Flashcards in L23/24: Introduction to Engineering Decision Making Deck (48):
Two types of uncertainty
- aleatory uncertainty
- epistemic uncertainty
What is aleatory uncertainty?
natural randomness in the phenomena we are dealing with
What is epistemic uncertainty?
inaccuracy in our understanding and our models for prediciting reality
Basic options for making decisions based on incomplete knowledge and information.
- ignore the uncertainty (work with best point estimates)
- allow for uncertainty using intution (or engeering judement)
- adopt a scientific approach (use probabiliy and statistical analysis)
How to evaluate a solution to assess how well it has worked?
- has a change in the design approach or procurement process led to a decrease or increase in failures
- has changing the process for producing a material resulted in a better or worse material
Why are some people reluctant to concede there is uncertainty?
- "politics of uncertainty", might be perceived as bein inconsistent with being an expert
Type 1 error:
Accused is not guilty but is concluded as guilty
Type 2 error:
Accused is guilty but is found to be not guilty
What is the focus of risk management?
Making decisions in the face of uncertainty, which entails identifying probability and consequences of making wrong decisions.
What is the essence of Bayesian Decision Theory?
Using additional data to reduce the probability of making wrong decisions.
What is the "state of nature"?
The true value of the uncertain variable. It cannot be determined with absolute confidence.
How to handle the 'state of nature'?
Apply a probability distribution for the state of nature then use statistical decision theory.
Prob. dist. may be estimated using engineering judgement. Additional information may be required in some cases.
Notes on Decision Trees
- can have any number of actions and states; as this increases the decision tree gets more dense
- if have finite number of states use probibility mass function to describe probabilities
- if have infinite number of states use probability density function to describe probabilities
A decision is sensitive if:
- one test is done and the decision is different for different test results
- more than one test is done and the decision changes as new test results come to hand and the probability distribution for the state of nature are updated.
(sensitivity decreases as the number of tests increases.
Aim of doing tests:
- to obtain better information on the state of nature to assist making a decision
Result of doing a test
- might give a posterior probability distribution which exhibits less variance or uncertainty
may not change the decision
When to use preposterior analysis?
Where there are several possible tests, to identify which test (if any) should be done.
- before posterior analysis
Preposterior Analysis involves:
- updating the probability distribution for the state of nature, and deciding on which action to take
- calculating posterior probabilities for the state of nature and then deciding which action to take (given an experiment has been done and the results are known)
- deciding whether an experiment should be done and which experiment
When should tests be done?
When the expected value of the information obtained from the experiment exceeds the cost of the test.
What are the two stages in the decision tree involved in posterior analysis
- action - a
- state (of nature) - theta
What are the four stages in the decision tree involved in preposterior analysis
- test - e
- result - z
- action - a
- state (of nature) - theta
What is Allais' Paradox?
Decision makers do not use a rational approach.
Not making a decision on the basis of expected utilities is not irrational, and is simply the result of the way people value the possible outcomes.
The rational approach to identifying the optimum decision is to take account of both:
- the probability of each possible outcome
- the consequence (or utility) of each possible outcome
The rational approach involves:
calculating the expected utility of each action and choosing the action with the maximum expected utility
What are the requirements for a robust numerical measure of preference?
- reflects the decision maker's subjective preferences
- provides a scale preserving the ordering of expected values
What is required in a decision situation?
a value system
Why is dollars not always the best value system for decisions?
- possible loss of $5000 is far more serious for an individual than a large industrial firm
What did the 3 rational mathematicians not include in their attempt for a robust numerical measure?
They postulated what a rational decision maker ought to want, they did not:
- consider what a decision-maker actually wants
- allow for subjectivity
Explain the standard gamble.
Based on a particular form of decision tree, with one action leading to a certain outcome and the other to a gamble.
Allows subjectivity to be taken into account, while preserving the ordering of expected values.
Criterion of Pure Pessimism (or 'maxi-min criterion') involves:
- identify for each action the minimum utility
- choose the action with the largest minimum utility
The pure pessimism criterion assumes?
that whatever action is chosen, the state of nature will be that which gives the worst possible outcome
The criterion of Pure Optimism (or 'maxi-max criterion') involves:
- identify for each action the maximum utility
- choose the action with the largest maximum utility
The pure optimism criterion assumes
that whatever action you choose, the state of nature will be that which gives the best possible outcome
The criterion of regret involves:
- identify the regret for each action and state of nature
- identify for each action the maximum regret
- choose the action with the smallest maximum regret
the probability that a component (or system) will function properly.
In reliability engineering it is necessary to:
- estimate the reliability of components
- the reliability of systems made up of components who reliabilities are known
Two basic types of systems:
If a component in a series system fails does the system survive?
No. Series system survives if and only if all components survive.
Explain the level of redundancy for parallel systems
If k is the minimum number of properly functioning components for the system to function properly then the level of redundancy is equal to (n-k).
n is number of components
When does a parallel system fail?
When the level of redundancy is exceeded. That is more than (n-k) components fail
The reliability o a network might be deemed unsatisfactory for various reasons:
- the risk in some event is too high
The issue is which component should be improved to maximize the improvement in network reliability
it is assumed that the consequence of failure does not depend upon which components fail.
What did Birnbaum suggest to maximise the improvement in network reliability (R)
To improve the link a with the highest Reliability Importance (RIa).
What did Birnbaum's reliability importance suggest to improve network reliability for system with links in series?
Improve the less reliable link
What does Birnbaum's reliability importance suggest to improve network reliability for system with links in parallel?
Improve the more reliable link.
What does Henley and Kumamoto suggest to maximise the improvement in network reliability (R)?
To improve the link with the highest Criticality Importance (CIa)
What did Henley and Kumamoto's criticality importance suggest to improve network reliability for system with links in series?
CI provides no help in deciding which link to strengthen