Time plots In applications like process control, detecting trends - - PowerPoint PPT Presentation

ST 370 Probability and Statistics for Engineers

Time plots In applications like process control, detecting trends and other changes in a process is important. Plotting data values against the time at which the observation was made is a key step. Example: chemical concentrations

conc <- read.csv("Data/Table-15-03.csv")$Concentration; plot(conc, type = "b") # Target concentration is 100 grams per liter: abline(h = 100, col = "green") # Lower Control Limit is 96 grams per liter: abline(h = 96, col = "red") # Plot cumulative deviations from target: plot(cumsum(conc - 100), type = "b")

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ST 370 Probability and Statistics for Engineers

Example: global temperature

temperature <- read.csv("Data/Temperature.csv"); temperature <- ts(temperature, start = 1850); plot(temperature) # Fit a simple model: tempModel <- read.csv("Data/TempFit.csv"); tempModel <- ts(tempModel, start = 1850); matplot(time(tempModel), tempModel, type = "l", lty = 1)

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ST 370 Probability and Statistics for Engineers

Scatter plots When exploring the association of one variable with another, such as the pull-strength and wire-length variables, the scatter plot is an important tool:

# wireBond <- read.csv("Data/Table-01-02.csv") pairs(wireBond)

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ST 370 Probability and Statistics for Engineers

Quantile Plots In a sample of observed data values, the ordered values are called the

• rder statistics. Each order statistic is a quantile of the sample.

The R function ppoints() shows the fraction represented by each

• rder statistic.

Probability theory gives a theoretical quantile for each fraction, under the assumption that the sample follows a given distribution, usually the normal distribution. The quantile-quantile plot is a graph of the sample quantiles against the theoretical quantiles. The R function qqnorm() makes Q-Q plots. Example: Compressive strengths

qqnorm(alloy)

4 / 4 Descriptive Statistics Q-Q plots