This is exactly what PingPlotter does - it uses ICMP echo requests / replies and measures latency and packet loss.

Run PingPlotter continuously. Look for periods of high latency volatility (jitter), packet loss, or areas where latency is higher than normal. Use the facilities in PingPlotter to locate the hop that is most likely to contribute to the problem. Depending on where this hop is, take action based on the results you find (that action might be to decrease your internet usage while making a call, or it might be to contact your ISP to have them research the problem).

For some examples of how to do this, see http://www.pingplotter.com/tutorial and look at the "Interpreting results" section.