ELEVLI et al: MAINTAINABILITY ANALYSIS OF MECHANICAL SYSTEMS OF ELECTRIC CABLE SHOVELS 267Journal of Scientific & Industrial Research

Vol. 67, April 2008, pp. 267-271

*Author for correspondence

Tel: +90 274 2652031/4207; Fax: +90 274 2652066

E-mail: selevli@dumlupinar.edu.tr

Maintainability analysis of mechanical systems of electric cable shovels

Sermin Elevli1*, Nevin Uzgoren2 and Mehmet Taksuk3

1Industrial Engineering Department, 2Department of Business Administration,

Dumlupinar University, DPU, Tavsanli Yolu 10. km, Kutahya, Turkey3Garp Linyitleri 0_letmesi Müdürlüü, 43300, Tavsanli-Kütahya, Turkey

Received 14 July 2006; revised 10 January 2008; accepted 15 January 2008

Present study determines maintainability of mechanical systems of electric cable shovels utilized in Garp Linyitleri

Isletmesi (GLI). Independent and identically distributed data are identified using tests for trends and serial correlation in order

to represent the repair time data probabilistically. Three probability distributions are tried as possible candidates to fit Time To

Repair (TTR) data. Finally, maintainability for different time periods and Mean Time To Repair (MTTR) values of shovels

have been estimated on the basis of fitted distribution models.

Keywords: Downtime/ Repair distributions, Maintainability, Mean time to repair (MTTR), Shovel

Introduction

Maintainability analysis is used to find best

possibilities of cost reduction by measuring effectiveness

and weakness of maintenance operation on mining

equipments. Reports1-8 are available on the maintenance

data analysis of mining equipments. In these studies,

except some reports1,3,8, more attention has been given

to Time between Successive Failures (TBFs) data than

Time to Repair (TTR) data. Kumar & Klefsjo2 and

Barabady7 used Power Law Process Model, which

assumes TBFs as a function of time. In other studies,

graphical and analytical techniques have been used to

fit data set using probability distributions. Best-fit

probability distribution model then used to predict failure

behavior of equipment and to calculate reliability.

Maintainability Analysis: A Tool for Availability Improvement

Maintainability is the probability that equipment

can be repaired and returned to an operational state in a

given time when each level of maintenance is performed

by skilled personnel using prescribed procedures and

resources. As per the Rule of Thumb, a greater

operational availability is achieved by either decreasing

downtime or increasing uptime. The rule requires

statistical study of failure and repair data in order to

compute reliability and maintainability characteristics

of the system. However, in some cases, the problem of

analyzing data is due to the lack of information

concerning the time between failures. In these

conditions, maintainability calculation is the only way

to draw concrete conclusions about the status of system.

In practice, availability of systems is never perfect due

to occurrence of failures. It always takes finite amount

of time (downtime) to make system operational. It is the

length of time during which equipment is not

operational9.

Mean Time to Repair (MTTR), a measure of

maintainability, is the mean time required to perform

repair work assuming that spare parts and skilled

personnel are available10. Some important factors for

maintainability are11: i) Design and use of equipment

should be such that failure is immediately noticed and

quickly localized; ii) Vulnerable components should be

easily accessible; iii) maintenance personnel should be

competent, well trained and have necessary tools and

test equipment; and iv) Adequate spare parts should be

accessible.

TTR for specific equipment is a random variable

due to the influence of different factors on downtime.

Distributions that describe TTR are called repair

distributions (downtime distributions). Let T be repair

time random variable, then maintainability function M(t)

is as12,13

268 J SCI IND RES VOL 67 APRIL 2008

( )t

0

M(t)=P(T t)= f t dt≤ ⋅∫ ...(1)

This study presents maintainability analysis to

reduce maintenance and operation cost of electric cable

shovels.

Experimental Details

Data of seven electric cable shovels (S10, S12,

S14, S16, S17, S18 & S19) for a period of 12 months

was obtained from a coal company, Garp Linyitleri

Isletmesi (GLI), Kutahya, Turkiye. Operation and

maintenance cards for cable shovels of GLI were

gathered for one-year period. Statistical assessment of

data (Table 1) indicates that S17 (lowest average repair

time, 3.93; range, 16.10; and standard deviation, 3.75)

is significantly better than others. On contrary, in spite

of having highest average repair time, standard

deviation of S10 is lower than that of S12, S14 and

S16. So, it is not possible to rank shovels according to

their condition by using summary statistics. However,

S10, S14 and S16 with high average repair times were

taken into consideration.

Results and DiscussionPresence of Trends and Serial Correlation

Independent and identically distributed (iid) TTR

data should be firstly verified before the application of

repair/downtime distributions13. The iid data are free

from trends and serial correlation. Without considering

this factor before applying standard probabilistic and

statistical methods, the validity of any result is

questionable14. If the data are not iid, a nonstationary

model such as the Nonhomogeneous Poisson Process

should be used to describe the data.

Cumulative TTR has been plotted against

cumulative number of repairs/failures for each shovel. A

linear plot of graph of cable shovel S17 indicates that

there is no observable trend in the data (Fig. 1). Therefore,

local trends in Fig. 1 can be considered insignificant. A

test for serial correlation is performed by means of

plotting the (i-1)th TTR against ith TTR. If TTR’s are

independent, then points should be scattered randomly

on the diagram and no regular pattern should be noticed.

As no distinct serial correlation was observed for the data

on serial correlation test for cable shovel S17 (Fig. 2),

the data is free of correlations. The iid assumption has

been examined analytically by using unit root test

(Table 2) and serial correlation test (Table 3). As no trend

and serial correlations were identified for all shovels, the

iid assumption is verified. Thus, the data can be fitted to

downtime distributions in order to find out best estimate

of the maintainability function.

0

10

20

30

40

50

60

0 20 40 60 80 100 120 140 160 180 200 220Cum. TTR

Cum.

Repa

ir No

Table 1—Summary statistics of repair data

Shovel Repair/failure Max. repair Min. repair Range Total repair Average repair Standard

number time, h time, h h time, h time, h deviation, h

S10 39 53.20 0.15 53.05 297 7.62 10.82

S12 80 73.30 0.15 73.15 457.75 5.72 12.85

S14 59 115.45 0.15 115.30 433.20 7.34 17.79

S16 22 51.40 0.30 51.10 152.65 6.94 12.47

S17 54 16.30 0.20 16.10 212.00 3.93 3.75

S18 62 44.20 0.15 44.05 273.95 4.42 8.68

S19 29 26.05 0.30 25.75 119.50 4.12 5.60

Fig. 1— Trend test for TTR data (S17)

ELEVLI et al: MAINTAINABILITY ANALYSIS OF MECHANICAL SYSTEMS OF ELECTRIC CABLE SHOVELS 269

Determining Best- Fit Theoretical Probability Distributions

Once the data are identified to be free of

correlations and trends, the time- independent

distribution model gives the best estimate of

maintainability function. In this study, the choice of

distribution has been carried out by means of STAT-

GRAPHICS statistical software package to fit theoretical

probability distributions and to determine their

parameters. The Kolmogorov-Smirnov (K-S)

nonparametric test has been applied to find the best fit

distribution models for the data set. Results of each

model (Table 4) under K-S test indicate maximum

deviation between cumulative distribution of the data

and the theoretical probability distribution of the model

for each shovel5. Significance level (α, 5%) has been

assumed to determine a maximum acceptable limit of

this deviation.

Approximate significance levels have been also

given with DN values (Table 4). DN values marked by

asterisk have not been accepted at 5% significance level.

Lognormal distribution1 with lowest DN value provides

0

4

8

12

16

20

0 2 4 6 8 10 12 14 16 18TTR (i)

TTR (

i-1)

Table 2— Unit root test results ( 0 1i i tTTR TTRβ δ ε−∆ = + + )

Shovel 0β δ τ (Dickey-Fuller MacKinnon Decision*

test statistics) critical values

(%1)

S10 6.82 -0.87 -5.30 -3.62 No trend

S12 6.16 -1.08 -8.51 -3.52 No trend

S14 6.76 -1.03 -9.07 -3.52 No trend

S16 8.48 -1.17 -5.21 -3.79 No trend

S17 3.98 -1.01 -7.20 -3.56 No trend

S18 4.49 -1.03 -7.91 -3.54 No trend

S19 3.93 -1.14 -9.08 -3.69 No trend

*Reject null hypothesis that trend exist, if τ f MacKinnon Critical Value

Table 3—Serial correlation results of TTR data

Shovel* Pearson correlation Sig. (2-tailed)

(lag-1)

S10 0.130 0.435

S12 -0.068 0.554

S14 -0.033 0.776

S16 -0.173 0.454

S17 -0.10 0.945

S18 -0.029 0.824

S19 -0.220 0.261

*No correlation foundFig. 2—Test for serial correlation for TTR data (S17)

the best fit for TTR data except for S17 (Table 4). K-S

test results of S17 indicate that best fitted distribution is

weibull distribution. DN values of S17 for lognormal

and weibull distributions are very close to each other.

MTTR and M(t) Calculations

Once the data has been fitted to a probability

distribution, MTTR and M(t) of each shovel can be

calculated using the fitted distribution (Table 5). To

evaluate MTTR values, a Pareto Diagram has been

drawn (Fig. 3). S10 has been found with the highest

MTTR value and it is almost 25% of the total of all

MTTR values (Fig. 3). Thus, S10 is significantly worse

than others in terms of maintainability. S10 is followed

by S16 and S14. MTTR values of S17 and S18 are very

close to each other and in best condition in comparison

with others.

M(t) values of S18 with lowest MTTR is higher

than others for each time until t=9 h (Table 6). As

permissible time to repair increases, M(t) values of

shovels get closer. S10 with highest MTTR takes lowest

270 J SCI IND RES VOL 67 APRIL 2008

Table 4—Determining of best- fit theoretical distribution for TTR data

Shovel Exponential Lognormal Weibull Best Fit

Est. K-S Test Est. K-S Test Est. K-S Test Distribution

Parameter Parameter Parameter

S10 λ=0.131 DN=0.3138*X =0.913 DN=0.1365 α=5.660 DN=0.1554 Lognormal

(0.001) s=1.656 (0.461) β =0.667 (0.303)

S12 λ=0.175 DN=0.2742*X =0.702 DN=0.0863 α=4.030 DN=0.1525* Lognormal

(0.000) s=1.331 (0.590) β =0.687 (0.048)

S14 λ=0.142 DN=0.3745*X =0.859 DN=0.1369 α=4.552 DN=0.2038* Lognormal

(0.000) s=1.356 (0.219) β =0.657 (0.015)

S16 λ=0.138 DN=0.3370*X =0.862 DN=0.1784 α=5.352 DN=0.1848 Lognormal

(0.017) s=1.437 (0.516) β =0.693 (0.470)

S17 λ=0.255 DN=0.1138 X =0.882 DN=0.0982 α=4.048 DN=0.0872 Weibull

(0.487) s=1.090 (0.675) β =1.079 (0.806)

S18 λ=0.226 DN=0.3091*X =0.410 DN=0.1020 α=3.102 DN=0.1545 Lognormal

(0.000) s=1.380 (0.540) β =0.675 (0.103)

S19 λ=0.243 DN=0.2467 X =0.682 DN=0.1490 α=3.694 DN=0.1756 Lognormal

(0.0587) s=1.248 (0.540) β =0.835 (0.333)

*Not suitable distribution (Reject null hypothesis if DN> 0.051.36DN =

n)

Table 5—MTTR results of shovels

Shovel Best fit theoretical MTTR Standard

distribution h deviation, h

S10 Lognormal 9.81 37.38

S12 Lognormal 4.89 10.81

S14 Lognormal 5.44 11.96

S16 Lognormal 6.91 16.93

S17 Weibull 3.94 0.02

S18 Lognormal 3.90 9.33

S19 Lognormal 4.31 8.34

Table 6—M(t) values of shovels

Shovel Permissible time (t), h

1 2 3 4 5 6 7 8 9 10

S10 0.29 0.45 0.54 0.61 0.66 0.70 0.73 0.76 0.78 0.80

S12 0.30 0.50 0.62 0.70 0.75 0.79 0.82 0.85 0.87 0.89

S14 0.26 0.45 0.57 0.65 0.71 0.75 0.79 0.82 0.84 0.86

S16 0.27 0.45 0.57 0.64 0.70 0.74 0.77 0.80 0.82 0.84

S17 0.20 0.37 0.52 0.63 0.72 0.78 0.84 0.88 0.91 0.93

S18 0.38 0.58 0.69 0.76 0.81 0.84 0.87 0.89 0.90 0.91

S19 0.29 0.50 0.63 0.71 0.77 0.81 0.84 0.87 0.89 0.90

S18S17S19S12S14S16S10

10

9

8

7

6

5

4

3

2

1

0

25

20

15

10

5

0

Pe

rce

nt, %M

TT

R, h

Shovel number

Fig. 3—Pareto diagram of MTTR values of shovels

ELEVLI et al: MAINTAINABILITY ANALYSIS OF MECHANICAL SYSTEMS OF ELECTRIC CABLE SHOVELS 271

M(t) value for each time length after 4th h.

Maintainability of S17 increases faster than that of others

as permissible time to repair increases (Fig. 4).

Conclusions

Application of statistical based maintainability

analysis provided further insight for maintenance

characteristics of each shovel. Cable shovels S10 and

S16 require special attention. It is suggested that the

implementation of preventive maintenance policy should

be reviewed, adequate stock level of critical spare parts

should be maintained, and the maintenance crew should

be trained regularly in order to increase maintainability

of shovels. Besides, it would be useful a replacement

analysis especially for S10.

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Fig. 4—M(t) values of S10, S18 and S17

for different times

M, t

0.200.300.400.500.600.700.800.901.00

1 2 3 4 5 6 7 8 9 10t

S10S18S17

1.00

0.90

0.80

0.70

0.60

0.50

0.40

0.30

0.20