Part B | 24.2
530 Part B Autonomous Ocean Vehicles, Subsystems and Control
modeling AUV failure distribution with time. The first
study on AUV reliability estimation was conducted by
Griffiths et al. [24.16]. Failures of Autosub1 AUV were
collected from its first mission within Empress Dock,
in Southampton in June 1996, to a science campaign
on board the RV Calanus at Oban in November 1999.
During this time, the vehicle conducted 216 missions
covering 2125 km. Fifty failures were recorded, giving
a probability of failure per mission of 0:231. Pareto analysis showed that human error, acoustic telemetry failure,
and failure to dive were the top three failure modes in
Autosub1’s failure history. This report used statistical
models for predicting the failure probability as function of mission length. The dataset used for this analysis
consisted of the distance traveled for each mission and
whether the mission ended due to a fault. Each entry
was classed as censored or not censored. A censored
observation is one where the mission was terminated
not due to failure, whereas a noncensored data captures
the distance at which a failure took place. Two types of
functions were defined directly from the data [24.12].
The first function, the probability of failure F.x/, where
x stands for an instantiation of distance X. In mathematical terms, this is captured by F.x/ D P.X < x/, where
P.X < x/ is obtained directly from the probability function that is fitted to the historic data and lower case x
is an instantiation of X. The second function of interest
is the reliability, otherwise known as survival function,
is the probability of survival, R.x/. The reliability is the
complement of the probability of failure, it is mathematically defined as R.x/ D 1 F.x/ D 1 P.X < x/. It
stands for the probability of the system surviving without failure, the distance x.
Griffiths et al. fitted three well-known distributions
to the historic data: Weibull, log logistic, and log normal. Results showed that the probability of a fault
occurring in a 100 km mission was 0:352 using the
Weibull, 0:334 for the log logistic, and 0:309 for the
log normal. Software reliability was studied separately
using two independent software reliability models: the
Poisson model and the Littlewood model. Both models
lead to the same reliability estimate for a 100 km mission of 0:93 for the software.
The dataset was later updated to include Autosub2
science missions on MV Terschelling at three sites on
the west coast of Scotland in March and April 2000,
equipment trials at Plymouth and a science campaign
in the Strait of Sicily in June 2000. A total of 869 km
were covered in 24 missions [24.12]. Here the authors
fitted six different distributions to the data: extreme
value, normal, logistic, and their logarithmic versions:
Weibull, log normal, and log logistic. The logarithmic
distributions provided a better fit to the data than their
linear counterparts. The Weibull distribution showed
the highest failure rate, and, to err on the conservative,
was chosen as the preferred parametric model. Results
were similar to those previously reported.
The first reported work on the effects of upgrades
on the reliability growth for AUVs was presented in
2003 [24.17]. The dataset consisted of Autosub missions considered in [24.12] plus missions that were
conducted in two engineering trials in June 2002 and
September/October 2002. The purpose of these trials
was to test new software that gave enhanced autonomy.
The results of the analysis showed reliability growth
prior to the missions carried out in June 2002. However, after the upgrades there was an increasing failure
rate. These were worrying results because the vehicle
was due for an under ice campaign in February–March
2003. The team used the reliability model to estimate
the number of missions, with an acceptable number of
faults, needed to ensure reliability growth. The analysis concluded that 10 missions were required with
distances varying from 5 to 144 km in length, with only
two high-impact faults allowed on the shorter missions.
A study in reliability growth was carried out for
the Dorado AUV designed and operated by Monterey Bay Aquarium Research Institute (MBARI) in
preparation for an Arctic campaign in the following
summer [24.13]. The dataset consisted of mission data
collected during operations in 2003 and 2004, where the
vehicle had traveled approximately 1700 km in Monterey Bay, California. Several failures emerged; the
analysis considered only failures that resulted in an
abort – a total of 14. Basic trend analysis using the
Laplace test yielded the conclusion that the AUV reliability exhibited an increasing trend. This was verified
using two independent reliability growth models due to
Duane and Crow. Both use graphical approaches to support reliability growth analysis. The estimation of the
mean time between failures (MTBF) was conducted for
different groups of failures; set according to their criticality. The estimated MTBF for the extremely critical
faults was 167:8 h.
Reliability estimation based on revealed operational
history helps those involved understand better the failure pattern of these autonomous vehicles, enabling the
implementation of failure mitigation mechanisms during the operational lifetime of the AUV. However, for
early lifetime, this failure history is not available. For
the early lifetime of a vehicle, the reliability of a vehicle
can be estimated using reliability modeling techniques.
These are discussed in the next sections.
24.2.2 Reliability Modelling
Reliability modeling aims to estimate system’s reliability based on its intended functionality, and design
530 Part B Autonomous Ocean Vehicles, Subsystems and Control
modeling AUV failure distribution with time. The first
study on AUV reliability estimation was conducted by
Griffiths et al. [24.16]. Failures of Autosub1 AUV were
collected from its first mission within Empress Dock,
in Southampton in June 1996, to a science campaign
on board the RV Calanus at Oban in November 1999.
During this time, the vehicle conducted 216 missions
covering 2125 km. Fifty failures were recorded, giving
a probability of failure per mission of 0:231. Pareto analysis showed that human error, acoustic telemetry failure,
and failure to dive were the top three failure modes in
Autosub1’s failure history. This report used statistical
models for predicting the failure probability as function of mission length. The dataset used for this analysis
consisted of the distance traveled for each mission and
whether the mission ended due to a fault. Each entry
was classed as censored or not censored. A censored
observation is one where the mission was terminated
not due to failure, whereas a noncensored data captures
the distance at which a failure took place. Two types of
functions were defined directly from the data [24.12].
The first function, the probability of failure F.x/, where
x stands for an instantiation of distance X. In mathematical terms, this is captured by F.x/ D P.X < x/, where
P.X < x/ is obtained directly from the probability function that is fitted to the historic data and lower case x
is an instantiation of X. The second function of interest
is the reliability, otherwise known as survival function,
is the probability of survival, R.x/. The reliability is the
complement of the probability of failure, it is mathematically defined as R.x/ D 1 F.x/ D 1 P.X < x/. It
stands for the probability of the system surviving without failure, the distance x.
Griffiths et al. fitted three well-known distributions
to the historic data: Weibull, log logistic, and log normal. Results showed that the probability of a fault
occurring in a 100 km mission was 0:352 using the
Weibull, 0:334 for the log logistic, and 0:309 for the
log normal. Software reliability was studied separately
using two independent software reliability models: the
Poisson model and the Littlewood model. Both models
lead to the same reliability estimate for a 100 km mission of 0:93 for the software.
The dataset was later updated to include Autosub2
science missions on MV Terschelling at three sites on
the west coast of Scotland in March and April 2000,
equipment trials at Plymouth and a science campaign
in the Strait of Sicily in June 2000. A total of 869 km
were covered in 24 missions [24.12]. Here the authors
fitted six different distributions to the data: extreme
value, normal, logistic, and their logarithmic versions:
Weibull, log normal, and log logistic. The logarithmic
distributions provided a better fit to the data than their
linear counterparts. The Weibull distribution showed
the highest failure rate, and, to err on the conservative,
was chosen as the preferred parametric model. Results
were similar to those previously reported.
The first reported work on the effects of upgrades
on the reliability growth for AUVs was presented in
2003 [24.17]. The dataset consisted of Autosub missions considered in [24.12] plus missions that were
conducted in two engineering trials in June 2002 and
September/October 2002. The purpose of these trials
was to test new software that gave enhanced autonomy.
The results of the analysis showed reliability growth
prior to the missions carried out in June 2002. However, after the upgrades there was an increasing failure
rate. These were worrying results because the vehicle
was due for an under ice campaign in February–March
2003. The team used the reliability model to estimate
the number of missions, with an acceptable number of
faults, needed to ensure reliability growth. The analysis concluded that 10 missions were required with
distances varying from 5 to 144 km in length, with only
two high-impact faults allowed on the shorter missions.
A study in reliability growth was carried out for
the Dorado AUV designed and operated by Monterey Bay Aquarium Research Institute (MBARI) in
preparation for an Arctic campaign in the following
summer [24.13]. The dataset consisted of mission data
collected during operations in 2003 and 2004, where the
vehicle had traveled approximately 1700 km in Monterey Bay, California. Several failures emerged; the
analysis considered only failures that resulted in an
abort – a total of 14. Basic trend analysis using the
Laplace test yielded the conclusion that the AUV reliability exhibited an increasing trend. This was verified
using two independent reliability growth models due to
Duane and Crow. Both use graphical approaches to support reliability growth analysis. The estimation of the
mean time between failures (MTBF) was conducted for
different groups of failures; set according to their criticality. The estimated MTBF for the extremely critical
faults was 167:8 h.
Reliability estimation based on revealed operational
history helps those involved understand better the failure pattern of these autonomous vehicles, enabling the
implementation of failure mitigation mechanisms during the operational lifetime of the AUV. However, for
early lifetime, this failure history is not available. For
the early lifetime of a vehicle, the reliability of a vehicle
can be estimated using reliability modeling techniques.
These are discussed in the next sections.
24.2.2 Reliability Modelling
Reliability modeling aims to estimate system’s reliability based on its intended functionality, and design