how to perform Risk Analysis

Describe how to perform Risk Analysis during software testing.

While a test plan is being created, risks involved in testing the product are to be taken into consideration along with possibility of their occurrence and the damage they may cause along with solutions; if any. Detailed study of this is called as Risk Analysis.
Some of the risks could be:
New Hardware
New Technology
New Automation Tool
Sequence of code delivery
Availability of application test resources
Identify and describe the risk magnitude indicators: High, Medium and Low
High magnitude means the effect of the risk would be very high and non-tolerable. Company may face severe loss and its reputation is at risk. Must be tested.
Medium: tolerable but not desirable. Company may suffer financially but there is limited liability or loss of reputation. Should be tested.
Low: tolerable. Little or no external exposure. Little or no financial loss. Company’s reputation unaffected. Might be tested.
Three perspectives of Risk Assessment: Effect, Cause and Likelihood.
To assess risk by Effect, identify a condition, event or action and try to determine its impact.
To asses risk by Cause is opposite of by Effect. Begin by stating an undesirable event or condition and identify the set of events that could have permitted the condition to exist.
To asses risk by Likelihood is to determine the probability that a requirement will not be satisfied.

What is risk analysis? What does it have to do with Severity and Priority?

Risk analysis is a method to determine how much risk is involved in something. In testing, it can be used to determine when to test something or whether to test something at all. Items with higher risk values should be tested early and often. Items with lower risk value can be tested later, or not at all. It can also be used with defects. Severity tells us how bad a defect is: "how much damage can it cause?" Priority tells us how soon it is desired to fix the defect: "should we fix this and if so, by when?"
Defects with High Severity and Priority are tested first.