Lean Six Sigma with Python — Kruskal Wallis Test

How to replace Minitab with Python to perform Kruskal Wallis Test evaluating the impact of training on warehouse operators’ productivity

Lean Six Sigma with Python — Kruskal Wallis Test

How to replace Minitab with Python to perform Kruskal Wallis Test evaluating the impact of training on warehouse operators’ productivity

Article originally published on Medium.

Lean Six Sigma (LSS) is a method based on a stepwise approach to process improvements.

This approach usually follows 5 steps (Define, Measure, Analyze, Improve and Control) for improving existing process problems with unknown causes.

In this article, we will explore how Python can replace Minitab (Software widely used by LSS experts) in the Analysis step to test hypotheses and understand what could improve the performance metrics of a specific process.

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I. Problem Statement
Can we improve the operators' productivity by giving them a training designed by R&D team?
II. Data Analysis
1. Exploratory Data Analysis
Analysis with Python sample data from experiment with few operators
2. Analysis of Variance (ANOVA)
Verify the hypothesis that training impacts productivity
ANOVA assumptions are not verified
3. Kruskal-Wallis test
Confirm that the hypothesis can be generalized
III. Conclusion

I. Problem Statement

1. Scenario

You are the Continous Improvement Manager of a Distribution Center (DC) for an iconic Luxury Maison focusing on Fashion, Fragrances and Watches.

The warehouse receives garments that require final assembling and value-added service (VAS) during the inbound process.

Example of Job-Shop with 4 lines for Value Added Services in a Distribution Center of a Luxury Brand — (CAD Model by Author)

For each dress received your operators need to print a label in the local language and perform label sewing.

Example of label — (Image by Author)

In this article, we will focus on the improvement of label sewing productivity. Labels are distributed to the operators in batches of 30 labels.

The productivity is calculated based on the time (in seconds) needed to finish a batch.

4 workstations for label sewing — (CAD Model by Author)
Edit: You can find a Youtube version of this article with animations in the link below.

2. Impact of training your workforce

With the support of the R&D team, you designed training for the VAS operators to improve their productivity and reduce quality issues.

Does the training have a positive impact on the productivity of operators?

The training has a positive impact on the productivity of VAS operators.

Randomly select operators and measure the time per batch (Time to finish a batch of 30 labels in seconds) to build a sample of 56 records.

Data-driven analysis to test our hypothesis — (Image by Author)
You can find the full code in this Github repository: Link

II. Data Analysis

1. Exploratory Data Analysis

You can download the results of this experiment in this CSV file to run the whole code on your computer (here).

56 records
35 records of operators without training
21 records of operators with training

Box Plot

Box Plot of Experiment Results — (Image by Author)

Based on the sample data, we can see that the median and the mean of the is considerably lower for the operators who had training.

The training reduces the average time per batch.


Menu Graph > Box Plot > Simple > 1 Y with Groups

2. Analysis of Variance (ANOVA)

In this scenario, we want to check if the training (Variable X) is impacting the total time per batch (Variable Y).

Because X is a categorical variable (Training = Yes/No) and Y is numerical, the appropriate method is ANOVA.

ANOVA is a statistical method used to check if we can generalize the difference of means seen in the sample data to the entire population.

Step 1: Calculate the p-value

Source: Training
ddof: 11
ddof: 245.267
F: 17.1066
p-unc: 0.000151308
p: 20.173692p-value is below 5%


Menu Stats > ANOVA > One-Way

Step 2: Validate the assumptions of ANOVA

Based on the p-value, we know that the difference of mean is real and not due to random fluctuation.

However, before jumping to a conclusion we need to check that the ANOVA assumptions are satisfied

  • Residuals are naturally distributed
Distribution of Residuals — (Image by Author)

Answer: No

  • There are no outliers or irregularities
Versus Order — (Image by Author)

Answer: No

ANOVA requirements are not met, we need another method to confirm that the training actually impacts operators' productivity.


Menu Stats > ANOVA > One-Way > Graphs > Four in one

3. Kruskal-Wallis test

If your sample data fails to meet ANOVA requirements, you can use Kruskal-Wallis Test to check if the difference in means is due to random fluctuation.

statistic = 54.99
pvalue = 1.205e-13
p-value is below 5%


The p-value is below 5% so we can conclude that the difference of means is statically significant.

We can confirm that the training has a positive impact on the productivity of the operators.


Menu Stats > Non-parametric > Kruskal Wallis > Graphs > Four in one

III. Conclusion

This data-driven approach gave you enough elements to convince your management to invest in workforce training.

You brought enough insights with a moderate effort of experimentation by generalising patterns from sample data using statistics.

About Me

Let’s connect on Linkedin and Twitter, I am a Supply Chain Engineer that is using data analytics to improve logistics operations and reduce costs.


[1] ANOVA Analysis of Variation, Ted Hessing, Six Sigma Study Guide, link
[2] Scheduling of Luxury Goods Final Assembly Lines with Python, Samir Saci

Optimize Warehouse Value Added Services with Python | Samir Saci
Use Linear Programming to Increase your Production Capacity for the Final Assembly of Luxury Products