Need some help modifying script

I have a script that currently runs fine and I need to add or || (or) condition to the if statement and I'm not sure the exact syntax as it relates to the use of brackets.

my current script starts like this:

errLog="/usr/local/website-logs/error.log"
apacheRestart="service httpd restart"
failRegex="exit signal Segmentation fault"
scriptLog="/usr/local/websites-logs/`basename $0`.log"

while true; do
echo "`date` (re)starting control loop"
tail --follow=name --retry -n 0 "$errLog" 2>/dev/null | while read logLine; do
if [[ `echo "$logLine" | egrep "$failRegex"` ]]; then

I want to add an OR condition to my if statement and wondered if this is the correct syntax?

#!/bin/bash

errLog="/usr/local/website-logs/error.log"
apacheRestart="service httpd restart"
failRegex="exit signal Segmentation fault"
failRegex1="server seems busy"
scriptLog="/usr/local/websites-logs/`basename $0`.log"

while true; do
echo "`date` (re)starting control loop"
tail --follow=name --retry -n 0 "$errLog" 2>/dev/null | while read logLine; do
if [[ `echo "$logLine" | egrep "$failRegex"` ]] ||  [[ `echo "$logLine" | egrep "$failRegex1"` ]]; then

---------- Post updated at 12:38 PM ---------- Previous update was at 12:33 PM ----------

and is there some special need to the double brackets in this script I found online?

double square brackets will evaluate condition, and based on true or false flow will work
Single square brackets requires a value to evaluate for eg. if [ $var -eq 0 ]; then ... fi

Your IF syntax will work fine. You can use following to reduce OR:

if [[ `echo "$logLine" | egrep "$failRegex|$failRegex1"` ]]

Seems silly to echo then spawn egrep to see if a variable contains something. bash can do

if [[ $logLine = *$failRegex* ]] || [[ $logLine = *$failRegex1* ]]; then

posix can do

case "$logLine" in
  *"$failRegex"*|*"$failRegex1"*)
    ...
    ;;
esac

much appreciate - I am but a novice - I'll give your code a try!