🪁 Non-Parametric-Testing-for-Manufacturing-operations-in-Excel

This repository contains case studies from real-world manufacturing environments, demonstrating how non-parametric tests can be carried out in manufacturing operations using Microsoft Excel including:

1. Mann-Whitney U test

2. Kruskal Wallis Test

3. Mood's Median test

4. Freidman Test

5. 1-Sample sign test

6. 1-Sample Wilcoxon test

        Note: - Non-parametric tests cannot be executed in Excel through straightforward functions. Hence, they require manual calculations within the Excel document
              - For Mann-Whitney U test, users are supposed to refer to U-distribution table to determine the critical value 
   

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⚽️ Non-parametric tests

Non-parametric tests do not make any assumptions about a distribution model where the data could fit. They compare groups of medians using the relative ranks of data within the groups. These graphs may skew right or skew left. Non-parametric tests are used when:

• Data does not follow a normal distribution
• Sample sizes are small or uneven
• Data is ordinal or has outliers
• We want to compare medians or ranks instead of means

These tests are powerful tools for robust, distribution-free inference, in real-world manufacturing scenarios where data violates parametric assumptions

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🏀 Mann-Whitney U Test

Mann Whitney test is a non-parametric test used to compare the center between two unpaired groups. The obtained U has to be equal to or less than the critical value.

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🏈 Kruskal-Wallis Test

The Kruskal-Wallis test is used for testing the source of origin of the samples. It is the only way to analyze the variance by ranks. The medians of two or more samples are compared to fixed the source of origin. It does not assume the normal distribution of the residuals

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⚾️ Mood's Median test

The Mood's Median test is a non-parametric test that is used to test the equality of medians from two or more different population. The test works if:

  - The output (Y) variable is continuous, discrete-ordinal or discrete-count
  - The input (X) variable is discrete with two or more attributes

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🎾 Friedman Test

The Freidman test is a form of non-parametric test that does not make any assumptions on the origin of the sample

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🏉 1-Sample Sign Test

1-Sample sign test is the simplest of all the non-parametric test that can be used instead of 1-sample test:

• Count the no of +ve values
• Count the no. of -ve values
• Test the values

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🥏 1-Sample Wilcoxon test

1-Sample Wilcoxon test is a non-parametric test which is equivalent to 1-sample T.Test and is more powerful than 1-Sample Sign test. It is used to estimate the population median and compare it to target or reference value. It assumes the existing sample is randomly taken from a population

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🏓 Case study: Non-parametric testing of Grinding machine in a steel manufacturing plant

🏏 Objectives

• Test whether two independent samples come from the same distribution (typically when normality can't be assumed) using Mann Whitney U test
• Test to compare three or more independent groups to assess whether their medians differ significantly using Kruskal-Wallis test (alternative to one-way ANOVA)
• Test to determine whether the medians of two or more independent samples are significantly different
• To detect differences in treatments across multiple test attempts when the same subjects are exposed to three or more conditions
• To test whether the median of a population differs from a specified value
• To determine whether the median of a population differs significantly from a hypothesized value, considering not just the direction of difference but also its magnitude

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🏸 Interpretation

1. Situation: The factory operates two machines to carry out Grinding operation. They want to compare the output Width by each machine to determine if the output is uniform to one another

           H₀: Median output widths of Machine A = Machine B
           H₁: Median output widths are different
   

   Inference: Mann Whitney U Test || From the excel analysis, U = 3 < 10 (U_Critical), we can reject H₀. It means that the data is not normally distributed. It can be used instead of 2-sample T.Test if normality/variance assumptions are violated

   Conclusion: There is statistically significant evidence that Machine A and Machine B of Grinding operation have different median output widths. Since A has lower output width comparatively in all ranks, it's likely more efficient

2. Situation: The manufacturing plant uses three different suppliers for steel raw materials: Supplier A, Supplier B, and Supplier C. The Procurement Manager wants to determine if material hardness differs significantly across these suppliers

           H₀: The raw material hardness of all the suppliers are equal
           H₁: At least one supplier's raw material hardness is different
   

   Inference: Kruskal-Wallis Test || From the excel analysis, χ² (H_statistic) = 71.98 > 5.99 (H-critical), we can reject H₀. It means that at least one supplier's material hardness differs meaningfully from the others

   Conclusion: There is a statistically significant difference between the medians of at least one pair of groups

3. Situation: The manufacturing plant operates three resources (A, B, C) in grinding line and want to test if the median cycle time differs significantly between them

            H₀: All the grinding resources maintain equal median cycle time
            H₁: At least one grinding resource cycle time median is different
   

   Inference: Mood's Median Test || From the excel analysis, χ² = 0.16 < 5.99 (χ²_Critical), we fail to reject H₀. It means all the grinding resources maintain equal median cycle time

   Conclusion: There is no statistically significant difference among the medians of all the three grinding resources

4. Situation: The manufacturing plant operates three resources (A, B, C) in grinding line and wants to evaluate whether machine type affects the productivity (units/hour) of operators. Each operator works on all three machines

            H₀: All the operators' productivity remains the same across the machines
            H₁: At least one operator's productivity is different across at least one machine
   

   Inference: Friedman test || From the excel analysis, χ² (F-statistic) = 1105 > 5.99 (F_Critical), we can reject H₀. It means that at least one operator's productivity differs meaningfully from the others

   Conclusion: There is a statistically significant difference between the productivity of at least one operator

5. Situation: The grinding machine that is expected to produce 45 units/hour. The planning manager collected 17 hourly observations and want to know if the machine underperforms or performs consistently

            H₀: Median produce = 45
            Hₐ: Median produce ≠ 45
   

   Inference: 1-Sample sign test || From the excel analysis, p-value = 0.332 > 0.05, we fail to reject H₀. It means that grinding machine is producing around the target median value (45)

6. *Situation: The manufacturing plant wants to validate whether a grinding machine produces maximum sheet thicknesses the differ from the target thickness of 0.756 mm

            H₀: Median MaxThickness = 0.756 mm
            H₁: Median MaxThickness ≠ 0.756 mm
   

   Inference: 1-Sample Wilcoxon Test || From the excel analysis p-value = 0.0021 < 0.05, we can reject H₀. It means that the grinding tool's output significantly differs from 0.756 mm

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🎣 Repository structure

CharacteristicValue4_dataset.xlsx - Analysis

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🥊 Excel functionalities used

• IF()
• IFS()
• COUNTIF()
• COUNTIFS()
• MIN()
• ABS()
• SUMIF()
• RANK.AVG()
• RANK.EQ()
• CHISQ.TEST()
• BINOM.DIST()
• MEDIAN()
• COUNTA()
• UNIQUE()
• PIVOT TABLES
• RAND()
• RANDBETWEEN()
• SIGN()
• ROWS()

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🥋 Requirements

• Microsoft Excel 2016 or later
• Business Statistics, Six Sigma, Matrices, Probability

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"The goal is to turn data into information, and information into insight" - Carly Fiorina