Markov Analysis
Markov Analysis is a probabilistic technique that aids in the process of decisionmaking by providing a probabilistic description to various outcomes. It is however not a recommended analysis, it does not provide recommended decisions. Thus, Markov Analysis is not an optimization technique but a descriptive technique resulting in probabilistic representation.
Characteristics of Markov Analysis
Markov Analysis is applicable to systems which evolve from one state to another over time. The probability of such a change is independent of the history of the system. Meaning, all the information you require has been captured in the present state and one does not require the knowledge of states prior to that to analyze the future movement of the system.
The most commonly known application of Markov Analysis is the brand switching problem. Wherein one analyses the behavior of a customer towards shifting to another brand. This transition probability is independent of his past affiliations.
Let us try and understand the concept through a similar problem. Suppose we have two clothing brands, Vevi and Kevi, and a customer who buys new clothes every other month.
Now suppose the customer purchases Vevi’s products in month0. Let the probability of shifting to Kevi in month1 be 0.3 and that of staying with Vevi be 0.7. Similarly, the probability of shifting from Kevi toVevi be 0.1 and of staying with Kevi be 0.9.
We can represent this information as follows:
This Month 
Next Month 

Vevi 
Kevi 

Vevi  0.7  0.3 
Kevi  0.1  0.9 
This representation is called Transition Matrix and the probabilities represented are called Transition Probabilities. This is a Markov Process and we are doing a Markov Analysis.
It is to be understood that the summation of any row equals 1. As the events are Mutually Exclusive & Collectively Exhaustive (MECE). Meaning, in any given month the customer has to buy from either Vevi or from Kevi. Supposing, only two clothing brands exist in our hypothetical world.