PROBLEM:

The engineer is interested in a particular gas (C2F6) and gap (0.80 cm) and wants to test four levels of power settings: 160W, 180W, 200W, and 220W. The engineer decided to test five wafers at each level of power. The experiment is replicated % times; runs are made in random order.

# Create a vector for the Power levels
power <- c(160, 160, 160, 160, 160,           # Five entries for power level 160
           180, 180, 180, 180, 180,           # Five entries for power level 180
           200, 200, 200, 200, 200,           # Five entries for power level 200
           220, 220, 220, 220, 220)           # Five entries for power level 220

# Create a vector for the corresponding observations
observation <- c(575, 542, 530, 539, 570,     # Observations corresponding to power 160
                 565, 593, 590, 579, 610,     # Observations corresponding to power 180
                 600, 651, 610, 637, 629,     # Observations corresponding to power 200
                 725, 700, 715, 685, 710)     # Observations corresponding to power 220

# Combine the power and observation vectors into a data frame
data <- data.frame(Power = power, Observation = observation)

# Print the data frame to verify its structure
data
##    Power Observation
## 1    160         575
## 2    160         542
## 3    160         530
## 4    160         539
## 5    160         570
## 6    180         565
## 7    180         593
## 8    180         590
## 9    180         579
## 10   180         610
## 11   200         600
## 12   200         651
## 13   200         610
## 14   200         637
## 15   200         629
## 16   220         725
## 17   220         700
## 18   220         715
## 19   220         685
## 20   220         710

The data provided is a table showing observations of power output (in watts) across five trials. There are four different power levels: 160W, 180W, 200W, and 220W. For each power level, there are five observations, indicating possible measurements of power output in different trials.

EXPLORATORY DATA ANALYSIS

Descriptive Statistics:

# Load the dplyr library for data manipulation
library(dplyr)

# Calculate descriptive statistics grouped by Power levels
summary_stats <- data %>%
  group_by(Power) %>%                        # Group the data by the 'Power' column
  summarize(
    Mean = mean(Observation),                # Calculate the mean of 'Observation' for each power level
    Median = median(Observation),            # Calculate the median of 'Observation' for each power level
    Min = min(Observation),                  # Find the minimum 'Observation' for each power level
    Max = max(Observation),                  # Find the maximum 'Observation' for each power level
    SD = sd(Observation),                    # Calculate the standard deviation of 'Observation'
    Q1 = quantile(Observation, 0.25),        # Calculate the 1st quartile (25th percentile) of 'Observation'
    Q3 = quantile(Observation, 0.75),        # Calculate the 3rd quartile (75th percentile) of 'Observation'
    IQR = IQR(Observation)                   # Calculate the interquartile range (IQR) of 'Observation'
  )

# Print the summary statistics table
print(summary_stats)
## # A tibble: 4 × 9
##   Power  Mean Median   Min   Max    SD    Q1    Q3   IQR
##   <dbl> <dbl>  <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1   160  551.    542   530   575  20.0   539   570    31
## 2   180  587.    590   565   610  16.7   579   593    14
## 3   200  625.    629   600   651  20.5   610   637    27
## 4   220  707     710   685   725  15.2   700   715    15

The table above suggests that as power increases, the mean and median observation values increase, indicating a positive relationship between power and observations. Also, observations are generally symmetrical at 180W and 220W, with slight skewness at 160W and 200W. Further, standard deviation and IQR are fairly stable, with minor increases in variability at 200W compared to 160W and 180W, but a lower standard deviation at 220W suggests more consistent observations at higher power.

Boxplot of Observations by Power Level

# Create a boxplot of Observations grouped by Power levels
boxplot(data$Observation ~ data$Power, 
        main = "Boxplot of Observations by Power Level",  # Title of the boxplot
        xlab = "Power (W)",                              # Label for the x-axis (Power levels)
        ylab = "Observation",                            # Label for the y-axis (Observation)
        col = "lightgreen",                              # Set the fill color of the boxplots to light green
        border = "darkgreen")                            # Set the border color of the boxplots to dark green

From the boxplot, we can see that at 160W, the observations are more tightly distributed around the lower range (530–575). At 180W, the observations show a slightly wider range (565–610). At 200 W, there is a noticeable increase in the spread of observations, with a wider range (600–651). At 220 W, the observations are again more spread out but tend to be in a higher range (685–725).

Scatterplot of Power vs Observation:

# Plot a scatterplot of Power vs Observation
plot(data$Power, data$Observation, 
     main = "Scatterplot of Power vs Observation",  # Title of the plot
     xlab = "Power (W)",                           # Label for the x-axis (Power)
     ylab = "Observation",                         # Label for the y-axis (Observation)
     pch = 19,                                     # Use solid circles as the plotting symbol
     col = "darkgreen")                            # Set the color of the points to dark green

# Add a regression line to the scatterplot
abline(lm(Observation ~ Power, data = data),       # Fit a linear model (lm) to the data and add the regression line
       col = "red")                                # Set the color of the regression line to red

The scatterplot indicates a positive relationship: as the power increases, the observation also increases. A linear trend line has been added to the scatterplot, showing that the relationship between power and observation is approximately linear.

Conclusion:

Overall, the descriptive statistics suggest that as power increases, so does the central tendency of the observations. Also, the scatterplot line suggest a positive linear relationship between power and observation. Moreover, the boxplot indicates increasing variability in observations with higher power levels.