Reliability Engineering and System Safety 84 (2004) 209–218 www.elsevier.com/locate/ress
Industrial Case Study
A model for optimal armature maintenance in electric haul truck wheel motors: a case study Benjamin Lhorentea, Diederik Lugtigheidb,*, Peter F. Knightsc, Alejandro Santanad a Komatsu Chile, Av. Americo Vespucio 0631, Quilicura, Santiago, Chile Condition-Based Maintenance Laboratory, Department of Mechanical and Industrial Engineering, University of Toronto, 5 King’s College Road, Toronto, Ont., Canada M5S3G8 c Canadian Chair of Mining and Associate Professor, Pontificia Universidad Catolica de Chile, Centro de Mineria, Av. Vicuna MacKenna 4860, Santiago, Chile d Reliability and Development of Komatsu Chile, Av. Americo Vespucio 0631, Quilicura, Santiago, Chile
b
Received 25 September 2003; accepted 24 October 2003
Abstract The objective of the work presented in this paper is the determination of an optimal age-based maintenance strategy for wheel motor armatures of a fleet of Komatsu haul trucks in a mining application in Chile. For such purpose, four years of maintenance data of these components were analyzed to estimate their failure distribution and a model was created to simulate the maintenance process and its restrictions. The model incorporates the impact of successive corrective (on-failure) and preventive maintenance on necessary new component investments. The analysis of the failure data showed a significant difference in failure distribution of new armatures versus armatures that had already undergone one or several preventive maintenance actions. Finally, the model was applied to calculate estimated costs per unit time for different preventive maintenance intervals. From the resulting relationship an optimal preventive maintenance interval was determined and the operational and economical consequences and effects with respect to the actual strategy were quantified. The application of the model resulted in the optimal preventive maintenance interval of 14,500 operational hours. Considering the failure distribution of the armatures, this optimal strategy is very close to a run-to-failure scenario. q 2004 Elsevier Ltd. All rights reserved. Keywords: Weibull analysis; Armatures; Electric motors; Repairable system; Maintenance optimization
1. Background In 1996, Komatsu Chile (KC) put into operation a fleet of haul trucks in a mining application in Chile. KC delivered these machines under a repair and maintenance contract, taking full responsibility of all repair and maintenance work at guaranteed availability and maintenance costs. The haul truck is an electric drive DC truck. This means that propulsion is delivered to the rear wheels by means of two parallel electric DC wheel motors. The wheel motors receive rectified electric power from the main alternator working in conjunction with a diesel engine. The wheel motors are mounted on the truck’s axle box and provide * Corresponding author. Tel.: þ 1-416-946-5528; fax: þ1-416-946-5462. E-mail addresses:
[email protected] (D. Lugtigheid),
[email protected] (B. Lhorente),
[email protected] (P.F. Knights),
[email protected] (A. Santana). 0951-8320/$ - see front matter q 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.ress.2003.10.016
the function of axle, transmission and wheel motor at the same time. The wheel motor’s main components are the wheel hub, ring gear structure, planetary gears, sun gear and armature, see Fig. 1. The armature is the rotor of the electric motor and can be removed from it independently. It primarily consists of bearings, commutator, brushes, spools and poles. The armature commutator consists of copper bars and mica plates. The mica plates physically separate and isolate the copper bars and provide a radial pressure to ensure the commutator’s stability. The mica bars have less altitude than the copper bars and are located below the commutator’s superficial area to prevent interaction with the sliding brushes on the area. The copper bars have a wedge shape form and together form a cylinder. Each bar has a riser for connection to the armature’s spools.
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Fig. 1. Wheel motor components.
According to a recent study on the trucks at the same mining operation, the wheel motors together with its armatures are the most critical system of the machine. It can be classified ‘acute and cronic’ (Knights [1] and Turina [2]), meaning a high failure frequency and a high mean time to repair. At the same time the armature is considered to be critical because of its high maintenance costs. Due to the high criticality of the armatures in terms of reliability, availability and costs, a study was performed to define how the component’s operational parameters as well as its costs could be improved. This was done through the development and application of an optimal preventive maintenance (PM) model to determine the PM strategy that minimizes costs per unit time. As well, the impact of this strategy on the haul trucks’ operational parameters was evaluated. The findings of this study are presented in this paper.
2. Problem formulation The current PM strategy is to carry out PMs at intervals of 9,000 operational hours. If an armature failure occurs beforehand, a corrective maintenance (CM) is carried out. Although PMs and CMs are different types of events, the armature reconditioning activities to be undertaken are the same. The occurrence of armature failures is directly related to the PM interval. Longer PM intervals will cause more failures to occur, and vice versa. The objective of this study is to determine the optimal trade-off between CM and PM that minimizes the operating costs per unit time of the armature. A key activity of the reconditioning process is commutator resurfacing. This activity consists of equalizing the commutator’s surface by removing a thin layer of material from the external surface of the copper bars and mica plates. A new commutator has a diameter of 16.500 and the limit for proper operation is 15.500 . In case of a CM, on average 0.2500
of material is removed and, in case of a PM, only 0.1500 . This means that the total useful life is limited by the amount of material that is removed1 and whenever an armature reaches the diameter limit of 15.500 , the PM or CM activity cannot restore the proper functioning of the component and a new armature must be purchased. The repair costs for reconditioning are the same for both a PM or a CM. Besides the diameter restriction, the armature has a maximum total useful life of 40,000 h. This means that after 40,000 accumulated operating hours, independently of its diameter, the armature must be replaced by a new one. The costs of a new armature are approximately 13 times the cost of reconditioning and we shall refer to the purchase of a new armature as a result of any of these two restrictions as ‘renewal’. The optimization horizon is 40,000 hours. This means that if a new armature is needed within this period, KC must incur full cost. On the contrary, no costs for KC are incurred. The objective is to define an optimal age-based PM strategy over a period of 40,000 h. In practical terms, this means defining a PM interval resulting in the least cost per unit time.
3. The general PM model For every component under an age-based PM policy there exist two types of maintenance actions: preventive (PM) and corrective (CM). The mean time to failure (at which a CM must be carried out) and the PM interval together with their probabilities of occurrence are interrelated. Longer PM intervals result in greater mean times to failure. But at the same time the probability of occurrence of a failure at higher PM intervals is higher. These relationships can be used to define the optimal PM interval that minimizes the costs per unit time. Defining: Cp Cf Tp FðTp Þ RðTp Þ
PM Costs (US$) CM Costs (US$) PM interval (operating hours) Probability of a failure occurring before reaching the PM interval Tp Survival probability equal to 1 2 FðTp Þ
Thus, within the age-based PM policy two different cycles can be distinguished: the component survives Tp and a PM is carried out incurring a cost Cp or the component fails beforehand and a CM must be carried out incurring a cost Cf : For this model the expected costs per unit time in 1
It is important to mention that the amount of material removed from the commutator’s surface per PM or CM is less than the given values. However, while in operation, the commutator looses material as well and the given values are average values of the differences in diameter between two consecutive maintenance actions.
B. Lhorente et al. / Reliability Engineering and System Safety 84 (2004) 209–218 Table 1 Amount of data in data sets Group
Left-hand armature
Right-hand armature
1 2 3
64 40 41
63 37 35
145
135
Total
function of Tp can be written as (Jardine [3]), CðTp Þ ¼
Cp RðTp Þ þ Cf FðTp Þ ; Tp RðTp Þ þ MðTp ÞFðTp Þ
ð1Þ
where MðTp Þ represents the mean time to failure of an armature subject to corrective maintenance with a PM interval of Tp and, FðTp Þ ¼
ð Tp
f ðtÞdt
ð Tp MðTp Þ ¼
ð2Þ
0
tf ðtÞdt
0
FðTp Þ
;
ð3Þ
where f ðtÞ is the probability density function (p.d.f.) of the times to failure. Whenever the p.d.f. of the times to failure of the component is known, the costs per unit time can be minimized over Tp ; resulting in the optimal PM interval Tpp :
211
failure characteristics. Before using the component’s maintenance history to estimate its p.d.f., the data should be thoroughly analyzed. The nature of the reconditioning process is to restore the proper functioning of the component and reduce its risk of failure. Although the probability of failure should be reduced by a CM or PM, it is unlikely that its behavior will be identical to that of a new component (so called goodas-new or GAN). It is more likely that its failure rate is higher than that of a new component, but less than just before the maintenance action was carried out (so called better-than-old-but-worse-than-new or BOWN). The same reasoning holds for armatures undergoing a second, third, etc. maintenance. It has been shown that an armature’s physical state changes with each maintenance through a reconditioning process. This might affect the armature’s p.d.f. For this reason, the failure data was separated into three groups: new armatures (before the first PM or CM, group 1), after the first but before the second PM or CM (group 2), and after the second PM or CM (group 3). At the same time a separation was made between right-hand and left-hand side armatures. This was done to verify whether or not the failure characteristics of armatures are different in these cases. The amount of data in each data set is shown in Table 1. The data in each set consisted of failures and suspensions. The latter correspond to PMs (reconditioning before failure has occurred). These data were gathered from August 1996 until March 2001.
4. Data treatment and analysis
4.1. Data distribution and independence
From the model presented above it can be seen that the definition of the p.d.f. is critical to the process of determining Tpp : The p.d.f. describes the component’s
The first check undertaken was to examine whether or not the data in each data set were independent and identically distributed. If this were not the case, an
Fig. 2. Trend plots for left-hand side (left) and right-hand side (right).
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erroneous estimation of the p.d.f.’s would result. A serial correlation test was applied to test for independency of the data. This test consists of ranking the failure times (not suspensions) according to their date of occurrence, making pairs ðXi ; Xi21 Þ of each two subsequent failure times for i ¼ 2…n where n is the amount of observed failures and plotting them. If the position of the data points is randomly distributed among the graph, the data can be considered independent (Vagenas et. al. [4]). All subsets showed this behavior, so it was assumed that the data in each of the six datasets were independent. To verify whether the data in the different data sets were identically distributed, trend plots were used. These are obtained by plotting the accumulated times to failure against accumulated failure number (ordered according to date of occurrence). In the case that the graph shows a unique linear trend, the failure data of the subset can be considered identically distributed. In the case that the graph shows two or more linear segments, it can be concluded that at a certain moment in time the failure distribution of the subset changed.
This can occur due to changes in maintenance procedures or in operational parameters such as, haul routes, climatic conditions or other external factors. In this study, whenever this was detected, only data belonging to the most recent distribution was considered. This was done because the objective of this study is to determine the best strategy under actual circumstances. In Fig. 2 the trend plots for left and right-hand armatures before the first maintenance are shown. 4.2. Histograms The next step in the data analysis process was to analyze how failure frequencies relate to accumulated operating hours and month of occurrence for each of the different data sets. This was done to get a clearer understanding of the variation of failure frequencies with respect to the position of the armature, accumulated operating hours and calendar time. The following observations were made.
Fig. 3. Failure frequencies versus time (all groups).
B. Lhorente et al. / Reliability Engineering and System Safety 84 (2004) 209–218
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Table 3 Left-hand armature Weibull parameters Parameter
Group 1
Group 2
Group 3
Total
b h t0
0.809 36,286 0
1.247 6,382 0
1.235 5,264 0
1.043 12,304 0
4.4. Distribution fitting For the determination of the p d.f. in this study, the Weibull distribution was chosen, due to its flexibility in representing components with constant, increasing and decreasing failure rates. This property is particularly useful when dealing with different failure distributions among the data sets of groups 1, 2 and 3, as was the case in this study. The p.d.f. of the three parameter Weibull distribution is, 0 b t 2 t0 b21 2 t2t h f ðtÞ ¼ e ð4Þ ; for t . t0 : h h
Fig. 4. Failure frequency versus time (all groups).
† The failure frequencies versus time and operating hours are very similar for left and right hand armatures. This was confirmed by a statistical hypothesis test. See Fig. 3. † The failure data of group 1 showed higher failure frequencies at higher operating hours. However, groups 2 and 3 showed more failures concentrated at lower operating hours. † Failure frequencies are highest during first quarters. First quarters contain 39% of the total failures and the second, third and fourth 23, 18 and 20%, respectively. The first quarter of each year coincides with the occurrence of adverse climatic conditions in the region where the mine is located. This particular climatic event is associated with heavy rain and electric storms, which affects the operating parameters of the armature and causes additional failures (see Fig. 4).
Where b is the shape parameter, h is the scale factor or characteristic life and to is the failure-free time. The data in this study consisted of times to failure (CMs) as well as PMs (suspended or censored data). For this reason the data were adjusted according to mean and median ranks before the actual fitting process (O’Connor [5]). The fitting process was carried out in Excel, using linear regression. The results of the fitting process are shown in Tables 3 –5. From these tables it may be concluded that:
The 280 data of the six data sets consisted of 156 failures (CMs) and 124 suspensions (PMs). Table 2 shows the causes of failure of the 156 failures. The dominant failure mode is flashovers and for a considerable amount of failures (32) no cause was identified.
† For new armatures (group 1), the shape parameter varies between 0.8 and 0.9 and is less than 1 which indicates infant mortality. † For armatures that have undergone one or more maintenance (groups 2 and 3), the shape parameter varies between 1.0 (constant failure rate) and 1.3, indicating near-randomness of the failure data. Some wear is evident and the characteristic life is much smaller than group 1. † In all data sets the shape parameter increases with every maintenance. This validates the conclusions drawn from the histograms, that with every maintenance action the mean life of the component diminishes and failure rates increase.
Table 2 Causes of failure
Table 4 Right-hand armature Weibull parameters
4.3. Causes of failure
Cause
Amount
Parameter
Group 1
Group 2
Group 3
Total
Flashover Ground fault/short circuit Unknown
118 7 32
b h t0
0.897 11,014 0
1.012 7,538 0
1.215 5,149 0
1.119 6,914 0
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Table 5 Total armature Weibull parameters Parameter
Group 1
Group 2
Group 3
Total
b h t0
0.866 24,918 0
1.163 6,785 0
1.276 5,147 0
1.082 6,914 0
† The shape parameters of left and right hand armatures are very similar, validating the conclusions drawn from the histograms. With the exception of the characteristic life difference for the group 1 right-hand and left-hand armatures, it was concluded that there was little difference between the failure parameters for right and left hand armatures. In the interests of developing a uniform maintenance policy, it was decided to use the Weibull parameters for each group without discriminating between right and left-hand failures (see Table 5).
5. Model application In order to apply the general optimal PM model to define the optimal PM interval Tpp ; some adjustments have to be made, and in order to do so the following variables are defined: Mn ðTp Þ Mean time to a CM before the nth maintenance given PM at Tp . Fn ðTp Þ Accumulated failure probability before the nth maintenance given PM at Tp . Rn ðTp Þ Survival probability before the nth maintenance given PM at Tp : VC The length of the optimization horizon (operating hours) CA Cost of a new armature (US$). As in the general PM model, there exist two different cycles. The armature can be preventively maintained at time Tp at a preventive maintenance cost Cp with a survival probability of Rn ðTp Þ; or can fail at time Mn ðTp Þ with a corrective maintenance cost Cf and a failure probability Fn ðTp Þ: The successive occurrence of these cycles form maintenance sequences, Si ; with each sequence giving an armature life of Vi operating hours prior to renewal. These can be represented by means of a maintenance probability tree, as shown in Fig. 5. The tree must be interpreted as follows. We start with a new armature (left node). Two scenarios might happen: the armature fails with probability F1 ðTp Þ or survives until the PM interval Tp with probability R1 ðTp Þ: In both cases, the armature must be reconditioned incurring a cost of Cf or Cp ; after which the armature is put back into operation. Now, the same scenarios might happen once again, but with respective probabilities F2 ðTp Þ and R2 ðTp Þ; as the armatures
Fig. 5. The maintenance probability tree.
have been reconditioned one time and now its failure characteristics are described by the p.d.f. of group 2. The i ¼ 1…k different sequences represent all possible successive maintenance (PM or CM) events between t ¼ 0 and t ¼ VC . However, besides preventive and corrective maintenance, armature renewals take place and these must be incorporated in the maintenance tree. Within a cycle,2 renewals, PMs and CMs are mutually exclusive events. This means that whenever a cycle has been completed within any sequence i (this can be at time Tp or Mn ðTp Þ), instead of a PM or CM cost Cp or Cf ; a renewal cost CA is incurred when at least one of the following conditions is met: † The useful life of the armature has reached the maximum,VM † If rij represents the amount of material to be removed from the commutator surface in maintenance j since the last renewal P i 21 of the armature of sequence i; then if rij , 1 2 nj¼1 rij ; ;i; j a renewal must take place. Therefore, sequences may vary in length in terms of the number of cycles of which they consist, however, accumulated sequence operating hours cannot exceed the length of the optimization horizon, VC . The cycle number of a sequence is denoted by j, which can have values between 1 and ni (where i is the sequence number) and it resets itself to 1 whenever a renewal takes place. Additionally the following variables are defined. Ci Accumulated maintenance costs of sequence i: Pi Probability of sequence i: ai ; bi ; ci Integer variables indicating amount of PMs (before the first, second and after third maintenance) occurring in sequence i: 2 A cycle refers to the time between two successive event (these can be PMs, CMs or renewals).
B. Lhorente et al. / Reliability Engineering and System Safety 84 (2004) 209–218
215
di ; ei ; fi Integer variables indicating amount of CMs (before the first, second and after third maintenance) occurring in sequence i: CðTp Þ Expected total costs of tree with PM interval of Tp : CM ðTp Þ Expected maintenance cost of tree with PM interval of Tp : CR ðTp Þ Expected renewal cost of tree with PM interval of Tp : In this way, the following set of equations represent the final model: Pi ¼ R1 ðTp Þai R2 ðTp Þbi R3 ðTp Þci F1 ðTp Þdi F2 ðTp Þei F3 ðTp Þfi
ð5Þ Fig. 6. Results.
Vi ¼ ðai þbi þci ÞTp þdi M1 ðTp Þþei M2 ðTp Þþfi M3 ðTp Þ
ð6Þ
Ci ¼ ðai þbi þci ÞCp þðdi þei þfi ÞCf
ð7Þ
6. Results
The expected maintenance and renewal costs are: Xk C i Pi CM ðTp Þ ¼ Xi¼1 k VP i¼1 i i CR ðTp Þ ¼
ð8Þ
CA k X V i Pi
ð9Þ
i¼1
Thus the total expected costs for a PM interval of Tp is: CðTp Þ ¼ CM ðTp Þ þ CR ðTp Þ
ð10Þ
The values of CðTp Þ are different for every Tp due to differences between maintenance trees in terms of sequence probabilities, amount of maintenance and renewals. However, the tree configuration (number of cycles per sequence) also changes in discrete steps according to Tp : In the case of the armature maintenance problem, it was decided to construct maintenance trees for 250 , Tp , 17; 000; with steps of 250 h. This was based upon the fact that the maximum observed lifetime between two successive maintenance actions was 17,000 h. Within this PM timespan, 16 different maintenance tree configurations could be constructed (see Table 6).
The results were simulated using a Microsoft Excele spreadsheet, and are presented in Fig. 6. In Fig. 6 it can be seen that the expected total useful life of the armatures increase with higher Tp intervals, however, this increase gradually diminishes. The reason for this is that at low Tp intervals the armature’s total useful life is restricted by its diameter restriction. At higher values of Tp the maximum useful life restriction ðVM Þ becomes dominant. As well it can be seen that, for all values of Tp ; the expected renewal cost per unit time is much higher than the expected maintenance cost per unit time. This is to be expected, as the cost of renewal is 13 times the costs of preventive and corrective maintenance. The maintenance costs decrease continuously as Tp increases. The renewal costs decrease in general terms but its evolution is discrete, with local gradually increasing slopes and abrupt falls. This is caused by the 16 different maintenance trees and the fact that only an integer amount of armatures is purchased within the optimization horizon VC : The maintenance costs per unit time curve does not present an optimal value. It decreases continuously with time. At the same time the renewal costs per unit time decrease as well, however, it does step-wise. The minimal costs per unit time are found at Tpp ¼ 14; 500 hours with a value of C*3 US$ per hour. Beyond Tpp the expected total costs per unit time are constant at a value of 1.022 times this minimum.
Table 6 Different maintenance probability trees Tree no.
Range Tp
Tree no.
Range Tp
1 2 3 4 5 6 7 8
250 # Tp , 6; 750 6; 750 # Tp , 8; 000 8; 000 # Tp , 9; 000 9; 000 # Tp , 9; 250 9; 250 # Tp , 10; 000 10; 000 # Tp , 10; 500 10; 500 # Tp , 10; 750 10; 750 # Tp , 11; 750
9 10 11 12 13 14 15 16
11; 750 # Tp 12; 000 # Tp 13; 500 # Tp 14; 500 # Tp 14; 750 # Tp 15; 250 # Tp 15; 500 # Tp 16; 750 # Tp
7. Sensitivity , 12; 000 , 13; 500 , 14; 500 , 14; 750 , 15; 250 , 15; 500 , 16; 750 , 17; 000
To check how sensitive the optimal PM interval Tpp was, a sensitivity analysis was conducted for the shape parameter b and the corrective maintenance costs Cf ; which are the two most critical variables of the model in terms of sensitivity.
3
Value suppressed for comercial reasons.
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B. Lhorente et al. / Reliability Engineering and System Safety 84 (2004) 209–218 Table 9 Sensitivity of Cf
Table 7 Confidence interval for b
bcalc bmax bmin
Group 1
Group 2
Group 3
0.866 1.065 0.704
1.163 1.384 0.977
1.276 1.582 1.029
Besides, in this study Cf was chosen equal to Cp as the costs of preventive and corrective reconditioning are equal for Komatsu Chile (KC). However, for the mining company using the trucks in their production process, these costs would not be the same. For them, corrective maintenance is more costly than preventive maintenance as these incur an opportunity cost related to the unscheduled production losses. The sensitivity analysis would make clear whether the optimal PM interval for KC is an optimal policy for the mining company at the same time. For the shape parameter, b; 95% confidence intervals were defined (see Table 7). The optimal PM interval and expected costs per unit time were calculated and the results are shown in Table 8. From these results it can be seen that with higher values of b the optimal PM interval decreases. However, since C* is small, the differences in costs per hour are minimal. In order to verify the sensitivity of Cf ; the same calculations were made for values of Cf times 1/3, 3, 5 and 10. The results are shown in Table 9. The optimal PM interval for lower values of Cf remains the same as the original, 14,500 h. With triple values of Cf the optimal solution is 15,500 h. This solution is optimal for values of Cf until five times the original value. In the extreme case of 10 times the original value, the optimal PM interval is 17,000 h. In general terms the model is not very sensitive to changes in Cf : Any optimal solution for KC will be very close to optimal for the mining company as well. So it may be concluded that: † 13; 500 # Tpp # 16; 750; when b takes its 95% confidence extreme values. † 14; 500 # Tpp # 17; 000; when Cf takes values of 1/3 to 10 times its original value. To analyze the model’s results in more detail, four scenarios were defined and their results compared:
Cf Tpp CðTpp Þ=C p
Cf 5
Cf 10
15,500 1.194
15,500 1.381
17,000 2.657
Tp CðTpp Þ=C p
Base case
Original case
Optimal case
Extreme case
9,000 1.261
10,000 1.253
14,500 1.000
17,000 1.022
† Original case: Tp ¼ 10; 000 h, which was the original PM interval KC used in the beginning of the contract. † Optimal case: Tp ¼ 14; 500 h, which is the optimal value according to this study. † Extreme case: Tp ¼ 17; 000 h, which is the maximum value Tp might take as no armatures have lasted more than 17,000 h in between maintenance actions. A summary of these cases is presented in Table 10.
8. Operational consequences For the four cases, the expected amount CMs and PMs during the useful life of an armature are the following, see Table 11: Taking into account the fleet size and its utilization, these numbers could be translated into amount of PMs and CMs per year, using the following relationships (Wong et. al. [6]). n s tul sp sf u
Amount of components in the fleet. Amount of total maintenance (PM and CM) per year. Total useful life of an armature in terms of operating hours Amount of PMs per year. Amount of CMs per year. Utilization in terms of operating hours per armature per year.
Table 11 Amount of maintenance during armature’s useful life
Table 8 Sensitivity of b
CðTpp Þ=C p
14,500 0.873
Cf 3
Table 10 Comparison of cases
† Base case: Tp ¼ 9; 000 h, which is the actual PM interval of KC.
Tpp
1 3
bmin
bcalc
bmax
16,500 0.993
14,500 1.000
13,500 1.022
Base case
Original case
Optimal case
Extreme case
PMs CMs
2 4
2 4
1 4
1 4
Total
6
6
5
5
B. Lhorente et al. / Reliability Engineering and System Safety 84 (2004) 209–218 Table 12 Expected maintenance per year
PMs CMs Total
AP
Base case
Original case
Optimal case
Extreme case
25 70 95
21 69 90
12 66 78
10 63 73
The expected amount of total maintenance per year can be expressed as: s ¼ sp þ sf
ð11Þ
where; sp ¼
n·u·AP tul
sf ¼
n·u·AF tul
ð12Þ
In the case of KC, there are 78 armatures and the average operating hours per year are 6,100. Applying the above equations results in Table 12. The total amount of maintenance per year decreases with increasing Tp . This holds for CMs and PMs. The base case with Tp ¼ 9; 000 h is the worst scenario in terms of amount of maintenance per year and the extreme case with Tp ¼ 17; 000 h the best. Using the same methodology and incorporating the fact that it takes approximately 12 h to change-out an armature in case of a PM or CM, Table 13 represents the impact of each of the four scenarios on fleet availability. The total downtime in terms of unavailability is worst for the base case with a total unavailability due to armature maintenance of 13.0%. The original case improves 0.7% with respect to the base case, the optimal case 2.3% and the extreme case 3.0%. Although in terms amount of maintenance and availability the extreme case has the best results, in terms of costs this is not the case. The annual savings with respect to the base case for the three cases are:
Table 13 Impact on fleet availability
Unavailability Difference w.r.t. base case
† Original case: US$ 5,800 † Optimal case: US$ 163,900 † Extreme case: US$ 153,400 This means that changing the actual PM interval to the interval of any of the three alternative cases results in annual savings between US$ 5,800 to 163,900. Within the three alternatives the optimal case is best.
Expected amount of PMs during useful life of an armature. Expected amount of CMs during useful life of an armature.
AF
217
Base case (%)
Original case (%)
Optimal case (%)
Extreme case (%)
13.0 0.0
12.3 0.7
10.7 2.3
10.0 3.0
9. Conclusions and recommendations New armatures experience infant mortality. On the contrary, once maintained the armature’s p.d.f. changes dramatically, showing random failure behavior with short expected life between successive maintenance actions. The position of the armature on the truck (left or right hand side) does not significantly influence its failure characteristics. The dominant failure mode is flashovers, which occur more frequently during first quarters. This increase in failure frequency is believed due to the particular climatic situation during those months. The optimal PM interval Tpp is equal to 14,500 h. This optimum moves between 13,500 and 16,750 h when varying the shape parameter b within its 95% confidence interval. At the same time, Tpp moves between 14,500 and 17,000 h when changing the cost of corrective maintenance Cf between its extreme values. Three feasible maintenance policies can be recommended: † The first one is maintaining the armature preventively every 14,500 h. This is the best policy in terms of costs and is the optimal solution to the maintenance problem. Total savings with respect to the actual replacement policy are US$ 163,000 annually and, in terms of fleet availability, 2.33%. † The second one is maintaining the armature every 17,000 h. Taking into consideration that no armature so far has lasted more than 17,000 h, this policy is equivalent to a run to failure (on-condition) policy. The savings with respect to the actual policy are US$ 153,400 annually. This is US$ 10,600 less than would have been saved by implementing the optimal policy. However, the run to failure policy results in higher fleet availability. The savings in terms of availability with respect to the actual policy are 3.0, 0.7% more than the optimal case. † The third alternative would be to implement a run-tofailure policy for new armatures and a PM interval for armatures of group 2 and 3. This, however, is more complex to administrate from a practical point of view.
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Acknowledgements The authors would like to thank the contributions and support of Enrique Affeld, Operations Manager of Komatsu Chile.
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