reliability and maintainability analysis of transport

RELIABILITY AND MAINTAINABILITY ANALYSIS OF TRANSPORT

BUSES IN EDUCATIONAL INSTITUTE

Gururaj K. Inamdar1 & Ajinkya P. Gaikwad2

1Assistant Professor, Dept. of Mechanical Engg.,

SVERI College of Engineering, Pandharpur, Maharashtra, India.

[email protected]

2M.D. APG Enterprises, Ankoli, Maharashtra, India.

[email protected]

Abstract

The transportation system plays an important role in a day to day life, either it will be a

private, public or own transportation system, to analyze the probability of failures occurs in

transportation system and prevent it we have to analyze the reliability, availability and

maintainability analysis (RAM) of the bus, it has great influence on cost, time, service,

comfort, quality and quantity. The buses which are used in educational Institute for

transportation are important part of the education system, it is desired to analyses the RAM of

the educational transport buses. To increase the availability and maintainability and reliability

of the buses. For the study and analysis of RAM of an Educational Institute transport buses,

the literature review has been carried out and is followed by failure field data collection and

RAM analysis using MINITAB software package. Failure field data of 2 years were collected

and analyzed using QC tools like Pareto Chart and Histogram Charts. The de descriptive

statistics of the data analyzed, and to choose the type of distribution used for analysis of

Reliability and Maintainability of buses, goodness-of-fit test – Anderson–Darling statistics is

applied. Then, hazard rate of models is estimated and results are presented. It was found that

1) the availability of the bus for transportation is 95.25% and went down to 85.22%. 2) the

prevailing three failure modes have the 78.51% of all the failures of the bus, 3) the average of

the failure is every 16.71 operation hrs. and the mean time to repair (MTTR) is 0.82 hours.

Keywords: Reliability, Maintainability, Transport buses, MTTR.

1. Introduction

The transportation system plays an important role in a day to day life, either it will be

a private, public or own transportation system, to analyze the probability of failures occurs in

transportation system and prevent it we have to analyze the reliability, availability and

maintainability analysis (RAM) of the bus, it has great influence on cost, time, service,

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comfort, quality and quantity. In literature, various studies deal with RAM of the

manufacturing industries, food industries, process industries are available. But, there is

scarcity of the RAM analysis in Educational transportation i.e. service sector. This work is

about on study of RAM of an educational transport buses. State the objectives of the work

and provide an adequate background, avoiding a detailed literature survey or a summary of

the results.

1.1 Area of study

We have chosen Sinhgad Institutes Pandharpur for study of RAM of educational

transport buses. Which is located in Pandharpur village of Solapur district, India. A problem

of education transport buses is identified. The Sinhgad Institute Korti, Campus has 30 buses

for transportation of students from their home to College and vice-versa. In this institute near

about 3000 students are taking education from pre-primary to M.E. Institute provide bus

facilities to more than 30 villages students. The cost of transportation in the rural area is not

beneficial for the institute because of the maintenance of the buses as well as the performance

of the buses. So for that purpose we are going to study the whole transportation system

1.2 Description of Educational Transport Bus

The transport is the main in our daily life for any purpose, one of them is educational

transportation for student transportation from home or a predefined station to school or

college and vice-versa via bus. The bus consists of no of parts and different systems like

suspension system, braking system, engine system, Electrical system, steering system,

transmission system etc. Each of them is dependent on each other except lighting system

which affect for specified period of time. The bus follows common control transmission

system i.e. Transmission of power from engine to rear wheel via transmission system

controlled by electrical system, which is controlled by driver. Belo fig shows a different

systems and parts of the Bus.

1.3 Different Parts and System of Bus:

1.3.1 Chassis

A chassis consists of an internal vehicle frame that supports an artificial object in its

construction and use, can also provide protection for some internal parts. An example of a

chassis is the underpart of a motor vehicle, consisting of the frame (on which the body is

mounted). If the running gear such as wheels and transmission, and sometimes even the

driver's seat, are included, then the assembly is described as a rolling chassis.

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1.3.2 Engine: An engine or motor is a machine designed to convert one form of energy into

mechanical energy. Heat engines burn a fuel to create heat which is then used

1.3.3 Transmission system: The mechanism that transmits the power developed by the engine

of automobile to the engine to the driving wheels is called the. Transmission System

1.3.4 Suspension system: The mechanism which absorbs the shocks and vibration coming on

the bus called as suspension system or it is the system of tires, tire air, springs shock

absorbers linkages that connects a vehicle to its wheels and allows relative motion between

the two.

1.3.5 Steering system: It is a collection of components, linkages, etc. which allows any

vehicle to follow the desired course or direction.

1.4 Detail Working of Transport Bus

The main parts and systems are show in above figures. So the working of each bus is same

which is as follows:

The Engine system generates the power using chemical power obtained from fuels

like Diesel, which is in the form of rotational energy is transmitted to the wheels of bus using

transmission system, which consist of different parts like clutch, flywheel, Propeller,

Universal joint, differential etc. The braking system is used to have control on the bus i.e.

while stopping the bus. Suspension system is more important for the bus to have a comfort as

well as the smooth working of other systems of the bus. There are 15 buses in the institute

which are used to transportation of students. This buses are work in two shift for a day. Each

shift is of 4 hr. so the total working hours a bus is 8 hours per day.

1.5 Failure field data The buses are operating in two shifts per day, one shift is of 4 hours and 5 days per week. So

the effective work of bus is of 8 hours per day, so within the frame of this study we assume

system depended failure in it. Which means that the bus may only fails when it is running.

Failure and repair data of the bus of 25 months were collected. The maintenance policy

applied is corrective maintenance, when failure occur the external service center or

mechanical works for the repair and necessary corrective maintenance operation to repair the

failure. Corrective maintenance comprises action taken to the restore a failed component or

system to the operational state. Corrective maintenance actions are unscheduled actions

intended to restore the bus from a failed state into a working state. The bus driver is

responsible for the keeping hand written record for the failure per shift as well running of the

bus per shift in the individual bus register. The field data of 228 failure recorded of the bus

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for a period of 500 continuous working days was analyzed. Records include the failure that

had occurred per shift, the action taken to repair the failure, the down time and the time of

failure. Bus contains a maintenance record register at office and daily record book, this record

book has details of trip, meter reading, running time and maintenance details.

With reference of available data in the register we divided the failures in the 12 failure

modes which are shown in the Table 2. which Shows the failure modes and their impact on

the transportation 228 failures were counted for the entire transport system in 12 failure

modes. TTF of bus is defined as the time that elapse from the moment the bus goes up and

starts operation after a failure until the moment it goes down again and stops operation due to

new failure. TTR is defined as the time that elapse from the moment the system stops

functioning until the moment it starts operating again both TTF and TTR are measured in min

Table 1. Description of failures modes and their impact on the bus quality.

Failure Mode

Description Effect of failure

Fm.1 Fastener failure Noise, Vibration, Failure of other systems.

Fm.2 Defective suspension system Less comfort, more vibration.

Fm.3 Defect in engine system Stops the whole bus or reduction in efficiency.

Fm.4 Defect in steering system Less effective turning cause accidental condition.

Fm.5 Defect in tires Stops the bus, Reduced efficiency.

Fm.6 Defect in body Cause noise and vibration.

Fm.7 Defect in frame Frame may brake

Fm.8 Defect in braking system Accidental condition occur due to no control on

Fm.9 Defect in electric system Loss of control on bus

Fm.10 Defect in engine cooling system Engine fails

Fm.11 Defect in transmission system Transportation system fails

Fm.12 Defect in sensor Loss of control on bus

Table 2. Literature Review

Author Research

Types

Tools & techniques Area of research

Remark

Saraswat & Yadava, (2008)

Review RAM Analysis -

literature is collected from major journals and conference proceedings, the period covered is from 1988 to 2005.

Tsarouhas , P. H., et al. (2009)

Empirical Histogram, Pareto,

Descriptive Statistics, Minitab.

Service Industries (Food)

The models presented by author are expected to be a useful tool to assess the current conditions, and to predict the reliability for upgrading the maintenance policies of the production line.

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Rajpal, et al. (2007),

Case study

CMRAM (composite measure comprising linear combination of reliability, availability, and maintainability)

Air Transportation ( Helicopter )

To capture the effect recent maintenance and other activities the Weibull Distribution is used to fit the failure data of overlapping intervals of operating time.

Bedewy (1989),

Empirical principles of

Reliability, availability and maintainability

Service industry (Public Transport Vehicle)

Compared three deign of vehicle using reliability and availability concepts.

Panagioti s, et al., (2009)

Case Study

Histogram, Pareto, Descriptive Statistics, Minitab

Service Industries (bread Production industry)

Author has Classified the primary failure modes in categories based on failure data of a Bread production line.

2. Literature Review

More research work has been done in the field of reliability, availability and

maintainability. The literature review of some papers is given below which gives more

information about their contribution in Reliability, availability and maintainability of

different production lines, public transportation system, machines, industries, etc.

3. Methodology

For the study and analysis of RAM of an Educational Institute transport buses, the

literature review has been carried out and is followed by failure field data collection and

RAM analysis using MINITAB software package. Failure field data of 2 years were collected

and analyzed using QC tools like Pareto Chart and Histogram Charts. The de descriptive

statistics of the data analyzed, and to choose the type of distribution used for analysis of

Reliability and Maintainability of buses, goodness-of-fit test – Anderson–Darling statistics is

applied. Then, hazard rate of models is estimated and results are presented.

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4. Results and Discussion

4.1 Pareto Analysis

It is a statistical technique in decision making used for selection of a limited number of

tasks that produce significant overall effect. The Pareto Analysis is done for bus. In Fig. 2 the

Pareto diagram for all failure modes occurring in an educational transport bus is displayed.

Fig. 2 Pareto diagram for the failure modes of bus in transportation.

Problem Formulation

1 . Area of study

2 .Description of bus

Failure field data collection

1 . Categorization of failure modes

2 . Collection of the TTF and TTR of buses from the maintenance register.

Result and Discussion

Determination of R and H rate models

Conclusion

Fig. 1 Flow chart of methodology

Mode of Failure

Pareto Analysis of Bus

Count Cum %

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The following observations were made. I. The failure mode 1(Fm.1) has the highest number

of failure 68.81%. II. Equally important failure mode 2(Fm.2) that has 6.8% of failure (III) the

first four failure modes in diagram stand for the 88.07% of all the failures of the transport bus.

In Fig. 3, the histograms of failure and repair data for TTF and TTR at line level were

shown. The histogram arises from grouping the failure and repair times into classes and

plotting the frequency of observation per class versus the interval time of each class. The TTF

displays a max frequency between 16 to 20 hrs., whereas the TTR shows peak at initial, and

then decreases.

Fig. 3 Histogram of TTF and TTR for Bus

4.2 Descriptive Statistics of the Failure and Repair Data:

The descriptive statistics of the basic feature of the failure and repair data for TTF and

TTR are presented in order to obtain qualitative and quantitative analysis of the failure data

for the educational institute bases. Thus, it is possible to extract the min and max vale of the

sample, mean, standard deviation (SD), Coefficient of variation, skewness and kurtosis of the

failure data at failure modes and the entire bus level. The standard deviation of the random

variable, is defined as the square root of the variance and is often used in place of the variance

to describe the distribution spread. Since the coefficient of variation of a random variable is

defined as the ratio of the standard deviation over the mean of the random variable, it is a

dimension less measure of the variability of the random variable.

Availability =

Where, MTTF = Total hours of operation / no failures.

And MTTR = Total Maintenance time / no of failures.

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Table 3. Descriptive statistics for TTF of all failure modes and entire transportation system

N Min Max Mean SD SV Skewness Kurtosis Sum

TTF Fm.1 150 10.4 22.9 16.72 3.44360 11.85840 -0.303938 -0.747586 2508

TTF Fm.2 15 11.3 20.18 16.72 2.24034 5.019157 -0.784622 1.2035310 250.9

TTF Fm.3 14 11.39 19.5 16.067 2.30740 5.324125 -0.734437 0.5290324 224.95

TTF Fm.4 4 15.6 22.85 19.002 3.67533 13.50809 0.109677 -5.1703216 76.01

TTF Fm.5 3 15.73 17.51 16.733 0.91139 0.830633 -1.049943 - 50.2

TTF Fm.6 6 12.99 19.51 16.666 2.40746 5.795866 -0.645093 -0.6251975 100

TTF Fm.7 1 23.9 23.9 23.9 - - - - 23.9

TTF Fm.8 13 11.95 19.82 16.72 2.23325 4.987433 -0.810631 0.58564201 217.36

TTF Fm.9 3 17.2 21.7 19.113 2.32433 5.402533 1.194201 57.34

TTF Fm.10 5 13.3 19.14 16.72 2.50480 6.27405 -0.684038 -1.8961112 83.6

TTF Fm.11 6 12.64 19 16.666 2.35663 5.553706 -0.968840 0.9743866 100

TTF Fm.12 8 10.55 20 16.75 3.74496 14.0248 -0.925477 -0.9379412 134

TTF System 228 10.4 23.9 16.781 3.17891 10.10552 -0.305429 -0.4403727 3826.16

Table 4. Descriptive statistics for TTR of all failure modes and entire transportation system

N Min Max Mean SD SV Kurtosis Skewness Availability

TTR Fm.1 150 0.1 0.8 0.5 0.21078 0.0444 -0.97934 -0.28326 97.06

TTR Fm.2 15 0.8 2.1 1.5 0.34226 0.1171 0.513476 -0.54268 91.61

TTR Fm.3 14 0.8 2.9 2 0.62634 0.39230 -0.09718 -0.64645 89.32

TTR Fm.4 4 1.2 1.9 1.5 0.31622 0.1 -1.7 0.632455 92.68

TTR Fm.5 3 2.7 3.4 3 0.36055 0.13 - 1.152069 84.80

TTR Fm.6 6 1.3 1.8 1.5 0.17888 0.032 0.585 0.943341 91.74

TTR Fm.7 1 2.5 2.5 2.5 - - - - 90.53

TTR Fm.8 3 0.4 0.6 0.5 0.1 0.01 - 0 97.10

TTR Fm.9 13 0.9 1.8 1.5 0.24152 0.05833 2.19116 -1.174366 92.72

TTR Fm.10 5 0.2 0.8 0.5 0.22360 0.05 0.2 5.552E-16 97.10

TTR Fm.11 6 0.9 1.8 1.5 0.32249 0.104 2.78476 -1.610066 91.74

TTR Fm.12 8 0.3 0.8 0.5 0.2 0.04 -1.72857 0.285714 97.10

TTR System 228 0.1 3.4 0.8267 0.62863 0.39518 1.956482 1.474435969 95.30

The descriptive Statistics of the bus were obtained by using excel software package,

which is putted in tabular form as shown in Table 3 and Table 4. The major observations were

made from the Table 3, following observations were made for bus system the mean TTF is

16.78 hrs., meaning that every 16.78 h a failure occurs in the bus, there for every Third day of

working we have a failure. Sample size is quite small of Fm. 7, so there is not enough data to

compute TTF. In case of TTR of Table 4: I) The mean TTR is 0.826 h means most of the

failures will repaired in 0.826 h. and II) The TTR of bus system is skewed.

4.3 Reliability and Maintainability analysis

The bus exhibits availability 95.28%. In the transportation time there is 30 min per

shift is allowed to the driver for leaving and coming in the bus by students. Thus there are two

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shifts per day × 30 min per day. This means that 60 min per day are spent for brake of driver

thereby causing finally an additional 10.67% gap in the transportation. Therefore, the actual

time available for transportation is 95.28%-10.67%=84.61%. It is well known that a bus can

transfer students effectively and within time when availability is up to 95% or above. The

transportation system is marginally positive.

To avoid inexact operation time of bus, the solid working time of bus may increase.

There are three ways to boost the solid working time of bus: 1) reduce the brake or time gap to

deliver and receive the students. 2) Reduce the frequency of the failures, 3) reduce the

duration of failure (Buzacott and Shanthikumar, 1993; Gershwin, 1994). The 1st approach is

very difficult to imply because it is necessary time required to student. The last two

approaches are determined by good operating practice. Both approaches, standing for

necessary steps towards development, were considered. The main objective is to reduce the

downtime by increasing the TTF and reducing the TTR. To identify the best distribution to

use for modeling the failure and repair data, and diversity of functions that describe that

distribution, we applied the goodnessof –fit test using software package MINITAB. It

provides goodness- of – fit test –Anderson – Darling for the maximum likelihood and least

square estimation methods.

Table 5. Anderson-Darling Statistics for TTF and TTR for All Failure Modes and Bus System Distribution Fm.1 Fm.2 Fm.3 Fm.4 Fm.5 Fm.6 Fm.7 Fm.8 Fm.9 Fm.10 Fm.11 Fm.12 System T T F

Weibull 3.26 1.01 0.97 2.92 3.46 2.02 - 3.52 1.13 2.417 2.082 1.93 2.812 Lognormal 5.254 1.22 1.18 2.89 3.49 2.11 - 3.46 1.39 2.479 2.195 2.118 6.756 Exponential 96.76 10.7 10.4 4.10 4.54 4.82 - 4.37 9.09 4.476 4.906 5.208 155.40 loglogistic 6.332 1.19 1.15 2.90 3.50 2.13 - 3.45 1.37 2.505 2.199 2.173 7.274 Smallest extreme value 4.126 1.02 0.99 2.92 3.45 2.00 - 3.54 1.11 2.401 2.066 1.875 3.985 Normal 3.506 1.09 1.04 2.88 3.49 2.06 - 3.46 1.24 2.457 2.139 2.038 3.74 logistic 4.46 1.07 1.02 2.89 3.49 2.08 - 3.46 1.23 2.483 2.143 2.096 4.233 T T R

Weibull 4.43 1.14 1.13 2.84 3.52 2.37 - 3.44 1.25 2.322 2.25 1.973 8.073 Lognormal 8.75 1.47 1.56 2.77 3.45 2.06 - 3.44 1.57 2.401 2.476 1.86 2.964 Exponential 48.9 8.43 6.38 4.01 4.38 4.93 - 4.22 8.75 3.218 4.594 3.535 16.243 loglogistic 9.34 1.44 1.54 2.77 3.45 2.04 - 3.44 1.53 2.407 2.483 1.91 2.97 Smallest extreme value 6.65 1.18 0.97 2.88 3.53 2.5 - 3.44 1.18 2.36 2.14 2.05 47.751 Normal 4.52 1.17 1.10 2.78 3.46 2.09 - 3.44 1.34 2.31 2.32 1.803 14.036 logistic 5.71 1.14 1.10 2.77 3.45 2.06 - 3.44 1.32 2.304 2.329 1.836 14.621

In Table 5 the Anderson – Darling statistics of the most common distributions for TTF

and TTR for all failure modes, and whole bus system were presented. A smaller statistic

indicates that the distribution fits the data better, some of the failure modes are follows normal

distribution and some weibull, Lognormal, Exponential, and etc. which is shown in tables, the

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bus system of bus also follows different distribution for different buses for TTF and TTR.

Here we are focused only on the distribution of the whole bus system failure data instead of

different failure modes, and the whole system is indicated in table by ‘system’. The

distribution which is good for system is lowest value in the table to analyze the data further.

The distribution followed by the failure filed data is webull distribution for TTF and

Lognormal for TTR. Some of the failure is not follow any distribution because there is no

sufficient data to calculate the Darling-Anderson statistics, for calculation of Darling-

Anderson statistics there should be more than two distinct values are required.

Fig. 3 Probability density functions, survival functions, probability plot, and hazard functions

from TTF and TTR

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The hazard rate functions at the entire bus systems for both TTF and TTR present a

pick for bus: (a) the TTF continuously increasing failure rate up to an average 30 hours (b)

The TTR initially has increasing repair rate up to 0.76 hours and then decreasing repair rate,

meaning that if a repair process has not been completed in the first 0.50 to 1 hours and going

on for a rather long time, then this indicates serious problems in the bus.

4.4 Determination of Reliability and Hazard rate models for the education transport bus

Reliability is the probability that the bus will perform defined functions, under stated operating

conditions, for a given period of time. The buses as mentioned above consist of auxiliary

systems and parts in series with different transfer mechanism and controlled by driver and

auxiliary automated control system. A series will function if and only if all of its components

are functioning properly. If a sub system or component failed, then the bus will stop or the

other systems are not working properly as a result the delay in the time to reach the campus

and also loss of concentration on studies of student due to comfortless travelling. It is assumed

that the components or sub systems are independent, that is, the failure of one component or

sub-system does not affect the reliability of the other component or sub-system. Thus

operation of bus is ensured only if all components or sub-systems are operating:

(1)

The bus follows the Weibull and Lognormal, failure law, and we assume T as the continuous

random variable representing the time to failure. The corresponding probability density

functions are: For Weibull

(2) The mean TTF, standard deviation of the bus is

Mean TTF= (3)

SD (4)

Where, Γ is Gama function. Hazard rate function:

, � ≥ 0 (5) For Lognormal

(6)

Mean TTF = ��(�+0.5�2) (7)

SD= (8)

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Table 6.a Distribution analysis of TTF for Table 6.b Distribution analysis of TTR for Bus Bus

Distribution Analysis: TTF Distribution Analysis: TTR Variable: TTF

Count Variable: TTR

Count Censoring Information Uncensored value

Censoring Information Uncensored value

228 228 Estimation Method: Least Squares (failure time(X) on rank(Y)) Estimation Method: Least Squares (failure time(X) on rank(Y)) Distribution: Weibull Distribution: Lognormal Parameter Estimates Parameter Estimates

Parameter Estimate

Standard

Error 95.0% Normal CI

Parameter Estimate

Standard Error 95.0% Normal CI

Lower Upper Lower Upper Shape 6.39889 0.312337 5.81509 7.04129 Location -0.46012 0.0498708 -0.55787 -0.36238 Scale 17.998 0.196544 17.6168 18.3873 Scale 0.753032 0.034969 0.687521 0.824786 Log-Likelihood = -583.898 Log-Likelihood = -155.227

Goodness-of-Fit Goodness-of-Fit

Anderson-Darling (adjusted) = 62.812 Anderson-Darling (adjusted) = 2.964

Correlation Coefficient = 0.972 Correlation Coefficient = 0.9 84

Characteristics of Distribution

Characteristics of Distributio n

Estimate

Standard Error

95.0% Normal CI

Estimate


Lower Upper Lower Upper Mean(MTTF) 16.756 0.203665 16.3615 17.1599 Mean(MTTR) 0.838123 0.0472668 0.750418 0.936078 Standard Deviation 3.05959 0.121527 2.83044 3.3073 Standard Deviation 0.732133 0.0735293 0.601316 0.89141 Median 16.996 0.208071 16.5931 17.4088 Median 0.631208 0.0314788 0.57243 0.696022

First Quartile(Q1) 14.8137 0.251001 14.3298 15.3139 First Quartile(Q1) 0.37983 0.0209541 0.340903 0.423202 Third Quartile(Q3) 18.9405 0.194211 18.5637 19.325 Third Quartile(Q3) 1.04895 0.0578677 0.941451 1.16873 Interquartile Range(IQR) 4.12682 0.17618 3.79557 4.48699 Interquartile Range(IQR) 0.669124 0.0474258 0.582338 0.768842 Table of Percentiles Table of Percentiles

Percent Percentile

Standard

Error 95.0% Normal CI

Percent Percentile


Lower Upper Lower Upper 1 8.7702 0.354819 8.10163 9.49395 1 0.109489 0.0104474 0.090813 0.132005 5 11.3145 0.323481 10.6979 11.9666 5 0.182912 0.0139248 0.157559 0.212346 10 12.6616 0.298003 12.0908 13.2594 10 0.240468 0.0161229 0.210856 0.274238 20 14.2371 0.263863 13.7292 14.7638 20 0.334912 0.0193939 0.298978 0.375164 30 15.3198 0.23991 14.8567 15.7973 30 0.425279 0.0225974 0.383217 0.471957 40 16.2044 0.221771 15.7755 16.6449 40 0.521577 0.0264187 0.472285 0.576014 50 16.996 0.208071 16.5931 17.4088 50 0.631208 0.0314788 0.57243 0.696022 60 17.7537 0.198602 17.3687 18.1473 60 0.763883 0.0386919 0.691691 0.843609 70 18.5277 0.194064 18.1512 18.912 70 0.936853 0.04978 0.844194 1.03968 80 19.3875 0.196592 19.006 19.7767 80 1.18964 0.0688887 1.062 1.33262 90 20.5036 0.212919 20.0905 20.9252 90 1.65687 0.11109 1.45284 1.88956 99 22.8493 0.288973 22.2899 23.4228 99 3.63895 0.347228 3.01825 4.3873 99.9 24.344 0.358068 23.6523 25.056 99.9 6.46838 0.769834 5.12259 8.16772 Table of Survival Probabilities Table of Survival Probabilitie s

Time Probability 95.0% Normal CI

Time Probability

95.0% Normal CI

Lower

Upper Lower

Upper 0.5 1 1 1 0.25 0.890638 0.855091 0.919443 1 1 1 1 0.5 0.621511 0.5701 0.670855 2 1 1 1 1.25 0.182111 0.144301 0.225574 4 0.99993 0.99982 0.99998 1.5 0.125182 0.0940567 0.162865

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8 0.99443 0.99026 0.99682 2 0.062823 0.042538 0.089956 16 0.62439 0.56998 0.67396 3 0.019229 0.01076 0.032799 32 0 0 0 6 0.001393 0.000497 0.003585 40 0 0 0 12 0.000046 0.000009 0.000206 68 0 0 0

As regards Table 6.b, the conclusion derived for bus TTR are as follows:

a) 25% of the failures will be repaired within 0.37983 hours, whereas the half (50%) of

the failures will be repaired in 0.631208 hour. b) From the table of percentile with 95%

confidence interval, one can perceive that 5% of the failures will be repaired within 0.182912

hour. c) From the table of survival probabilities with 95% confidence interval, the probability

to repair the bus in less than 0.25 hour, is 0.109362 the probability to repair the bus in less

than half hour (30 min) is 0.378489, and, finally, the probability to repair the bus in less than

1.5 hour is 0.874818.

From Table 6.a, a) the time within which the 25% of the failures are expected to occur,

is 14.8137 of operating hours, whereas the time within which, the half (50%) of the failures

are anticipated to happen, is 16.996 of operating hours. b) From the table of percentile with

95% confidence interval, it is evident that the time within which, the 5% of the failures are

expected to happen, is 11.3145 operating hours. c) From table of survival probabilities with

95% confidence interval, it is found out that after 1 Hours (60 min) of operation the

probability of properly functioning of the bus is 100%. After a shift (8hr) of operation, the

probability of properly functioning of the bus is 99.44 % and after a working week the

probability of proper function of the bus is just 0 %.

5. Conclusion

In this research work we examined Reliability, availability and maintainability in case of

educational institute bus transit in Sinhgd Institute Pandharpur taluka in Solapur district. It

was pointed out that

• Availability of bus is 95.28. Although the mean TTF is 16.71hours; that is every 3rd

working day a failure occurs in bus, whereas mean TTR is 0.82 hour.

• The failure mode 1(Fm.1) has the highest number of failure 68.81%. Equally important

failure mode 2(Fm.2) that has 6.8% of failure, the first four failure modes in diagram

stand for the 88.07% of all the failures of the transport bus.

• Analysis of reliability and hazard rate models for Bus, are estimated. Bus is having

reliability 99.44% after working for 8 hrs. shift. From analysis it is observed that the TTF

sample followed webull distribution, and lognormal is followed TTR sample.

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Further research can be extended to Preventive maintenance scheduling of bus and classify

buses in low, medium and High performance and also root planning, assignment of a driver

can be studied for better transport management.

References

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maintainability of public transport vehicles. Reliability Engineering & System Safety, 26(3), 271-277.

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quality in maintenance engineering, 12(3), 205-238.

• Rajpal, P. S., Shishodia, K. S., & Sekhon, G. S. (2007). Reliability, Availability, and Maintainability of Intermittently-used Repairable Systems. Defence Science Journal, 57(2), 211.

• Saraswat, S., & Yadava, G. S. (2008). An overview on reliability, availability, maintainability and supportability (RAMS) engineering. International Journal of Quality & Reliability Management, 25(3), 330-344.

• Sharma, R. K., & Kumar, S. (2008). Performance modelling in critical engineering systems using RAM analysis.

Reliability Engineering & System Safety, 93(6), 913-919.

• Thomas H. Maze and Allen R. Cook, “Maintenance Performance Measurement”, Transportation Research Record 1140.

• Tsarouhas, P. H., Arvanitoyannis, I. S., & Varzakas, T. H. (2009). Reliability and maintainability analysis of cheese

(feta) production line in a Greek medium-size company: A case study. Journal of Food Engineering, 94(3-

• Tsarouhas, P. H. (2009). Classification and calculation of primary failure modes in bread production line.

Reliability Engineering & System Safety, 94(2), 551-557.

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reliability and maintainability analysis of transport

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