A painting of vertical bars sweeping from red through orange and yellow into teal

Week: Failure Modes & Effects Analysis

Recitation 2: Distributions & Descriptive Statistics

Practicing Descriptive Statistics

Tim Fraser, PhD

Research Associate, Systems Engineering
Cornell University

SYSEN 5300: Systems Engineering & Six Sigma

for Design and Operation of Reliable Systems

Risk Analysis with a particular emphasis on risk assessment and risk characterization. The key modeling tools we will study are how to conduct Failure Modes and Effects Analyses including the development of fault trees and event trees under uncertainty.
Modeling Reliability Modeling component and system reliability, including the use of physical acceleration models. Reliability is the ability of a system or component to perform its required function under stated conditions for a specified period of time. Reliability analysis is an element of risk analysis. In general risk analysis is substantially broader including explicit treatment of the consequences of different types of failures.

Quality Control Six sigma and statistical process control for quality control and improvement. A key process in the operation of reliable systems is the development and effective use of mechanisms to detect when performance is deteriorating so that corrective action can be taken.
System Improvement Improvement and optimization of system design for reliability. This will lead us to study design of experiments and the estimation of response surfaces that can greatly catalyze innovation, problem solving, and discovery.

Today's Class

Louisiana Parishes Practice
Product Comparison Practice

Painted stacked bars in cream, yellow, pink and magenta

Practice Exercises

Recitation 2

Louisiana Parishes

A corgi puppy's head peeking in from the side

Load Data

Use the readr package to load most types of data into R.

la_parishes.csv is a dataset of Louisiana Parishes (counties) describing their outcomes after the 2005 Hurricane Katrina disaster.

# Load packages
library(readr)
library(dplyr)

# Read in your dataset
la = read_csv("workshops/la_parishes.csv")

# View la parishes data
la %>% glimpse()
la %>% head()

Satellite view of Hurricane Katrina over the Gulf of Mexico

Analyze your vector in the la_parishes dataset
- Make a histogram with hist()
- Calculate size, mean, median, min, max, & range
- What do they tell you about your distribution?
- Summarize your findings in 2 sentences.

Analyze your vector in the la_parishes dataset
- Calculate standard deviation, variance, coefficient of variation, & standard error
- What do they tell you about your distribution?
- Summarize your thoughts in 2 sentences

Analyze your vector in the la_parishes dataset
- Calculate skewness and kurtosis.
- What do they tell you about your distribution?
- Summarize your thoughts in 1 sentence.

Analyze your vector in the la_parishes dataset
- Calculate parameters for each distribution (except weibull)
- Simulate 100 observations each.
- Visually compare your vector with the simulated data.
- Which matches your vector best?

Practice Exercises

Recitation 2

Product Comparisons

Cheese!

Three firms are producing cheese in Upstate New York.

Firms randomly selected units of cheese of the production line (?) and evaluated how long it took for that cheese to mold, defining that as time to failure, measured in hours.

Cheese!

a = c(50, 70, 125, 235, 230, 200, 180, 260, 300, 500, 275, 280)

b = c(300, 380, 250, 50, 55, 57, 60, 65, 100, 150, 250, 200,
      150, 175, 225, 200, 225, 250)

c= c(400, 300, 400, 300, 350, 200, 250, 300, 330, 375)

Using your powers of descriptive statistics, evaluate these distributions. Which firm would you buy your cheese from? A, B, or C?