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.

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Lean Six Sigma with Python — Kruskal Wallis Test

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

This approach usually follows five 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 (a software widely for LSS experts) in the Analysis step.

The idea is to use statistical tools to test hypotheses and improve the performance metrics of a specific process.

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SUMMARY
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 experiments with operators
2. Analysis of Variance (ANOVA)
Verify the hypothesis that training impacts productivityANOVA assumptions are not verified
3. Kruskal-Wallis test
Confirm that the hypothesis can be generalized
III. Conclusion

Problem Statement


Scenario

You are the Continuous 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.

A 3D layout of a warehouse VAS process. It shows various workstations, including areas for label printing and sewing. The warehouse racks are filled with cartons, and workstations are aligned
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, operators need to print a label in the local language and perform label sewing.

A close-up of a clothing care label with instructions for washing and care. It includes symbols for hand washing, avoiding bleach, warm ironing, not dry cleaning, and not tumble drying

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.

A 3D layout of label sewing stations in a warehouse VAS process. Four sewing stations are aligned along racks, each station equipped for label sewing. The layout emphasizes the distribution a
4 workstations for label sewing — (CAD Model by Author)

You can find a YouTube version of this article with animations in the link below.

Impact of training your workforce

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

Question
Does the training have a positive impact on operator productivity?

Hypothesis
The training has a positive impact on VAS operators' productivity.

Experiment
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.

A diagram showing the process to evaluate the impact of warehouse operator training on productivity using Kruskal Wallis Test with Python. Two groups of operators are randomly selected: one g

Data Analysis

Exploratory Data Analysis

You can download the CSV file containing the experiment results from my GitHub repository.

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

Box Plot

Box plot comparing the productivity (time per batch) of trained versus untrained operators. The plot shows significantly lower median times for trained operators, indicating improved producti

Based on the sample data, the median and mean are considerably lower for operators who received training.

Hypothesis
The training reduces the average batch time.

CodeMinitab

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

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: 20.173692
p-value is below 5%

CodeMinitab

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
Q-Q plot showing standardized residuals versus theoretical quantiles to check the normality assumption of residuals in an ANOVA analysis. Most data points follow the red diagonal line, but th

Answer: No

  • There are no outliers or irregularities
Line plot of residuals plotted in sequence to check for patterns or irregularities over time. The plot shows frequent oscillations, indicating that residuals fluctuate and do not follow a con

Answer: No

Conclusion
ANOVA requirements are not met.

We need another method to confirm that the training actually impacts operators' productivity.

CodeMinitab

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

Kruskal-Wallis test

If your sample data fails to meet ANOVA requirements, you can use the 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%

Conclusion

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

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

CodeMinitab

Menu Stats > Non-parametric > Kruskal Wallis > Graphs > Four in one
Do you want to implement it?
🔗
You can find the full code in this Github repository: Link

Conclusion

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If you have any question, feel free to ask it here: Ask a Question

This data-driven approach provided sufficient evidence to convince your management to invest in workforce training.

You provided 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 who is using data analytics to improve logistics operations and reduce costs.

If you’re looking for tailored consulting solutions to optimize your supply chain and meet sustainability goals, feel free to contact me.

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