Re: Risk assessment technique that fits the context of organization
IEC 31010 is an entire catalog of risk assessment techniques. The keywords in your paraphrased extract do not identifiably match with any one topic in the standard.
If it comes down to basics, then yes what Rob says is the first point. Choose the right tool (or assessment technique) for the job you are doing.
Only you know the context in which your organisation operations (swiftness of operations, necessary detail, regulatory requirements). Keeping that in mind, the following steps will lead you to
Table A.1 of IEC 31010 shows you where techniques are applicable (either strongly recommended or simply feasible) or whether they are regarded as a poor choice or impossible, and thus stated as "not applicable". Using it as a starting point:
1. Know what each phase (identification, analysis (consequence/effect, probability, level of risk/severity), evaluation) of risk management is about.
2. Determine which phase you are in, and/or will be covering in the future. Life-cycle and regulatory requirements play a heavy role in this.
3. Then read the more detailed sections on the applicable techniques.
4. Choose the ones that suits your situation best. Some even have specific standards explaining them more in depth (e.g.
FMEA, FTA).
5. Execute.
Do note that though FMEA is stated to be strongly applicable in any phase, this doesn't automatically make it the best all of the time (especially since a specific failure mode can have complex and even independent failure mechanisms/causes, and diverse effects).
Sometimes using a different tool when you're entering a different phase is simply easier, more efficient or more effective depending on what you are managing the risk of.