ISE 315: Engineering Statistics
Lecture 1 Handout: Course Introduction and Overview
Instructor: Mansur M. Arief, PhD
Course: ISE 315 - Engineering Statistics
Reference: Montgomery & Runger, Applied Statistics and Probability for Engineers, 6th Ed.
Learning Objectives
After completing this reading, you should be able to:
- Understand the course structure, policies, and expectations
- Explain why statistics is essential for engineering practice
- Identify real-world applications of statistical methods in various industries
- Describe the general statistical approach to problem-solving
- Distinguish between the two main branches of statistical inference
1. Course Overview
1.1 Course Information
| Detail | Information |
|---|---|
| Course Code | ISE 315 |
| Credit Hours | 3 |
| Prerequisites | ISE 205 (Probability) or STAT 319 |
| Semester | 252 |
| Lectures | Sundays and Tuesdays, 12:30 PM – 1:45 PM |
| Location | Building 24, Room 240-1 |
1.2 Required Materials
Textbook: Montgomery & Runger, Applied Statistics and Probability for Engineers, 6th Edition, Wiley
Additional Resources:
- Gradescope: Homework assignments and quizzes
- Blackboard: Announcements, schedules, slides, and solutions
- Course Website (TBA): Supplementary readings, AI tutor, and extra office hours
1.3 About Your Instructor
Mansur Maturidi Arief, PhD
| Background | Details |
|---|---|
| Education | PhD in Mechanical Engineering, Carnegie Mellon University |
| Previous Roles | Research Engineer, Stanford Intelligent Systems Lab; Executive Director, Stanford Center for AI Safety |
| Research Interests | AI safety and certification, decision-making under uncertainty |
| Office | Building 22, Room 219 |
| Office Hours | See Blackboard for schedule |
2. Course Structure and Policies
2.1 Grading Policy
| Component | Weight |
|---|---|
| Attendance and Participation | 5% |
| Homework and Quizzes | 30% |
| Midterm Exam 1 | 20% |
| Midterm Exam 2 | 20% |
| Final Exam | 25% |
| Total | 100% |
2.2 Letter Grade Scale (Tentative)
| Grade | Range | Grade | Range |
|---|---|---|---|
| A+ | 96–100 | C+ | 70–77 |
| A | 90–95 | C | 65–69 |
| B+ | 85–89 | D+ | 60–64 |
| B | 78–84 | D | 50–59 |
| F | Below 49 |
2.3 Attendance Policy
- Regular attendance is expected and will be monitored
- A DN grade may be assigned for excessive absences exceeding 20% of class meetings
- Active participation in class discussions is encouraged
2.4 Academic Integrity
Academic integrity is taken seriously in this course:
- All submitted work must be your own
- Cheating or plagiarism will result in a zero grade and disciplinary action
- When in doubt about what constitutes academic dishonesty, ask!
2.5 Homework Policy
- Assignments are posted weekly and due at the beginning of class
- Late submissions: 20% penalty per day, maximum 2 days late
- Submit your own work—do not copy from classmates or AI tools
- Homework is essential practice; completing it honestly prepares you for exams
2.6 Exam Schedule
| Exam | Coverage |
|---|---|
| Midterm 1 | Chapters 7–10 |
| Midterm 2 | Chapters 10–12 |
| Final Exam | Chapters 12–14 |
Note: Exact dates will be synchronized with other sections. No makeup exams without prior approval and valid documentation.
3. What Will We Learn?
ISE 315 provides the statistical foundation for engineering decision-making. The course is organized into three main parts:
Part 1: Estimation
- Point estimation: How do we best estimate unknown parameters from data?
- Sampling distributions: How do statistics vary from sample to sample?
- Confidence intervals: How do we quantify uncertainty in our estimates?
Part 2: Hypothesis Testing
- One-sample tests: Does the data support a claim about a population parameter?
- Two-sample tests: Are two populations significantly different?
- Goodness-of-fit tests: Does the data follow a hypothesized distribution?
Part 3: Modeling
- Simple linear regression: How do we model relationships between two variables?
- Multiple regression: How do we model relationships involving multiple predictors?
- Design of experiments (introduction): How do we efficiently collect data to answer questions?
4. Why Statistics for Engineers?
Engineers deal with uncertainty every day. Statistical methods provide the tools to make informed decisions despite this uncertainty.
4.1 Quality Control
Engineers constantly ask questions like:
- Is this batch of components within specifications?
- How many defective items should we expect in production?
- When should we adjust the manufacturing process?
Example: A semiconductor manufacturer needs to determine whether a new fabrication process produces chips with acceptable defect rates. Statistical sampling and hypothesis testing allow them to make this decision without inspecting every single chip.
4.2 Process Improvement
Statistical methods help answer:
- Did the new process actually improve yield?
- Which factors have the greatest effect on output quality?
- How should we set process parameters to optimize performance?
Example: An oil refinery wants to maximize gasoline yield. Designed experiments and regression analysis can identify which temperature and pressure settings optimize the cracking process.
4.3 Reliability Engineering
Critical questions in reliability include:
- What is the expected lifetime of this component?
- When should we schedule preventive maintenance?
- How confident are we in our reliability estimates?
Example: An autonomous vehicle company needs to estimate the mean time to failure of LiDAR sensors. Sampling distributions and confidence intervals help them make warranty decisions with quantified risk.
4.4 Design and Testing
Engineers must determine:
- How many samples do we need to detect a meaningful difference?
- Is the new design statistically better than the current one?
- Can we trust the results of our tests?
Example: A safety team evaluating an AI chatbot needs to estimate the rate of harmful responses. Sample size calculations ensure they collect enough data to make reliable safety claims.
5. Real-World Applications
Statistical methods are applied across every engineering domain:
Manufacturing
- Six Sigma quality control: Reducing defects to 3.4 per million opportunities
- Process capability analysis: Ensuring processes meet specifications
- Acceptance sampling: Making accept/reject decisions on incoming materials
Oil & Gas Industry
- Reservoir estimation: Quantifying uncertainty in oil and gas reserves
- Equipment reliability: Predicting failures and optimizing maintenance
- Safety risk assessment: Evaluating probabilities of hazardous events
Supply Chain
- Demand forecasting: Predicting future demand from historical data
- Inventory optimization: Balancing holding costs against stockout risks
- Supplier quality evaluation: Comparing vendor performance statistically
AI & Robotics
- Testing AI systems: Validating safety-critical autonomous systems
- Communicating AI risk: Quantifying and explaining uncertainty in AI predictions
- AI safety: Ensuring AI systems behave reliably under rare conditions
As ISE students, you will use these statistical tools throughout your career!
6. The Statistical Approach
The practice of statistics follows a systematic methodology:
Define Problem → Collect Data → Analyze Data → Interpret Results → Make Decision
6.1 Define the Problem
Clearly state what you want to learn:
- What parameter are you trying to estimate?
- What hypothesis are you testing?
- What decisions will be based on the analysis?
6.2 Collect Data
Design a data collection strategy:
- How will you sample from the population?
- How many observations do you need?
- How will you ensure data quality?
6.3 Analyze Data
Apply appropriate statistical methods:
- Compute point estimates and confidence intervals
- Conduct hypothesis tests
- Fit regression models
6.4 Interpret Results
Translate statistical findings into practical conclusions:
- What do the numbers mean in context?
- How confident are you in the conclusions?
- What are the limitations of the analysis?
6.5 Make Decisions
Use the analysis to inform action:
- Should we change the process?
- Do we accept or reject the batch?
- Is further investigation needed?
7. The Two Branches of Statistical Inference
Statistical inference uses sample data to draw conclusions about populations. There are two main branches:
7.1 Parameter Estimation
Question: “What is the value of the parameter?”
We use sample data to estimate unknown population parameters:
- Point estimation: A single “best guess” for the parameter (e.g., $\hat{\mu} = \bar{x}$)
- Interval estimation: A range of plausible values with a specified confidence level (e.g., $\bar{x} \pm t \cdot \frac{s}{\sqrt{n}}$)
Example: Based on testing 50 sensors, we estimate the mean lifetime is 8,200 hours with a 95% confidence interval of (7,800, 8,600) hours.
7.2 Hypothesis Testing
Question: “Is the claim about the parameter true?”
We formulate competing hypotheses and use data to decide between them:
- Null hypothesis ($H_0$): The default claim (e.g., $\mu = 8000$)
- Alternative hypothesis ($H_1$): The competing claim (e.g., $\mu \neq 8000$)
- Decision: Reject or fail to reject $H_0$ based on the evidence
Example: We test whether a new manufacturing process has changed the mean component lifetime from the historical value of 8,000 hours.
8. From ISE 205 to ISE 315
In your probability course (ISE 205), you learned to reason from parameters to data:
- “If the population mean is $\mu = 50$, what is the probability of observing $\bar{X} > 55$?”
- You started with known parameters and predicted what data might look like
In this statistics course (ISE 315), we reverse the direction—reasoning from data to parameters:
- “Given that we observed $\bar{x} = 55$, what can we infer about $\mu$?”
- You start with observed data and make inferences about unknown parameters
| Course | Direction | Starting Point | Ending Point |
|---|---|---|---|
| ISE 205 (Probability) | Forward | Known parameters | Predicted data |
| ISE 315 (Statistics) | Backward | Observed data | Unknown parameters |
This reversal—called statistical inference—is what makes statistics so powerful for engineering practice.
9. Tips for Success
Do:
- ✓ Attend all lectures: Class participation builds understanding
- ✓ Practice problems regularly: Statistics requires active practice, not passive reading
- ✓ Start homework early: Don’t wait until the night before it’s due
- ✓ Ask questions in class: If you’re confused, others probably are too
- ✓ Visit office hours: Get personalized help when you’re stuck
- ✓ Form study groups: Explaining concepts to others deepens your own understanding
- ✓ Review before each exam: Cumulative review prevents cramming
Don’t:
- ✗ Cram the night before: Statistical reasoning takes time to develop
- ✗ Skip homework: The exam problems will be similar
- ✗ Wait until you’re completely lost to ask for help: Early intervention prevents bigger problems
- ✗ Memorize without understanding: You need to apply concepts to new situations
- ✗ Rely solely on lectures: Reading the textbook and working problems are essential
Statistics requires practice! The more problems you solve, the better you’ll understand. There is no shortcut—work through examples step by step until the reasoning becomes natural.
10. Course Focus Areas
Throughout ISE 315, we will focus on estimating and testing these key parameters:
| Parameter | Description | Point Estimator |
|---|---|---|
| $\mu$ | Population mean | $\bar{X}$ (sample mean) |
| $\sigma^2$ | Population variance | $S^2$ (sample variance) |
| $p$ | Population proportion | $\hat{p}$ (sample proportion) |
| $\mu_1 - \mu_2$ | Difference in means | $\bar{X}_1 - \bar{X}_2$ |
| $p_1 - p_2$ | Difference in proportions | $\hat{p}_1 - \hat{p}_2$ |
11. Summary
Key Takeaways from Lecture 1
-
Course logistics: Understand the grading policy, attendance requirements, and homework expectations. Check Blackboard regularly for announcements.
-
Statistics is essential for engineers: Every engineering discipline involves uncertainty. Statistical methods provide rigorous tools for making decisions under uncertainty.
-
Real-world applications abound: From quality control in manufacturing to safety assessment in AI systems, statistical thinking is central to engineering practice.
-
The statistical approach is systematic: Define the problem, collect data, analyze, interpret, and decide. This framework applies across all applications.
-
Two branches of inference: Parameter estimation asks “what is the value?” while hypothesis testing asks “is this claim true?” Both build on sampling distributions.
-
ISE 315 reverses ISE 205: Probability reasons from parameters to data; statistics reasons from data to parameters. This course teaches you how to make that inference rigorously.
-
Success requires practice: Attend class, start homework early, ask questions, and work through many problems. Understanding builds incrementally through active engagement.
Looking Ahead
In the next lecture, we will begin our study of point estimation and sampling distributions (Chapter 7):
- What makes a good estimator?
- How do sample statistics vary from sample to sample?
- How does the Central Limit Theorem enable inference?
These concepts form the foundation for everything else in the course.
Additional Resources
- Textbook: Montgomery & Runger, Chapter 7 (Point Estimation)
- Blackboard: Course syllabus, schedule, and announcements
- Office Hours: See Blackboard for schedule and location
Welcome to ISE 315! Let’s have a great semester.