application of probability to assess risk in management

8/12/2019 Application of Probability to Assess Risk in Management

1/16

APPLICATION OF PROBABILITY TO ASSESS

RISK IN MANAGEMENT DECISIONS, RISKANALYSIS

Jim Kennedy


2/16

CONCEPTS

Quantitative Risk Analysis is a tool used to

aid in management decisions when

uncertainty has to be considered.

A mathematical equation is a model

composed of one to an infinite number of

variables, and uncertainties.


3/16

VARIABLE OR UNCERTAINTY

Variables are controllable

Weight/volume of a chemical used in a reaction

Amount of antibiotic administered

Cost of a diagnostic test

Sensitivity and specificity of a diagnostic test

?

?


4/16

UNCERTAINTIES

Uncertainties are uncontrolled but

predictable.

Prevalence

Immune response

When will a shear pin break

Who will win the final four


5/16

PREDICTION=PROBABILITY=UNCERTAINTY

Uncertainty is the level of ignorance. Uncertainty is lessened by knowledge

Literature reviews

Expert opinions

Further data gathering and analysis

Until an uncertain event becomes 100% controlled it isa function of probability.

Uncertainties, like variables, may be discrete orcontinuous. Whether an unborn calf is male, female, or a hermaphrodite

would be a discrete uncertainty. The weight of a calf at birth is a continuous uncertainty, it

could weigh 75.0 lbs 75.1, 75.15etc. an infinite number ofpossibilities.


6/16

GRAPHICAL REPRESENTATIONS OF

UNCERTAINTIES

Discrete uncertainties and their probabilitiesare more easily understood if representedvisually by a bar graph.

Continuous uncertainties and theirprobabilities are more correctly representedby a line.

A graphical representation of an uncertaintyand its probability may be cumulative or maybe a single point.


7/16

SIMULATION MODELING

Using probability to make a management decision. Putting together a series of variables and uncertainties

into a mathematical formula produces a model.

Values to each variable and uncertainty can be given and

the outcome of the mathematical formula be determined,a deterministic model.

An alternate method is to assign probabilities to allor some of the uncertainties and allow the probability

distribution to determine a mean value , upper andlower limits, and a standard deviation for theuncertainty.


8/16

STOCHASTIC MODELING

Accounts for an uncertainty occurring dependent onthe probability of that uncertainty. We are uncertain of the prevalence of a disease within a

herd, but we can make a guess and assign a probability

to that guess.

Your best guess is that 10 of 100 animals areinfected, but you know that it is possible that noneare infected or that all are infected, you are

uncertain. If the decision to be made is metaphylaxis or not, a

stochastic model might allow the best decision be made.


9/16

MAKING THE MODEL

Assuming your decision rests on whethermetaphylaxis would be more cost effective than topull and treat you would consider factors such as: the cost of metaphylaxis

the cost to treat

the ability of the pen rider to pull sick animals

the number of head requiring treatment

how many animals will require treatment despitemetaphylaxis

how many animals die although treated

etc.


10/16

MODELS GET COMPLICATED QUICKLY

Most of the factors for consideration from the

previous slide are uncertainties

A model with too many uncertainties may produce invalid

results, you may end with odds of making the correctdecision based on the model of 50:50, you didnt need a

model just a coin.

To avoid the dilemma you make assumptions such as the

pen riders are the best or the treatment never fails, but

assumptions decrease the validity of the model.


11/16

OTHER ASSUMPTIONS

Besides the assumptions of the model you

also make assumptions about the probability

distribution of the uncertainties.

The more precisely the probability

distribution of an uncertainty can be defined

the more precisely the model will depict

reality.


12/16

SOME PROBABILITY DISTRIBUTIONS OF

INTEREST

Pert(3.0000, 8.0000, 10.000)

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

2.

0

3.

3

4.

6

5.

9

7.

2

8.

5

9.

8

11.

1

5.0% 5.0%90.0%

5.226 9.370

Pert DistributionNormal(7.0000, 1.5000)

0.00

0.05

0.10

0.15

0.20

0.25

0.30

3 4 5 6 7 8 910

11

< >5.0% 5.0%90.0%

4.533 9.467

Normal Distribution

HyperGeo(20, 12, 100)

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

-2 0 2 4 6 8

10

12

14

5.0%90.0%0.00 5.00

Hypergeometric DistributionUniform(0.0000, 50.000)

Valuesx10^-2

0.0

0.5

1.0

1.5

2.0

2.5

-10 0

10

20

30

40

50

60

90.0%2.50 47.50

Uniform Distribution


13/16

SIMULATION MODELING

Simply stated a random set of values are

placed into a mathematical formula and the

results recorded.

A list of values could be placed in a

spreadsheet and selected at random this

might not reflect the probability of the value

actually occurring.Different methods of random selection of the

values such as Monte Carlo or Latin

Hypercube sampling exist.


14/16

RANDOM SELECTION FOR SIMULATION MODELS

Monte Carlo and Latin Hypercube simulation

interpose the probability distribution of the

event on the selection of the random value.

The resulting difference between the two

methods in most cases is minor, Latin

Hypercube is faster (requires less cpu time)

than the Monte Carlo method.


15/16

AVAILABLE AT A PRICE

Software programs to do simulation modeling

are available, such as @Risk and Crystal

Ball.

These programs are pricey and offer some

challenge in applying.

Programs/software of this type are used by

industries and governmental agencies indecision making. I would suspect that one of

these programs may have been used to

reach a decision on the Wall Street bailout,


16/16

PREGNANCY TESTING 500# FEEDLOT HEIFERS

Question: Would it be more cost effective topregnancy test 5000 500# heifers or donothing?

Cost to pregnancy test Lost revenue for pregnant heifer

Prevalence of pregnant heifers in group

Which are variables and which areuncertainties?

application of probability to assess risk in management

Documents