One way to measure vulnerability at https://doi.org/10.1061/(ASCE)NH.1527-6996.0000290 including at the household level, but vulnerability as a process:

(a) https://www.acme-journal.org/index.php/acme/article/view/866

(b) https://doi.org/10.1007/s11069-016-2294-0

(c) https://doi.org/10.1007/s13753-015-0038-5

(d) https://doi.org/10.1111/area.12457

(e) https://jpopsus.org/full_articles/disaster-vulnerability-by-demographics

(f) http://trauma.massey.ac.nz/issues/2011-3/AJDTS_2011-3_03_Lewis.pdf

This link may be useful for your query. Article Assessment of climate change vulnerability in Chiti area of ...

There is information here https://www.atsdr.cdc.gov/placeandhealth/svi/index.html used by the Center for Disease Control (CDC) and the Agency for Toxic Substance and Disease Register (ATSDR) in the USA to produce a social vulnerability index for people to different stressors. It is based on US census data and uses data such as:

- Socioeconomic status (below poverty, unemployed, income, education level)

- Household composition & disability (aged 65 or older, aged 17 or younger, older than age 5 with a disability, single-parent households)

- Minority status & language (minority, speak English “less than well”)

- Housing type & transportation (multi-unit structures, mobile homes, crowding, no vehicle, group quarters)

However, there are many other ways to assess the social and economic vulnerability of households. One of the main drivers as to which measure you decide to use will be what data you have readily available at a household level (see the list above for some of the common variables which are required) .

Vulnerability to a household/inhabitation may be due to various risk/hazard and other factors and may depend upon time and local geo-environmental setting. It may vary in space and time depending upon various factors, be it anthropogenic changes being rendered to local geo-environment by the residents/local society concerned or be it situations such as extreme events.

Vulnerability: A generally applicable conceptual framework for climate change research

Social vulnerability indicators in disasters: Findings from a systematic review