## 3 Methodology
### Data Preparation
#### 3.3.1 Handling Missing Values  
Missing values, defined by the absence or unavailability of data for certain variables or observations within a dataset, can arise from a variety of factors such as errors during data collection or data that are inherently unobtainable. The presence of missing values significantly impacts the trustworthiness and accuracy of data analysis and modelling. Therefore, effectively addressing missing values is of paramount importance in the field of data mining. According to [29], the occurrence of missing values can be classified into three distinct types:  
* Missing Completely at Random (MCAR) refers to situations where the occurrence of missing values for a particular attribute is completely unrelated to any other data, whether observed or missing. In other words, the probability of an instance having a missing value is independent of the values of any variables, whether they are recorded or missing. * Missing at Random (MAR) indicates that the occurrence of missing values is related to the observed data but not to the values that are missing. The probability of a value being missing is dependent on the values of other variables within the dataset. MAR suggests that the missingness can be systematically estimated or predicted based on the available information from other observed variables, thus allowing for a structured approach to handle these missing values in analyses. * Not Missing at Random (MAR) indicates a scenario where the likelihood of an instance having a missing value for a particular attribute is influenced by the value of that attribute itself. In other words, the occurrence of missing values is dependent on the specific values that are missing. This dependency suggests that the missing data are related to inherent qualities of the data, making the handling of these missing values particularly challenging, as the reasons behind the missingness need to be explicitly modelled or accounted for in the analysis. The investigation conducted to identify missing values in the collected dataset revealed that these were predominantly due to gaps in the company's records. Notably, missing values were consistently linked to specific materials, with the same \"Material_Ref\" showing identical missing attributes across all related entries. This pattern strongly suggests that the missing values are directly related to the inherent characteristics of the materials, stemming from an absence of essential information in the company's records. This consistent occurrence underscores the need to address these gaps to improve data completeness and reliability. In the scenario where missing values are found exclusively in the \"Foil_thickness\" column for certain materials, it becomes apparent that the occurrence of missing values is dependent on the characteristics of the material attribute itself. This observation indicates that the missing data in the dataset are not randomly distributed but are instead directly related to the attributes of the materials. Consequently, this pattern of missingness is formally classified as NMAR, where the probability of missing data is influenced by the values that are missing. This classification is crucial for informing the appropriate strategies for handling missing data in the analysis. The only column in the dataset that exhibited missing values was the \"Foil_thickness\" column, which stores the micron measurement of the foil wrapping for each pallet. As shown in Table 2, the proportion of missing values within the \"Foil_thickness\" column, compared to the total number of observations in the dataset, was found to be low. This indicates that, while missing data are present, they affect only a small fraction of the overall dataset. Based on the findings in [PERSON] et al. [30] and [PERSON] et al. [31], it can be assumed that, in datasets with a minimal occurrence of missing data, typically, when the missing rate is below 10% or 15%, excluding missing data does not significantly impact the outcomes of data mining or analysis.