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.)
π― Dot Diagram of Wall Thickness = 3/32 inch
π 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 13.4 lbs. Does this mean the thicker wall design is better? Letβs compare both samples visually.
π Dot Diagram Comparison
π€ Questions for Engineering Decision
Is the difference in average pull-off force real or due to random variability?
Are 8 samples enough to make a confident decision?
What risks are involved if the change has no real effect but adds cost?
π 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.