# Forensic and Investigative Sciences - 2000 words

1

The RokitUK factory in Prestington has just patented a new super-fuel formed by amalgamating chemical X and chemical Y. These chemicals are harmless and environmentally friendly when separate, but when mixed there is a 45% chance of an unwanted side-reaction and a 10% chance of no reaction at all. The state diagram for this is sketched below. Calculate the time until the absorbing state given that the chemicals are initially seperate.

The time before reaching the absorbing state is also called the mean time to failure (MTTF). This is the “Laplace transform” of the rate of the disaster.

[15 marks]

2

Consider the following block diagram

What is the structure function [5 marks]

What are the minimal cut sets? [5 marks]

Can you draw the fault tree? [5 marks]

3

A complex building can be described as a series of passages and rooms which offer different “conductivity’s” for access (flow) of people. These values arise because of factors such as stairs, narrow walk ways, remoteness etc.

The Fire Chief at the scene of an incident has been given the following sketch map of the building:

S/He is told that the fire is located in room F and that there are two entrances to the building.

Redraw the picture for each of the two choices. (meaning the entrance you choose is on the left of the picture and the fire-room is on the right). [5 marks]

Find the structure function for each choice. [10 marks]

4

Your exam could be marked with a range of possible grades, simplified as on the following state diagram:

To begin with the chances are that you will pass with a standard result. Each 45 minutes (the time allocated for each answer) your grade could go up or down to a neighbouring grade or stay put.

There is a chance that your Genius is so great that the examiner cannot appreciate what you are saying and incorrectly marks it as nonsense.

What is your grade most likely to be after the 3 hour exam? [15 marks]

What (if any) are the steady state results for a group of 14 students? [20 marks]

5

A very new European “Rapid Reaction Force for Fire” has been created today and begins operation between three Countries “A”, “B” and “C”. It’s main resource is a super aircraft “Funderbird2” with a massive water cannon that even carries a small mini-submarine for fighting fires at sea. Unfortunately, it can only be in one Country at a time.

What is the matrix representation of this problem? [5 marks]

The probabilities of going to a fire in another Country, given that the force are in a given Country to begin with, are shown on the sketch above (any resemblance to any particular Country or Nation is purely coincidence and not intended). The probabilities were obtained as a weekly average using statistics for fires over many recorded weeks.

When will the plane take up permanent residence in one Country? [15 marks]

Skills: Research Writing

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