1. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –
INTERNATIONAL JOURNAL OF ELECTRONICS AND
6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 6, November - December (2013), © IAEME
COMMUNICATION ENGINEERING & TECHNOLOGY (IJECET)
ISSN 0976 – 6464(Print)
ISSN 0976 – 6472(Online)
Volume 4, Issue 6, November - December, 2013, pp. 43-48
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IJECET
©IAEME
IN SITU RELIABILITY EVALUATION OF SNOW DEPTH SENSOR OF
AUTOMATIC SNOW TELEMETRY NETWORK IN WESTERN
HIMALYAS
Neeraj Sharma, Rajesh Kumar Garg, Rajeev Kumar Das,
Ashwagosha Ganju, Ramanand
Snow and Avalanche Study Establishment (SASE), Sector-37A, Chandigarh, India
ABSTRACT
Environmental sensor networks offer a powerful combination of distributed sensing capacity
and real-time data visualization and analysis. Environmental sensor networks have been established
world over for monitoring multiple habitats at different scales. Due to the dynamics of the
environment and the variability on the sensor usage, electronic items in the field are usually exposed to
varying failure-causing stresses. Snow & Avalanche Study Establishment, (SASE) has established a
network of Automatic Weather Stations (AWSs) with several environmental monitoring sensors in the
North Western Himalayas for the hourly collection of snow and meteorological parameters at the Earth
Receiving Station. In the present paper, in situ reliability analysis of Campbell make SR 50 Snow
Depth Sensor integrated with the AWS network has been done based on the failure data observed from
2004 to 2012. The failure data was analyzed with quarterly time intervals for evaluation of the
statistical reliability, failure rate and failure density. It has been observed that the reliability of snow
depth sensor follows an exponential curve with a constant hazard rate of 0.071. The correlation
coefficient of fitted trend-line for reliability equation with the actual data comes out to be 0.939. Mean
Time to Failure so evaluated helps in prediction of the lifetime of sensors and efficient management of
spares for the network.
Keywords: Reliability, Sensor, Automatic Weather Station, Mean Time to Failure (MTTF),
Hazard Rate, Correlation, Life Testing Technique
1. INTRODUCTION
Sensors are very crucial elements in environmental monitoring systems for timely assessment of
their health and to take appropriate measures to prevent any failures which can lead to blank periods on
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2. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –
6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 6, November - December (2013), © IAEME
data acquisition. Reliability of sensors used for monitoring various parameters of critical systems is
very important for timely assessment of their health and to take appropriate measures for fault diagnosis
at incipient stages in order to prevent any catastrophic failures. Due to the dynamics of the environment
and the variability on the sensor usage, environmental sensors in the field are usually exposed to
varying failure-causing stresses. Some products are equipped with sensors and smart chips that measure
and record usage/environmental information over the life of the product. For some products, it is
possible to track environmental variables dynamically, even in real time, providing useful information
for field-failure prediction. In many applications, predictions are needed for individual units, giving the
remaining life of individuals, and for the population, giving the cumulative number of failures at a
future time. It is always desirable to obtain more accurate predictions for both the population and the
individuals. High reliability assurance of sensors requires the complete knowledge of their failure
characteristics. Sensor reliability is important in applications such as temperature, humidity,
precipitation and snow depth monitoring for environmental sensing networks. Such networks require
continuous reliable monitoring sensors to avoid unexpected failures which might result in huge data
loses from the network. It is always desired to have a better reliable sensor so that the downtime and
data loss from the network is minimized. This paper focuses on predicting the reliability and Mean
Time to Failure (MTTF) for snow depth sensor of an Automatic Snow Telemetry Network in Western
Himalayas. MTTF represents the average expected time that will elapse before a sensor has failed under
the provided conditions. Reliability modeling can be useful in prediction of failure times and planning
of spare sensors required for the network. An attempt is made in this paper to model the reliability
equation for the snow depth sensor based on the field failure data for past 08 years. The reliability
equation evaluated for the snow depth sensor gives a fair idea of the MTTF and failure rate of the
sensor.
The systems are maintained regularly to provide uninterrupted data round the clock. This
requires extensive eff or t for the up-keeping o f these stations in harsh, inaccessible areas of
the Himalayan region. The AWS systems have been maintained by manual efforts since the time
of installation.
2. AWS NETWORK IN HIMALAYAS
Automatic Weather Stations have been deployed in the north western Himalayan sector for
hourly transmission of snow and meteorological data from remote and inaccessible locations. The
deployment of AWS for monitoring of snow and meteorological parameters started in 2004. Since
then the data have closely been monitored to deduce the health of various sensors, data-logging and
transmission modules of AWS. A sensor or component referred to as a unit hereafter is said to have
failed when it doesn’t perform satisfactorily or doesn’t provide expected output. The pattern of
failure can be obtained from observing the failure rate characteristics as a function of time. Time to
failure of snow depth sensor has been observed in field locations to calculate the reliability of the
sensor. The reliability curve so obtained gives an idea about the failure rate and the MTTF of the
sensor which can be utilized for general analysis.
3. FIELD FAILURE DATA ANALYSIS
The data collected over the years has been analyzed to calculate the reliability of the snow
depth sensor. The data was grouped in class intervals of 3 months each. The corresponding failure
during the class interval was found out from the available data and the reports from the Earth
Receiving Station. The initial populations of 19 sensors have been taken into consideration and the
data has been taken starting from 2004 to 2012. It was observed that the last sensor from the 2004
batch failed after continuous operation for 8 years and 6 months. This study is based on the life
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3. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –
6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 6, November - December (2013), © IAEME
testing technique[1], in which a fairly good number of units are tested until the failure of complete
lot occurs. Thus the failure rate characteristics of the sensor with respect to time are studied from
the experimental field data. These data provide a basis for formulating or constructing
mathematically a failure model for general analysis. Based on the field failure data various terms
related to life tests can be defined and quantified[2].
Failure Rate (Z): Ratio of the number of failures (nk) during a particular (kth interval) unit interval to
the average population during that interval. It is also termed as Instantaneous Failure Rate.
Z=
nk
Avg Population in kth interval
Failure Density (fd): Ratio of the number of failures during a given unit interval of time to the total
number of units at the very beginning of the test.
fdk =
n
k
…..1
N
t
− z (ϕ ) d ϕ
fd (t ) = Z (t )e ∫
…..2
0
Reliability (R): The ratio of survivors at any given time to the total initial population.
R = Sk
N
…..3
t
R (t ) = e ∫
0
− z (ϕ ) dϕ
…..4
Mean Time to Failure (MTTF): The average time for a component/ sensor to fail.
MTTF =
1
N
∑ kn ∆t
k
…..5
∞
MTTF = ∫ R(t )dt
…..6
0
Probability of Failure :
F (t ) = 1 − R (t )
…..7
In the present paper the analysis is based on calculation of above listed parameters from the field
failure data and deduction of a reliability equation from the calculated parameters.
Where
N = Total Initial Population
n k = No of Failures in kth interval
S k = No of Survivors in kth interval
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4. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –
6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 6, November - December (2013), © IAEME
4. METHODOLOGY
The field failure data can be analyzed to obtain reliability, probability of failure, hazard rate
and other necessary parameters which relate to the performance of the sensor in the field. To draw
general conclusions from the behavioral patterns obtained from the field data, a mathematical
model representation for the failure characteristics becomes necessary. In the present work we have
tried to deduce a mathematical model[3] for the reliability of the Snow Depth Sensor. The
methodology for the evolving a mathematical model for the reliability of snow depth sensor is
based on the calculation of the reliability from the field data and fitting a reliability equation to
calculated data. The reliability corresponding to each quarter i.e. 03 months was plotted and an
exponential equation was fitted to the reliability values obtained from the experimental data. The
reliability equation thus generated is the basis of prediction of the hazard model for Snow Depth
Sensor[4]. The reliability, failure density, MTTF and Probability of Failure can be calculated by
substituting value of Z(t) in equation 2,4,6 & 8.
The reliability for the constant hazard model where λ is the hazard rate.
R(t ) = e−λ t
…..8
Failure Density
fd (t ) = λ e−λ t
Probability of failure
F (t ) = 1 − e−λt
Mean Time to Failure (MTTF)
∞
MTTF = ∫ R (t ) dt = 1
0
λ
5. RESULTS
The generated equation for reliability of Snow Depth Sensor is an exponential equation of the form
R (t ) = e−λ t
with λ = 0.071
The value of λ is obtained from the field failure data for the snow depth sensor.
This equation represents a constant hazard rate model with a hazard rate = λ and MTTF = 1 λ . The
constant hazard rate model[5] generated fairly matches the experimental results. In the present case
Z(t) = 0.071, a constant. The reliability equation is highly correlated with the experimental values of
reliability with an R2=.8297. The MTTF calculated from the generated model is quite close to the
MTTF calculated experimentally. The constant hazard model so predicted for the snow depth
sensor assumes that the hazard rate remains constant with time.
Various parameters obtained from the experimental results and the predictions from the model have
been compared in the Table 1.
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5. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –
6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 6, November - December (2013), © IAEME
Parameter
Experimental
Value
Estimated from
Hazard Model
Failure Rate
0.079
0.071
41.15 months
42.25 months
MTTF
Failure
0.013
0.03
Density
Table 1: Comparison of Experimental & Model Generated values
The reliability curve for the Snow Depth Sensor is shown in Fig 2.
Fig 2: Reliability Curve for Snow Depth Sensor Campbell SR 50
6. CONCLUSION & FUTURE WORK
In this paper the mathematical modeling of the failure rate and reliability of Snow Depth
Sensor deployed in the AWS network in Western Himalayas has been attempted. The results show
high correlation between the experimental values of reliability and that predicted from the model.
The reliability of Snow Depth Sensor has been estimated to be 0.46 with a constant hazard rate
model and MTTF of approximately 41.7 months. This study will provide a guideline[6] for
replacement and maintenance schedules of the sensor. Further the planning of spares for AWS
network can be done based on the results obtained. Future work will focus on mathematical
modeling of hazard rate for all sensors and then AWS as a whole system taking into account the
sensors as sub systems for the AWS system.
7. REFRENCES
[1] Jeff Anderson & John Wirt, Ultrasonic Snow Depth Sensor Accuracy, Reliability and
Performance, Western Snow Conference, 2008.
[2] LS Srinath, Reliability Engineering, Page 3-50 East West Press 1995.
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6. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –
6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 6, November - December (2013), © IAEME
[3] Morteza Alabaf Sabaghi, Mortality and Approximate Hazard Plots, E.C.O College of
Insurance, Allameh Tabatabai University, No. 1, Malek-o-Shoara Bahar, Taleghani Avenue,
Tehran 15717, Iran, Feb 2009.
[4] Alexandre P. Fischer, The Measurement Factors in Estimating Snowfall Derived from Snow
Cover Surfaces Using Acoustic Snow Depth Sensors, Journal of Applied Meteorology and
Climatology, Volume 50 2010.
[5] Stafford, Judith A. and McGregor, John D., “Issues in Predicting the Reliability of
Components,” Proceedings of the 5th ICSE Workshop on Component-Based Software
Engineering, Orlando, Florida, May 2002.
[6] B.E. Goodison et al, The WMO Solid Precipitation Measurement Intercomparison” - Final
Report, (WMO/TD - No. 872, IOM 67), 1998.
[7] Ramesh Kamath, Siddhesh Nadkarni, Kundan Srivastav and Dr. Deepak Vishnu Bhoir, “Data
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[8] Krishna Kumar M, Rajkumar S and Joe Paul J, “Miniaturized Planar Inverted F Antenna
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[9] P.T.Kalaivaani and A.Rajeswari, “The Routing Algorithms for Wireless Sensor Networks
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