🎲 1.4 - Probability and Probability Models

Key Question: How can engineers make confident decisions when working with only partial data (a sample)?

Probability models help quantify the risk of making incorrect decisions when only a sample of data is available. These models are essential for quality control, reliability engineering, and process monitoring.

Example Scenario – Wafer Inspection:
A semiconductor plant has 25 wafers in a batch. Only 1 is defective. If we inspect 3 wafers at random, what’s the chance we catch the bad one?

Probability Models Help Engineers:

Case: Process Control Using Acetone Concentration
Suppose a chemical process is designed to maintain acetone concentration at a target level. Engineers take hourly samples. They need to determine whether any shift in concentration is due to natural variation or a real process issue.

Solution: Use control limits based on a probability distribution (e.g., normal) to flag abnormal shifts.
New Example – Emergency Room Staffing:
In a hospital ER, managers must decide how many nurses to schedule each shift. If they overstaff, resources are wasted. If they understaff, patient wait times grow and care may suffer.

Solution: Analyze past arrival patterns (e.g., average number of patients per hour) and fit a probability model, such as a Poisson distribution. Then use that model to predict likely demand ranges and optimize staffing.

Why Probability is Critical:

Bottom Line:
Probability lets engineers make data-based decisions even under uncertainty. In Chapters 2–4, you’ll learn to apply these tools using distributions and sampling theory to control quality, reduce risk, and design better systems.