πŸ”§ Example 1.1 – Pull-off Force Variability

An engineer is designing a nylon connector for use in an automotive engine. The concern is that the connector might fail if its pull-off force is too low. The engineer considers a wall thickness of 3/32 inch and builds 8 prototypes. Their pull-off forces (in pounds) are:
[12.6, 12.9, 13.4, 12.3, 13.6, 13.5, 12.6, 13.1]
These values are **not all the same**, indicating there is variability in the measurements. Therefore, pull-off force is treated as a random variable.
Model: X = ΞΌ + Ξ΅

ΞΌ = true (constant) average pull-off force
Ξ΅ = random disturbance (e.g., test error, material difference, etc.)

🎯 Dot Diagram of Wall Thickness = 3/32 inch

πŸ” Considering an Alternative Design

The engineer thinks 13.0 lbs average pull-off force may be too low, so tries a thicker wall: 1/8 inch. New 8 prototypes give:
[12.9, 13.7, 12.8, 13.9, 14.2, 13.2, 13.5, 13.1]
The average increases to β‰ˆ 13.4 lbs. Does this mean the thicker wall design is better? Let’s compare both samples visually.

πŸ“Š Dot Diagram Comparison

πŸ€” Questions for Engineering Decision

πŸ“ˆ Population vs. Sample: Statistical Inference

These 8 connectors are a sample. The engineer wants to infer performance of **all future connectors** β€” the population. This reasoning is called: statistical inference.
Measurements from a sample are used to estimate values for the population.
This leads to **sampling error**, which can be controlled by good design and adequate sample size.