1. MONTE CARLO ANALYSIS
When a system contains elements that exhibit chance in their behavior, the Monte Carlo method of simulation may be applied

2. The technique breaks down into 5 single steps:
The basis of Monte Carlo simulation is experimentation on the chance (or probabilistic) element through random sampling.
The technique breaks down into 5 single steps:
Setting up probability distributions for important variables.
Building up cumulative probability distribution for each variable in step 1.
Establishing an interval of random numbers for each variable.
Generating random numbers.
Actually simulating a series of trials.

3. STEP 1: ESTABLISHING PROBABILITY DISTRIBUTION
The basic idea in Monte Carlo simulation is to generate values for the variables making up the model being studied. There are a lot of variables in real-world systems that are probabilistic in nature and that we might want to simulate. A few of these variables are:
Number of accidents.
Time between accidents.
Service time.
Time to complete project activities.
Number of employees, absent from work each day.

4. One common way to establish a probability distribution for a given variable is to examine historical outcomes.
The probability, or relative frequency, for each possible outcome of a variable is found by dividing the frequency of observation by the total number of observations.
Probability distributions, need not be based solely on historical observations. Often managerial estimates based on judgment and experience are used to create a distribution.

5. Historical number of road accident example:
Number of accidents
Frequency (Days) 10 1 20 2 40 3 60 4 5 30
Total
200

6. Probability of occurrence Cumulative probability
STEP 2: BUILDING A CUMULATIVE PROBABILITY DISTRIBUTION FOR EACH VARIABLE
No. of accident
Probability of occurrence
Cumulative probability
10 / 200 = 0.05
0.05 1
20 / 200 = 0.15
0.15 2
40 / 200 = 0.20
0.35 3
60 / 200 = 0.65
0.65 4
0.85 5
30 / 200 = 0.10
1.00
200 / 200 = 1.00

7. STEP 3: SETTING RANDOM NUMBER INTERVALS
No. of accident
Probability
Cumulative probability
Interval of random number
0.05
01 to 05 1
0.10
0.15
06 to 15 2
0.20
0.35
16 to 35 3
0.30
0.65
36 to 65 4
0.85
66 to 85 5
1.00
86 to 00

8. STEP 4: SIMULATING THE EXPERIMENT
Day number
Random number
Simulated daily accident 1 52 3 2 37 82 4 69 5 98 6 96 7 33 8 50 9 88 10 90
39 total 10-day accident
3.9 average

9. Expected daily accident:
= sum [(probability) x (number of accident)]
= (0.05)(0) + (0.10)(1) + (0.20)(2) + (0.30)(3) + (0.20)(4) + (0.15)(5)
= 2.95 accidents.