超过一定时间的文件的Linux shell脚本

我有一个MySQL数据库的备份，备份文件的名称中有时间和日期，如下所示：

daily_amavisd_2016-10-01_05h28m_Saturday.sql.gz 
daily_amavisd_2016-10-02_05h28m_Sunday.sql.gz 
daily_amavisd_2016-10-03_05h28m_Monday.sql.gz

我需要一个脚本来检查/backup/amavisd/daily文件夹中最旧的文件是否不超过一周。如果超过一周，它应该给我状态备份失败，如果不超过一周，它应该给我状态备份确定

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有人能帮我使用shell脚本吗？

如果您想打印文件名和状态，这可以帮助您

#!/bin/bash

find /backup/amavisd/daily/ -name '*.gz' -exec bash -c '
file_date=$(echo $1|cut -f 3 -d '_');
start_date=$(date +"%Y-%m-%d" -d "-7 days");
    if [[ "$file_date" > "$start_date" ]]; then
        echo "$1: backup OK"
    else
        echo "$1: backup failed"
    fi' -- {} \;

Eg

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非常感谢。但我只需要在最后1个状态OK或NotOK，因为我将在其他软件中使用该脚本。如果一个文件超过1周，则状态为NOT OK。

user@host:/tmp/test$ ./test.sh
backup/amavisd/daily/daily_amavisd_2016-10-01_05h28m_Saturday.sql.gz: backup OK
backup/amavisd/daily/daily_amavisd_2016-10-03_05h28m_Monday.sql.gz: backup OK
backup/amavisd/daily/daily_amavisd_2016-10-02_05h28m_Sunday.sql.gz: backup OK
backup/amavisd/daily/daily_amavisd_2016-10-07_05h28m_Monday.sql.gz: backup OK
backup/amavisd/daily/daily_amavisd_2016-09-07_05h28m_Monday.sql.gz: backup failed