Please check the following  invention , which provides a signal quality index which is a single parameter that includes all the information from several different signal quality parameters.

https://www.google.ch/patents/WO2008058268A1?cl=en

I guess that there is not an universal definition for the signal quality index. Such indices are used in different scientific areas to explain some characteristics of determined signals or sometimes, in combination with other signals. Therefore, the defined SQI could be related with signal strength (i.e., power peak) but in my opinion, you will not find any formal definition relating them.

Article Multimodal heart beat detection using signal quality indices

Dear Md Rakibul;

For first part question "Signal quality index" you can see :

-Signal Quality Indices and Data Fusion for Determining Clinical Acceptability of Electrocardiograms

www.robots.ox.ac.uk/~gari/.../IOP_ECG_SQI_Clifford_et_al.pdf

-Signal-Quality Indices for the Electrocardiogram and Photoplethysmogram: Derivation and Applications to Wireless Monitoring

ieeexplore.ieee.org/iel7/6221020/6363502/06862843.pdf...

For the second part "How to find signal strength form SQI " you can see

-Measuring Parameters for speech quality in cellular networks ...

www.academia.edu/.../Measuring_Parameters_for_speech_quality...

-Drive-Test Basic Radio Parameter - TelecomStudy18

telecomstudy18.blogspot.com › GSM

best regards

As Martín Martínez Villar stated, I don't think there is a unique definition of a signal quality index. However, if you consider for example the field of (biomedical) signal processing, by a signal quality index you usually mean a value between 0 and 1 (or 0 and 100%) that indicated how "good" (free from noise and other artifacts) the signal of interest is.