Which curve demonstrates the relationship between product failures over time?

The bathtub curve is the correct answer because it specifically illustrates the typical failure patterns of products throughout their life cycle. This curve consists of three distinct phases:

1. Early Failure Phase: This area represents the initial stage of a product's life where failures may occur due to manufacturing defects or issues related to design, often referred to as "infant mortality." In this phase, the failure rate is high but declines significantly over time as defective products are weeded out.

2. Normal Life Phase: Following the initial failures, the product enters a period of stable reliability where the failure rate remains relatively low and constant. This phase represents the expected operational life of the product, where it performs effectively.

3. Wear-Out Phase: Eventually, as the product ages, it reaches a point where the failure rate increases again due to wear and tear, signaling the end of its useful life. This is where maintenance or replacement becomes necessary.

The bathtub curve effectively captures these dynamics, making it an essential tool for understanding product reliability and failure rates over time. It assists quality managers in planning maintenance schedules and improving product design and manufacturing processes.

In contrast, the other curves mentioned do not represent this specific relationship between product failures and time. The