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

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.

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

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.

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.

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

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

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.

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

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.

Hypothesis
The training reduces the average time per batch.

CodeMinitab

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

CodeMinitab

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

Answer: No

• There are no outliers or irregularities

Answer: No

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

CodeMinitab

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.

Conclusion

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.

CodeMinitab

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.

References

[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

Samir SaciSamir Saci