Need Help with Model

I need help with the following...

I am using @Risk and am trying to set up a model. I finished an MBA level stats course, and am fairly familiar with @Risk. I am trying to work on my skills with this program.

I want to find out what are the chances of being at a certain promotion level (rank) within a military unit. All of the promotions/positions are specific to the unit. Therefore the rank distribution is discrete.

There are 68 people in this unit and are distributed amongst 3 ranks. The 3 rank positions and their discretedistribution are:
Level 6 0.62
Level 7 0.27
Level 8 0.11

There is also a normal distribution of the number of years a person has in the organization at each level.
Level 6 personnel have 8 years of service (mean) with a Std Dev of 4 years
Level 7 Personnel have 14 years of service (mean) with a Std Dev of 5 years
Level 8 are at 18 years (mean) with a std dev of 4 years

I want to run a simulation for each year of service from 10 years to 20 years to see what the chances are of being at each rank level (6, 7, or 8) for a given year.

Any help would be useful.



TS Contributor
See if I have got your idea.

The capacity of the unit is 68 people. Suppose all of them started the service at the beginning of the simulation, year 1. (This starting assumption can be changed)

For each newcomer of the unit, generate a categorical random variable to decide the rank. And generate the life time of this newcomer according to the normal distribution assumption (but have to truncate the normal distribution to avoid negative values).

When a person is leave, he/she is immediately replaced by another newcomer according to the above process. Repeat these procedures until the end of monitoring period. And you can count the number of people in each rank at the end.

Or, do you mean that those 68 people are always the same, but just they stay in the same rank for the given normal distributed time and switch the rank accordingly as if a renewal-reward process? Anyway just clarify first.
The way I have collected the data:

There are always 68 people in the organization, with the discrete distribution of the rank/positions I listed. When they leave (normally after a 20-year career), they are replaced through attrition. The new person entering the unit is placed at the Grade 6 level, and then people are promoted from within the unit up from the previous Grade level (1 person from Grade 6 to Grade 7; 1 person from Grade 7 to Grade 8).

What I have taken, in regards to the other distribution, is a snap-shot of the man-power of the unit on the 1st of January every year since 1999. For each January 1st (from 1999 - 2014), I was able to measure how many years a person had in the organization - AND how many years at the current grade/rank.
Next, I took the data for each grade and came up with the subsequent numbers.
So - over the past 15 years, the average number of years a person in Grade 6 had in the organization was "X" with a Std Dev of "Y." I did this for all three grade levels.

So - I have metrics on the three grade levels. One is a discrete distribution (number of total positions at that specific grade level in the organization at any given point in time), and the other is continuous (mean number of years a given Grade has in the unit measured over the past 15 year).

The problem I am trying to solve is: what is the RiskOutput function that will take this data and give me the probability that a random person from the unit will be at a specific grade level, at a given point in time. I want to have metrics for each specific year from 10 years in the organization up to 22 years (which is when most people leave the organization). So - if I were to look at the data under "14 years in the organization" I will be able to tell that a person can expect to have a "X%" chance of being at the Grade 6 level, a "Y%" Chance of being at the Grade 7 level, and a "Z%" chance of being at the Grade 8 level.
I realize this will be a generalized outcome (I won't be doing a regression analysis on such things as behavior, or career advancing choices). It is simply a time-series outcome.

Does this help clarify?
I have set up a lot of data already - I am just stuck on the @RiskOutcome function for the final probability measurement.

I guess a similar type of problem would be this:

Given the average life expectancy of males & females in the USA, Canada, and Sweden - what is the probability that a 90-year old female, chosen at random, will be Swedish (or American, or Canadian)?

The data concepts are the same (the female populations of those three countries have a discrete distribution - in relation to each other) - AND (the females from each country have a different average life expectancy).

Does this help clarify my problem?