Thousands of additional engines will have to be inspected for fan-blade cracks in an order prompted by the April 17 engine failure on a Southwest Airlines Co. flight that resulted in the death of a woman who was partially sucked out of a window.

The Federal Aviation Administration on Tuesday published a directive ordering U.S. airlines operating the CFM56-7B engine to conduct a round of inspections on fan blades that have made at least 20,000 flights. An emergency inspection order issued April 20 had focused on engines with 30,000 or more flights.

The directive was based on a service bulletin issued by engine maker CFM International Inc., a partnership between General Electric Co. and France’s Safran SA, and covers more than 3,700 engines, the FAA estimated.

The order was an attempt to prevent additional failures on one of the most popular jet turbines in the world. Fan-blade cracks are “likely to exist or develop in other products of the same type design,” the FAA said in the order.

A fan blade broke loose over Pennsylvania on the Southwest flight on April 17, spraying metal shards that shattered a window and caused the plane to lose pressure. A woman who was partially sucked out of the plane died.

The FAA’s latest order is focused on fan blades with specific serial numbers that have made at least 20,000 flights. Because airlines sometimes move blades from one engine to another and don’t have to keep track of each one’s use, blades with an undetermined number of flights are also subject to the inspections, the FAA said. The inspections must be completed by the end of August.

After those inspections, blades must be rechecked after 3,000 flights. Airlines must use devices capable of detecting cracks beneath the surface, such as ultrasonic sensors.

Southwest, the largest operator of the engine in U.S., has already committed to inspecting all fan blades in its fleet by mid-May, spokeswoman Brandy King said. American Airlines will perform inspections as part of routine maintenance and expects no schedule disruptions, according to spokesman Ross Feinstein.