Answer: Redundant chutes are used rather than back-up chutes because (for a given safety factor) they are lighter.

As an example, let’s approximate that both the weight and the effectiveness of chutes are proportional to the total surface area.

Let’s assume NASA is willing to accept a 1:10,000 failure rate and the failure rate of an individual chute is 1:100.

Design Team A recommends a single chute, with a back-up chute. Each chute weighs 100Kg, for a total of 200Kg

Design Team B recommends 3 chutes, but no back-up. Each chute has half the area of Team A’s chute, for a total of 150Kg

Both designs have a failure rate of 1:10,000. But Team B’s design is 25% lighter. Who gets the contract?

There are many factors which complicate this simplistic analysis. A failed chute could foul the deployment of the backup. Multiple deployments at the same time may increase the failure rate, etc.

Answer: Redundant chutes are used rather than back-up chutes because (for a given safety factor) they are lighter.

As an example, let’s approximate that both the weight and the effectiveness of chutes are proportional to the total surface area.

Let’s assume NASA is willing to accept a 1:10,000 mission failure rate and the failure rate of an individual chute is 1:100.

Design Team A recommends a single chute, with a back-up chute. Each chute weighs 100Kg, for a total of 200Kg

Design Team B recommends 3 chutes, but no back-up. Each chute has half the area (and half the weight) of Team A’s chute, for a total of 150Kg

Both designs have a mission failure rate of 1:10,000. But Team B’s design is 25% lighter. Who gets the contract?

There are many factors which complicate this simplistic analysis. A failed chute could foul the deployment of the backup. Multiple deployments at the same time may increase the failure rate, etc.