The maximum number of items for comparison is related to the inventory numbers of the item.  If the inventory is down to the number indicated, then an alert will appear on the shop indicating that inventory is low.  The following tutorial will show you how to set the number used by the Prestashop 1.5 to determine when to indicate that inventory is low.  It will also show how to disable this feature.

Set the Inventory Number for Low Stock Warning in Prestashop 1.5

1. Login to the Administration Panel as an Administrator
2. Hover over the menu bar where it says PREFERENCES, and then click on PRODUCTS in the drop down menu. Scroll down the list of options and look for Preferences: Products.  Select Maximum Number of Items for Comparison in the menu as shown below:
   
   
   
   
3. Type in the number of items you wish to use to alert your customers when inventory is low.  Use '0' to disable the feature.
4. Select the green SAVE button in the top right corner to save your changes.

When the option is enabled, the following screenshot indicates what you will see if you were to select a product where inventory is low: