For stability testing on the Wordpress you can use some useful tools:
1. WebPageTest
This is one of the most helpful tools available online to help you test the performance of your website. It runs your site from multiple locations around the globe using real browsers and at real consumer connection speeds.
The only disadvantage this site is that you sometime have to wait in queue for other tests to be completed.
http://www.webpagetest.org/
2. Pingdom
Pingdom speed testing is not only free, but also gives you full information about your site’s performance including load time, page size, and a detailed analysis of page. You can also measure how much time it takes to load all the elements on a specific page, you can then use that information to speed up your website.
Other features include testing from multiple locations, performance grade & tips, ability to share the results with your friends, and more.
Apart from all the great features, Pingdom also saves your performance history, so you can review it later and see how things change over time.
http://tools.pingdom.com/fpt/
3. GTMetrix
Another great tool for measuring your site’s performance and fantastic tool to have in your arsenal. This site not only gives you all the useful information you need to develop a faster and more efficient website, but also compresses the images that are slowing down your site for you.
This feature is quite useful, but if you have a ton of images, then you would be better off with Smush.it WordPress plugin.
http://gtmetrix.com/
Also you can use WordPress Split Testing Tools.
If you’re using WordPress, then it’s worth considering a tool designed specifically for the platform. While some of the tools in our last roundup (such as Google Content Experiments and Optimizely) also work with WordPress, here are a few more.
1. AB Press Optimizer
AB Press Optimizer allows you to test variations of page elements such as images and buttons and content, such as headlines and text on a self-hosted WordPress site. To use it, you need the plugin plus the ability to use shortcodes (though you can use PHP if you wish).
You can run and get real time reporting on unlimited experiments with unlimited visitors for the $39 personal license, though you will have to upgrade if you want additional support.
https://abpressoptimizer.com/
2. AB Theme Testing
If you’re running a WordPress site, sometimes you need to get back to design basics and test a couple of themes. That’s where AB Theme Testing is useful. It integrates with Google Analytics so you can see your data in your Analytics account. This plugin costs $19. The developers have used it to tweak their own site, as this case study shows.
https://premium.wpmudev.org/project/ab-theme-testing/
3. Simple Page Tester
Simple Page Tester says it’s an SEO friendly plugin that allows users to setup quick split tests. It works well with caching plugins and is available for free. You’ll need to upgrade to premium to work with custom post types, PHP template tags, Javascript and shortcodes and to get more in-depth analytics.
https://simplepagetester.com/