Quality Charts

• Run charts are valuable when

  • to look at data over time in a simple way
  • starting a project with no baseline data and/or have few points of data (<12)
  • do not need in depth analysis of the process being charted
  • have limited statistical expertise available

• As the project is progressed, if we have 12+ points of data and some statistical expertise, SPC charts can be used. SPC charts are like run charts with the addition of upper and lower control limits based on statistical calculations. These limits allow for more robust statistical analysis.

• Control charts (SPC) are valuable when

  • starting a project and have baseline data (at least 12 points)
  • have progressed in a project and have 12+ points of data and would like greater undersanding of the process
  • are interested more robust statistical processes for identifying special cause variation
  • have statistical expertise available

Run chart

Four rules are used to help interpret run charts by detecting non-random patterns (i.e. signals) in the data.

1. A run of 6 or more consecutive points above or below the centre line (a shift).

2. A trend of 5 or more consecutive points all going up or down.

3. Too few or too many runs

• A run is a series of points in a row on one side of the centre line (median). Too few or too many runs is a signal of a non-random pattern.
• To determine the number of runs count the number of times the line connecting the data points crosses the centre line and add 1.
• Consult Table to determine whether the number of runs is within the expected range, or whether there are too few or too many (indicating a non-random pattern).

4. An astronomical data point (an obviously different value that everyone would agree is highly unusual)

Control chart

Data visualization

Numerical data

• Continuous data is numerical data that can be measured
• Discrete data is represented by exact values that result from counting

Line charts

• to illustrate trends over time, line charts connect data points to reveal patterns and fluctuations (Refer to Quality charts)

Histogram

• to use for continuous data and distribution analysis
• to show the frequency distribution of values in a dataset.
• to be drawn with bin widths and number of bins. Contiguous bars representing intervals or bins that span from one number to another)

Boxplot

• to describe statistical summaries such as median, quartiles, and outliers, aiding in data distribution analysis

Scatterplot

• to showcase relationships between two continuous variables, identifying patterns and outliers through scattered data points.
• Regression analysis is scatterplot with regression lines, forest plots, heatmaps and coefficient chart

Categorical data

• Categorical data are data forms that are in categories and describe characteristics, or qualities, of a category

Bar chart

• to use for categorical data and group comparisons
• to compare values across different categories

Pie chart

• to display parts of a whole, pie charts offer a simple way to understand proportions and percentages

Pareto chart

• is one of 7 basic tools of quality
• is a chart that contains both bars and a line graph, where individual values are represented in descending order by bars, and the cumulative total is represented by the line.
• In order to lower/ increase the amount of … by 80%, it is sufficient to solve the first … issues.

Statistical Tests

Machine Learning

• Unsupervised Learning: to discover hidden patterns or structures in data
• Supervised Learning: for tasks that require predicting a specific output from input data with known labels
• Semi-supervised Learning: when there is a limited amount of labelled data available
• Deep Learning: or Neural Networks (fundamental algorithm), not rely on domain experts but mimics the iterative transmission of information in the human brain to automatically learn representations of data

Supervised Learning | Classification

Supervised Learning | Regression

Logistic Regression | Model Evaluation metrics

• AIC: the smallest AIC provides the best model
• AUC (area under the ROC curve): measures the entire two-dimensional area underneath the entire ROC curve (receiver operating characteristic curve is a graph showing the performance of a classfication model at all classification thresholds). AUC ranges [0,1], is the probability that the model ranks a random positive example more highly than a random negative, the closer to 1 the more correct predictions
• predict: predict the values based on the previous data behaviors and thus by fitting that data to the model
• plogis: Logistic Cumulative Distribution Function
• Cox and Snell R square: Analysis_Survival_Cox Regression. The coefficients in a Cox regression relate to hazard; a positive coefficient indicates a worse prognosis and a negative coefficient indicates a protective effect of the variable with which it is associated. It assume that the effects of the predictor variables upon survival are constant over time and are additive in one scale
• nagelkerke: a measure of goodness of fit in logistic regression analysis, a modification of the Cox and Snell R Square (likelihood ratio test statistic, an alternative index of goodness of fit related to the R2 value from linear regression). Ranges [0,1], closer to 1 indicating a better fit of the model. However, Nagelkerke R Square cannot be interpreted as easily. A common rule of thumb (<= 0.2: weak relationship, 0.2-0.4: moderate, >= 0.4: strong relationship). It’s important to note that the interpretation of Nagelkerke R Square should be taken with caution and should be supplemented by other measures of model fit, such as the Hosmer-Lemeshow test, AIC
• confusionMatrix: matrix between actual and predicted values
• vif = 1/(1-Ri^2) = 1/tolerance. Vif >4 or tolearance <0.25: multicollinearity might exist; vif >10 or tolerance <0.1: signigicant multicollinearity that needs to be corrected. Vif interpret if model has problems estimating the coefficient
• regTermTest: Wald tests and working likelihood ratio (Rao-Scott) tests assesses whether all coefficients associated with a particular regression term are zero (or have other specified values). It is particularly useful as a substitute for anova when the model is not fitted by maximum likelihood

Unsupervised Learning | Clustering

Unsupervised Learning | Dimension Reduction

Artificial Intelligence

RPA