prediction of repair & maintenance costs of diesel engine

International Journal of Recent advances in Mechanical Engineering (IJMECH) Vol.3, No.1, February 2014

63

PREDICTION OF REPAIR & MAINTENANCE

COSTS OF DIESEL ENGINE

D.R.Dolas1, M.D. Jaybhaye

2 , Sudhir. D. Deshmukh

3

1, 3

Department of Mechanical Engineering, MGM’s Jawaharlal Nehru Engineering

College, Aurangabad, Maharashtra – 431003, India. 2 Department of Production Engineering, College of Engineering Pune, Pune,

Maharashtra - 411005, India.

ABSTRACT

Diesel engine is widely use for different applications, the failure frequency of diesel engine is more

increase to increase the age & use of engine in order to take decision to replacement of engine on the basis

of Repair & Maintenance cost (R&M) & predication of future Repair & Maintenance costs of diesel engine

used in Borewell compressor. Present case study discusses prediction of accumulated R&M costs (Y) of

Diesel engine against usage in hours (X). Recorded data from the company service station is used to

determine regression models for predicting total R&M costs based on total usage hours. The statistical

results of the study indicates that in order to predict total R&M costs is more useful for replacement

decisions than annual charge.

KEYWORDS

Diesel Engine, R & M Cost, Maintenance, Regression Model, Age replacement model.

1. INTRODUCTION

Diesel engine is one of the most important power sources in different applications. Effect of

diesel engine power on Borewell compressor is considerable. The use of Borewell compressor for

making tube wells during latter decades resulted in rapid growth of farm & requirement drinking

water.

Costs of owning and operating including the preventive & corrective maintenance cost of diesel

engine is very important for deciding the appropriate time to replace the diesel engine on basis of

repair & maintenance cost. The new engine failure are occurring rarely therefore less

maintenance cost, but age increase the maintenance cost is increase.

G.M. Khoub et al. [1] presented the repair & maintenance cost model on the basis of mean

working hours & mean accumulated cost of MF285 tractor. To predicate repair & maintenance

cost the power model most suitable. Development of model for predication Repair & maintenance

cost for two wheel drive tractor & suggested strongly the polynomial model by Ranjba et al. [2].

Khodabakhshian R. & Shakeri M carried out the statistical analysis of different farm tractors on

the basis of repair & maintenance cost & total working hour using Preventive Maintenance [3].

Donca Gh. [4] mean accumulated maintenance cost of U683dt tractor analysis using different

model & recommended power model best model for predication the maintenance cost. The study

was conducted by Shahram et.al. [5] For JD-4955 tractors showed that the polynomial regression

model strongly recommended in order to predict accumulated R&M costs. R. Ahmad [6]

proposed a maintenance management decision model for preventive maintenance application &

determines the revised PM interval for machine. Fereydoun proposed model provides for the


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Prediction of repair and maintenance costs of Massey Ferguson 285 (MF-650) tractors &

suggested polynomial regression model [7]. Artificial neural network technique is used for

predication of repair & maintenance cost & recommended this is best tool. [8]. Isaac & et al. [9]

presented the cubic polynomial least square regression cost prediction. Sebo et al. [10] determine

optimum replacement model for replacement machine using least squares method. Y. H. Chien &

J. A. Chen [11] uses of age replacement model determine the average cost per unit time. K. Yao

& D. A. Ralescu [12] provide the age replacement policy involving random age has been

proposed & assumed the age of the unit is an uncertain. Shey Huei Sheu1 & Chin-Chih Chang

[13] using the age replacement models determine optimal age for preventive replacement cost can

be minimized.

The aim of this study is to provide a statistical analysis for the repair and maintenance costs of

diesel engine of application for Borewell compressor in order to present an appropriate

mathematical model implementation of appropriate models for the repair and maintenance costs

of diesel engine provide planner and policy makers and also owner an opportunity to evaluate

performance of diesel engine economic.

2. DATA COLLECTION

This study is carried out at authorized service station. Failure & maintenance cost data is

collected & sorted from forty same make & model diesel engine. Corrective & preventive

maintenance cost estimated using age replacement model.

3. DETERMINATION OF COST PER HOUR USING AGE

REPLACEMENT MODEL

To determine the repair & maintenance cost per hour using Age replacement model

C�T� = CfF�t� + CpR�t� ��

− − − −�1�

Age replacement model is more useful in practical application for the determine of Repair &

maintenance cost (preventive & corrective ) & estimate maintenance cost per hour. To determine

the cost function C (T). Using Weibull distribution model [6] is shown in equation. (2)

C�T� = Cf�1– ��

+ Cp��

��

��

− − − − −−− �2�

Where:

Cf - Failure cost Cp - Preventive replacement cost Cs – cost of spare parts

F (t) = Cumulative distribution function R (t) = Reliability function

F�T� = 1 − ��

�

R�T� = e�� η�β

F�T� + R�T� = 1

η – Scale parameters (characteristic life), β- Shape parameters (variation of the failure rate)

Failure cost & preventive replacement costs can be determine using following equations

C! = C" + C# & Cp = C$ + C# Where:

Cf - Failure cost Cp - Preventive replacement cost

Cr - Cost of replacement system & components

Cd - Cost of down time Ci - Cost preventive servicing

Cost of down time = one hour cost = 90 (ft) × 60 (Rs) = 5400× Failure / hour


65

Estimation of reliability of diesel engine using Weibull distribution using failure data &

maintenance cost per hour.

The system probability of failure function = F�T� = 1 − ��

�

− −− − − �3�

The system reliability function = R�T� = e�� η�β

− − − −− −�4�

F�T� + R�T� = 1 − − −− − �5� t = 3000 hours, β = 2.198 & η = 1929.46

F(t) =1 -�� ()(*+,(,..)�

(.+,* = 1 -��/.012��(.+,* = 1 -��/.34= 1- 0.14= 0.86

R(t) = 1-F(t) = 1-0.86 = 0.14

Table 1. Estimation of average cost per hour


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4. PREDICATION MODEL DEVELOPMENT:

To estimate the appropriate repair & maintenance cost model for diesel engine using different

regression models, as per different researchers presented & suggested the regression model for

farm tractors are [2], [3], [4].

Y = a + bx Linear

Y = a + bx + cx2 Polynomial

Y = a + lnbx Logarithmic

Y = ae<= Exponential

Y = ax< Power

Fig. 1 Regression models of maintenance cost of diesel engine


67

Development of appropriate mathematical model for predicting repair and maintenance

costs for diesel engine, using repair & maintenance cost of forty diesel engines Table 1.

The presented data in this Table 1 is used to analysis and determine the predicated repair

and maintenance cost per hour as shown in Table 2.

Table.2 Repair & Maintenance Cost per Hour

Fig. 2 Maintenance cost Predication Regressions model of diesel engine

y = 0.004x + 71.78

R² = 0.635

y = 61.81e4E-05x

R² = 0.472

y = 32.15ln(x) - 145.4

R² = 0.678

y = -1E-07x2 + 0.008x + 61.88

R² = 0.676

y = 5.551x0.348

R² = 0.693

-100

0

100

200

300

400

0 10000 20000 30000 40000 50000

Co

st/

Ho

urs

Time

C(T)Linear

(C(T))

Expon

.

(C(T))Log.

(C(T))

Poly.

(C(T))

Power

(C(T))


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Table.3 Regression models

Regression Models R

2

Linear Y = a + bx 0.635

Polynomial Y = a + bx + cx2 0.676

Exponential Y = ae<= 0.472

Logarithmic Y = a + lnbx 0.678

Power Y = ax< 0.693

5. RESULT & DISCUSSION

Table 3 presents regression models for predication the repair and maintenance cost per hour of

diesel engines. The Power model correlation coefficient is highest value(0.693) compared to

other models. Therefore recommended that the Power model best model for Borewell compressor

diesel engine

In the most of researchers published studies in this field of Farm equipment, machinery & tractors

suggested the Power model gave better cost prediction with higher confidence and less variation

than that of Exponential and logarithmic models. Because of, easiness in calculations, the small

difference between the correlation coefficients of Polynomial and Power models and using of

Power model by other researchers, As per Table3 other models are less significant.

6. CONCLUSION

The Repair & Maintenance costs prediction of Borewell compressor diesel engine & deciding the

time to replacement. The repair coefficients values are generally dependent on factors such as

research method performance and time spans, number and type of samples. Results of this study

indicated that the Repair & Maintenance costs per hour increased with engine age. This resulted

in a marginally increased total repair cost curve. These results also confirmed that there are

considerable variations in Repair & Maintenance costs among engine models as well as

individual ones. For circumstances similar to this study, estimates suggest that annual R&M costs

increase with age of engine. This method is more useful for replacement decisions than annual

charge.

ACKNOWLEDGEMENT

The authors are deeply grateful for help and guidance rendered by General Manager Mr. Yuvraj

Lavhale and employees of Trinity Mahalasa Durga sales & services, Aurangabad during field

studies.


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REFERENCES

[1] G.M. Khoub bakht, H. Ahmadi, A. Akram and M. Karimi,( 2008) “Repair and Maintenance Cost

Models for MF285 Tractor: A Case Study in Central Region of Iran,” American-Eurasian J. Agric. &

Environ. Sci., 4 (1): pp 76-80,

[2] Iraj Ranjba , Majid rashidi, Borzoo Gharee I Khabba,( 2010), “Prediction of repair and maintenance

costs of two-wheel Drive tractors in iran,” XVII th World Congress of the International Commission

of Agricultural and Biosystems Engineering (CIGR) pp 1-10

[3] Khodabakhshian R.& Shakeri M.,( 2011), “ Prediction of repair and maintenance costs of farm

tractors by using of preventive maintenance ,” International Journal of Agriculture Sciences, Vol. 3,

Issue 1, pp-39-44

[4] Donca Gh.,( 2011 )“Maintenance cost model for U683DT Tractor, “ Analele Universita Nii din

Oradea , Fascicula: Ecotoxicologie, Zootehnie i Tehnologii de Industrie Alimentara, pp 131-136

[5] Shahram Mohseni Niari, Raj Ranjbar and Majid Rashidi, (2012), “Prediction of Repair and

Maintenance Costs of John Deere 4955 Tractors in Ardabil Province, Iran,” World Applied Sciences

Journal 19 (10): 1412-1416

[6] R. Ahmad, S. Kamaruddin, I. Azid , I. Almanar ,( 2011), “Maintenance management decision model

for preventive maintenance strategy on production equipment,” J. Ind. Eng. Int., 7(13), pp 22-34

[7] Fereydoun Keshavarzpour, (2011), “Prediction of Repair and Maintenance Costs of Massey Ferguson

285 Tractors,” Agricultural Engineering Research Journal 1 (3), pp 63-67,

[8] Abbas Rohani, Mohammad Hossein Abbaspour-Fard , Shamsolla Abdolahpour, (2011), “Prediction

of tractor repair and maintenance costs using Artificial Neural Network,” Expert Systems with

Applications(Elsevier Ltd ) vol 38 pp 8999–9007

[9] Isaac, O. Ajao ,Adedeji, A. Abdullahi &Ismail, I. Raji,(2012) “Polynomial Regression Model of

Making Cost Prediction In Mixed Cost Analysis,” Mathematical Theory and Modeling Vol.2, No.2,

pp 14-23

[10] J. Sebo, J. Busa, P. Demec, J. Svetlík, (2013), “Optimal replacement time estimation for Machines

and equipment based on cost function,” METALURGIJA 52, 1, pp 119-122

[11] Y. H. Chien & J. A. Chen , (2007), “Optimal Age-Replacement Model with Minimal Repair Based

on Cumulative Repair Cost Limit and Random Lead Time,” Proceedings IEEE IEEM, pp 637-639

[12] K. Yao & D. A. Ralescu, (2013), “Age replacement policy in uncertain Environment,” Iranian Journal

of Fuzzy Systems Vol. 10, No. 2, pp. 29-39

[13] Shey Huei Sheu1 & Chin-Chih Chang,(2008), “ Optimal age-replacement model with minimal repair

based on a cumulative damage limit policy,” International Journal of Pure and Applied Mathematics,

Volume 48 No. 4, pp 569-584

Authors

Shri. Dolas Dhananjay R , BE (Mech) & ME- Mechanical (Design Engineering) working

as a Associate Professor in Mechanical engineering at MGM’S Jawaharlal Nehru College

of Engineering , Aurangabad . He has 6 publications in National/International conferences

& Journals & Pursuing PhD

Dr.Maheshwar D Jaybhaye, Ph.D (Mech.Prod.Engg.) Working as AssociateProfessoer,

Production Engineering Department at College of Engineering, Pune. He has 16

publications in National/International conferences & Journals. He is life member of ISTE,

Tribology Society India, Operation Research Society of India & Associate Member of

Associate Member Institution of Engineers (India). He is recipient of K.F.Antia memorial

Award (Gold Medal) from Institution of Engineers (India).

Dr. Sudhir D Deshmukh , Ph.D (Mechanical Engg.) working as Principal MGM’s

Jawaharlal Nehru College of Engineering, College, Aurangabad. He has more than 25

publications in his credit in National/International conferences &Journals. He is life member

of ISTE and Fellow Member of Institution of Engineers (India), Fellow of Institution of

Production Engineers, Chartered Engineer & Chairman, Quality Circle Forum of India

(QCFI), Aurangabad.

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