Download SAWE Presentation - International

The Use of Inferential
Statistics in Ships’
Stability Analysis
69th Annual International
Conference on Mass
Properties Engineering
May 26, 2010
Michael Diggs, Melissa Cooley & David Hansch
Naval Architects
Purpose of Damage Stability Analysis
• Produce a family of allowable KG curves to provide an overall
assessment of stability
• Demonstrate that the ship meets vulnerability or recoverability
requirements
• Provide technical guidance to ship designers for areas where
improvements can be made
• Ensure that damage stability performance is not degraded during
ship design and construction
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Traditional Approach to Damage Stability
• Navy Ships
– Deterministic approach
• Uses engineering judgment to analyze the worst cases
• Commercial Ships
– Safety of Life at Sea (SOLAS) and International Maritime Organization (IMO)
probability studies
• Provides an attained subdivision index
Useful and important but does not answer
What if…?
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What if…?
• Captain asks, “How likely am I to withstand a certain type of
damage?
• Requirement written in percentage
– Ship able to survive grounding X% of time.
– Ship able to perform it’s mission X% of time after damage.
Traditional approach does not address these questions
– Would have to analyze all cases to determine a passing percentage
– Does not allow you to determine the actual KG value to survive damage
a certain percentage of time.
Must use statistics
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Statistical Options
Two statistical options exist
• Bernoulli Trial
– Results from this approach are binomial, all damage cases are either
pass or fail
– Case KG is compared to Ship’s KG limit
– Calculate Percentage at Ship’s KG limit
– Requires a large sample size
• Inferential Statistics
– a mathematical method that employs probability theory for inferring the
properties of a population from the analysis of a sample taken from that
population
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Advantages of Inferential Statistics
• Uses the required KG of each case to predict the population of
required KGs
• Allows a smaller sample size
• Allows greater flexibility in determining the percentage of cases
which will pass for a given KG
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Assumptions / Sources of Uncertainty
Assumptions
• A Gaussian or normal distribution of the population of required KGs
• The analyzed sample is randomly selected from the population
Sources of Uncertainty
• Population may not be truly Gaussian
• The sample mean and standard deviation are not exactly the
population mean and standard deviation
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Estimating the Population from a Sample
• The sample mean and standard deviation provide estimates for the
population mean and standard deviation
• Confidence Intervals are attached to these estimates to yield the
range of values within which the population mean and standard
deviation are likely to reside
Ship Survival Probability vs. Limiting KG
(N)
1.000
Probability
0.800
0.600
Best Estimate
Low Mean, Low Std Dev
0.400
Low Mean, High Std Dev
High Mean, Low Std Dev
High Mean, High Std Dev
0.200
0.000
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Limiting KGs
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Validating the Assumption of a Normal
Distribution
• The validity of the inference to the population can be assessed
using a Chi-Square Goodness of Fit Test
Frequency
Distribution of the Sample Limiting KGs
(n=110)
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12
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8
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2
0
20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38
Limiting KGs
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Introduction of Trim
• Resultant trim is insensitive to initial KG
• If there are trim criteria for passing, failure of these criteria must be
separately analyzed and then combined with the failure due to lack
of KG cases
• This is accomplished by raising the KG required in order that the
overall passing rate is acceptable
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Differences between Inferential Statistics Analysis
and the SOLAS Probabilistic Analysis
• This inferential statistics analysis considers passing the criteria to
provide 100% likelihood of survival while SOLAS determines survival
probability for individual cases
• The SOLAS method requires analysis of every location on the ship
while the inferential statistics method allows for a sample of
damage locations to be used
• SOLAS method provides an Attained Subdivision Index which is
comparable to other ships while the inferential statistics method
presented provides a likelihood of survival for a given KG or a KG
required for a given likelihood of survival
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Conclusions
• Inferential Statistics is another tool for analyzing damage stability
• For ships of complex subdivision this tool reduces the amount of
calculations required to determine the likelihood of survival
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