed by the average percentage deviation between the predicted and the actual MTTFs for all commodities. In this case, the lowest percentage deviation corresponds to the highest accuracy. Other measures of accuracy were considered, such as analysis of goodness of fit against the full Weibull curve for each commodity; however, the use of a point estimate (MTTF) comparison was selected due to its widespread use in industry. The significance of a covariate is assessed by comparing the magnitude of the coefficient with the magnitude of the standard error associated with that coefficient. Under this method, a higher ratio of coefficient to standard error indicates higher significance for that coefficient. The aim is to identify only models whose covariates most impact the hazard rate of the asset. Selection criteria for the models are as follows:

Due to the low complexity of the models (<2 covariates), it was not deemed necessary to consider the Akaike information criterion. Models that meet the model selection criteria are collated for similar subsystems across similar equipment types. Significant covariates or combinations of significant covariates are identified for further discussion and investigation.

4.1. Relationships between Ore Characteristics and Failure Behaviour

A visual representation of the cylinders life in operations mining for different commodities was obtained by the Bayesian inference [19]. These representations show that the distributions of the Weibull scale parameter (η) of different commodities are different. The FEL lift cylinders for nickel sulphide operations in Figure 2 (a) are significantly different from those in coal and haematite operations. The FEL tilt cylinders for all commodities in Figure 2 (b) are different from each other, and dozer tilt cylinders for haematite operations in Figure 3 (b) are different from those in coal operations. It is important to note that these distributions are not frequency distributions of the times to failure.

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Figure 2:

Distribution of η for FEL lift cylinders and FEL tilt cylinders.

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Figure 3:

Distribution of η for dozer lift cylinders and dozer tilt cylinders.

The PHM was applied to the cleansed data, and the selection process was used to identify appropriate models for lift and tilt cylinders on FELs and dozers. Table 2 shows a list of models that met the model selection criteria for accuracy and significance. A P value for the PHA hypothesis test is also included for each covariate. The P values were obtained using the cox.zph function in the survival package in R [20].

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Table 2:

Models meeting the model selection criteria for tilt and lift cylinders on dozers and FELs.

Set	Covariates	Coefficient 1	Coefficient 2	Ratio Coef-SE1	Ratio Coef-SE2	PHA P value	MTTF deviation (%)
FEL-Lift	Abrasive index and absolute hardness	67.86	−0.22	1.77	1.8	0.597 0.587	3.81%
FEL-Lift	Nickel sulphide	−0.64	NA	1.60	NA	0.65	10%
FEL-Tilt	UCS andsilicon %	−0.014	0.37	2.71	1.5	0.666 0.934	5.49%
FEL-Tilt	Abrasive index andabsolute hardness	89.67	−0.29	2.16	2.21	0.11 0.11	5.3%
FEL-Tilt	Coal and nickel sulphide	0.42	−0.61	1.82	1.34	0.951 0.124	3.89%
Dozer-Lift	Absolute hardness and haematite	−0.046	2.82	2.84	3.02	<0.01 <0.01	6.3%
Dozer-Lift	Abrasive index and RIHN	8.25	−0.093	3.13	2.98	<0.01 <0.01	4.64%
Dozer-Lift	RIHN and haematite	−0.066	1.10	2.83	3.12	<0.01 <0.01	5.76%
Dozer-Tilt	No suitable models	NA	NA	NA	NA	NA	NA

Table 2 is organised as follows. Columns 3 and 4 show the coefficient values for the covariates listed in Column 2. Columns 5 and 6 show the ratios of coefficient magnitude to standard error with higher ratios indicating stronger significance. The P value for PHA hypothesis testing is shown in Column 7 with values greater than 0.1, indicating a failure to reject the PHA. The deviation between the actual and predicted value for the MTTF is shown in Column 8. The MTTF calculation takes into account both β and η values [21] as follows:

MTTF = ∫ 0 ∞ R ( t ) d t = η ( 1 β + 1 ) .

(1)

Table 2 shows that only 8 models from the 480 tested have significant relationships. These relationships apply to tilt and lift cylinders of FELs and lift cylinders of dozers. Most of the covariates are related to ore properties rather than ore types with absolute hardness and/or abrasion index appearing in four of the 8 models.

The three models for dozer lift cylinders (Table 2: Rows 7 to 9) violate the proportionality assumption with their P values for the PHA hypothesis test (Table 2: Column 7) less than 0.1.

Of the models for FEL tilt cylinders, the models for abrasive index and absolute hardness (Table 2—Row 5) and ore indicators for coal and nickel sulphide (Table 2: Row 6) have P values for the PHA hypothesis tests close to the threshold of 0.1 (0.11, 0.11, and 0.124, resp.). The covariate models created for dozer tilt cylinders did not yield any relationships of significance as no covariate selection combination was able to meet the accuracy criteria.

Table 3 summarises the list of parameters, and their occurrences in models are identified as significant. The “number of occurrences” is the number of times that covariate was present in models that met the model selection criteria. The “effect on hazard rate” uses the sign of the calculated coefficient to determine whether the covariate positively or adversely impacts the hazard rate.

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Table 3:

Covariates used in PHM that meet the model selection criteria.

Parameter	Numberof occurrences	Effect on hazard rate
Absolute hardness	2	Higher scratch resistance decreases the hazard rates
UCS	1	Higher UCS decreases the hazard rate
Si	1	Higher silicon % increases the hazard rate
Abrasive index	2	Higher AI increases the hazard rate
Ore indicators	3	Coal mines have higher hazard rates Nickel mines have lower hazard rates Haematite mines have lower hazard rates for FELsbut higher hazard rates for dozers
Most common model	Absolute hardness and abrasive index

In order to determine the magnitude of impact of each covariate relative to every other covariate, we normalise the measured covariate values in order to obtain a unit standard deviation. Table 4 shows the normalised coefficients for all models meeting the model selection criteria. It can be seen that the normalised covariates with the largest impact per standard deviation change in covariate values are the abrasive indexand absolute hardness with ranges of 5.86 to 7.66 and −6.05 to −7.9, respectively, This compares with covariates with less impact such as Si, with a normalised coefficient of 0.32.

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Table 4:

Normalised coefficients for models meeting model selection criteria.

Set	Covariates	Normalised coefficient 1	Normalised coefficient 2
FEL-Lift	Abrasive index andabsolute hardness	5.86	−6.05
FEL-Lift	Nickel sulphide	−0.64	NA
FEL-Tilt	UCS and silicon %	−0.59	0.32
FEL-Tilt	Abrasive index and absolute hardness	7.66	−7.9
FEL-Tilt	Coal andnickel indicators	0.42	−0.61

5.1. Analysis of Distributions and Weibull Parameters Based on Commodity Type

Examination of the distributions shown in Figure 2 (a) to Figure 3 (b) shows the following.

Tables 3 and 4 show that absolute hardness and abrasive index were parameters that had the highest rate of occurrence in all of the significant models. They were also the parameters with the highest impact per standard deviation change of observed covariate values.

5.2. Exploring the Relationship to Specific Physical Properties

The covariate models developed in this study identify, from a selected population of physical properties, those properties that impact the reliability of lift and tilt hydraulic cylinders on earthmoving mobile equipment. These properties are the abrasive index and absolute hardness of the mineral. To explore the relationship between what is observed in the data and what might be occurring in the physical environment, a review of common failure causes of hydraulic cylinders was conducted. The most common causes of cylinder failure (excluding rod breakage or alignment issues) are contamination, bearing and seal damage, chemical or heat degradation, and structural damage.

The coefficient calculated in this study for absolute hardness shows a decrease in hazard rate with absolute hardness. We postulate that the effect of a higher absolute hardness, which is the ability of a rock to resist scratching, decreases the ability of the material to create dust-sized particles. This results in a less dusty environment, which increases the reliability of a hydraulic cylinder due to less dust contamination of the hydraulic fluid or bearings. An increase in abrasiveness of the material appears to influence the reliability of the lift and tilt cylinders in some assets. In a high-dust environment, the ability of the particles to cause abrasive wear once in contact with the cylinder surfaces, bearings, or seals will accelerate deterioration.

The coefficient values and specific observed values for any commodity can be used to determine the magnitude of impact on the hazard rate for that commodity. In the case of the abrasive index and absolute hardness model, the coefficient values are 67.86 and −0.22, respectively (Table 2: Row 2, Columns 3 and 4). A FEL in a nickel sulphide mining operation with an abrasive index of 0.04 and absolute hardness of 15 would experience a modifying factor to the baseline hazard rate of 0.55 (45% lower than the baseline hazard rate). The baseline hazard rate represents the hazard rate of a fictional ore with an abrasive index of 0 and absolute hardness of 0. Similarly, a FEL in a coal mining operation with a low abrasion index of 0.01 and low absolute hardness of 2 would experience a modifying factor to the baseline hazard rate of 1.27 (27% higher than the baseline hazard rate). This implies that the lift cylinder of a FEL in a nickel mining operation experiences a hazard rate that is 43% of the hazard rate experienced by an equivalent FEL in a coal mining operation.

It is possible to apply the modifying factor for any specific commodity to obtain the commodity-specific hazard rate, survival curves, and associated Weibull parameters (β and η). The practical use of these coefficients is to extract operation-specific parameters from pooled data. These operation-specific parameters such as the MTTF, β, or η can be used to benchmark existing operations or provide insight when developing a mine site with differing operating conditions.

5.3. Organisational and Maintenance Properties

The analysis examined covariates representing the maintenance and operating conditions of the organisation including equipment size, equipment duty level, inspection intervals, and compliance to mechanical lubrication schedules. As a proxy, the scheduled compliance to a 250-hour engine service task was used. This maintenance work does not cover the cylinders specifically, but it is an indication of organisational commitment to scheduled maintenance. There are no direct data on scheduled maintenance compliance for the lift and tilt cylinders. Of these covariates only, the equipment duty level and compliance to mechanical lubrication schedules were found to be significant; however, they were not as significant as the ore properties. Equipment that was used for lower numbers of hours a day experienced higher hazard rates suggesting that deterioration due to time or exposure still occurs even when the equipment is not in use. Organisations with higher compliance to scheduled maintenance also experienced lower hazard rates. Further work in respect to developing and using organisational indicators as covariates is underway.

5.4. Sources of Uncertainty

There are a number of sources of uncertainty in this study due to the nature of failure data and also the simplifications inherent in compressing complex physical property distributions into a set of numbers. The original datasets contain data for all failure events, and there is considerable variability in the content of the fields and how data are represented. Extraction of failure and preventative replacement events was performed using an in-house data cleansing tool with the outputs cross-referenced against external data sources such as maintenance plans and external maintenance contracts. Incorporating data from these external data sources was done as follows.

Maintenance and repair contracts (MARCs) are specified time intervals wherein major maintenance and replacement activity is performed by an external contractor (most often the equipment vendor). Maintenance work performed under these contracts is recorded in the record system of the contractor rather than that of the mining company; it is therefore not included in the dataset. Data points immediately following a maintenance contract are removed as they also include times to failure/replacement of all maintenance work performed under the MARCs. Times between preventative replacements are compared against replacement intervals specified in the mining company's maintenance plan. Events marked as preventative replacements occurring significantly sooner than the planned replacement interval are treated as failures unless there is other evidence indicating that they were preventatively performed.

The dataset used includes 5 cases in which the number of failures is less than the number of suspensions. This can result in wider confidence intervals for both η and β values. Alternative methods of parameter estimation such as the Bayesian inference, as shown in Figure 2 (a), or hypothesis testing can be used [22]. In addition, in two cases for nickel, there are low data populations resulting in poor fit. More data are being sought for nickel in order to improve confidence in estimated parameters.

5.5. Further Research

A work is currently underway to extend the range of components and asset classes under analysis. This will include mechanical, electrical/electronic, hydraulic, and structural subsystem components and asset classes from both fixed-plant and mobile equipments.

It was found that the assumption of proportionality was rejected for both types of cylinders for the dozer equipment class as shown in Table 2. Further work will be undertaken to more adequately model these assets by stratifying the asset class further or choosing an alternative modelling approach.

Approximations of dust levels at each mine site were inferred based on the ability of the material to resist fragmentation. This may not hold true due to other factors and dust-creation mechanisms such as the use of dust suppression, blasting techniques, presence of clay or other fine-grained materials, and nonimpact-related dust-creating mechanisms. Further work will be performed in assessing dust concentrations experienced at the rock interface on a mine site-specific basis. Additional environmental parameters such as average temperatures and chemical compositions of rocks will be added to determine whether other extreme environmental conditions have a significant influence on equipment failure.

It has been noted that the use of purely physical properties as covariates may not be sufficient to explain the failure behaviour of equipment. Additional covariates associated with organisational processes, site factors, and environmental conditions can be added as they become available. Organisational processes to be added include the culture in which the asset is operated (including functional role and level of loading) and site factors such as asset age profile and pit characteristics (e.g., single/double benching, blasting characteristics) that are controllable by the organisation. Maintenance factors to be added in future work include the effect of maintenance, inspection, or condition monitoring activities specific to the component. The framework supports the extension of the number of covariates to n-parameter models.