On all major appliances, part of the serial number contains the date it was manufactured.
When I started doing expert witness work in the late 1990's, there were four major appliance manufacturers. Now there are only two:
In 2006, Whirlpool purchased Maytag.
In 2014, Electrolux purchased the appliance division of GE.
Sears doesn't manufacture any appliances. The first three digits of the model number specifies the manufacturer. Although the Kenmore model number is different than the manufacturer's, the code for the serial numbers is the same as the manufacturer's.
This list is in numerical order and more comprehensive and detailed: Detailed Kenmore List
I started doing forensic engineering work in the late 1990's. If I was looking at an appliance, on an insurance claim, the first question the adjuster had, was how old was the appliance. The insurance adjuster wanted to make sure that the appliance manufactured date was not past the "Statue of Repose". A Statute of Repose is similar to a Statute of Limitation. The appliance manufactures have lobbied state legislatures to pass laws that limit their responsibility for subrogation damages based on the age of an appliance. The manufacturer's argument is that if a product has lasted for ten years, then it is not defective in design, manufacturing or materials. Difference states have difference time limits, but ten years is the average. On the surface this sounds reasonable, but design defects often go undetected for a number of years. For example, in the 2014, there was class action lawsuit settlement against Electrolux for design defects in clothes dryers manufactured from 2002 through 2011. All states do not have Statue of Repose Laws. Two of states I do work in Mississippi and Louisiana do not have Product Liability Statute of Repose Laws, and the law passed by the Alabama Legislature has been found unconstitutional. The Statute of Repose for all 50 states are listed in the referenced tables: