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Traditional attribute control charts for nonconformities or defects, such as c or u charts, assume that all defect types are binary in nature. However, some defect types have varying degree of seriousness within them. As a result, the plotted value on the control chart may not capture the true quality status of the product in question. Moreover, in many situations, large products may have multiple types of defects. These defects may be different from one another in terms of their severity. The classification process in attribute inspection tasks for the traditional control charts does not consider the variability within some defect types. In other words, the transition between classes (i.e. from presence to absence of a defect) is sharp. However, determining what constitutes the presence or absence of a defect may be vague or "fuzzy", particularly when dealing with "borderline" situations. Furthermore, when there are multiple defect types, the common characteristic among them is the amount of money spent to correct them so that the product becomes defect-free. The objective of this research is to develop control charts based on modelling the fuzziness within defect types using fuzzy set theory and utilizing cost functions such as Taguchi's quality loss function. The first proposed control chart is designed to control the characteristic (base variable) when there is only one linguistic (fuzzy) defect type to consider. The second control chart is designed to control the rework cost incurred from correcting multiple types of defects. These defect types may either be binary, linguistic, or a combination of both. A variability index control chart is also developed to accompany the cost-based chart so that severity shifts within defect types can be detected. For each chart, formulations of the centerline and control limits for constant and variable sample sizes are presented. Using Monte-Carlo simulation, comparisons with traditional charts and sensitivity analysis have been conducted. The results show that the proposed control charts are superior to the traditional c and demerit systems charts. Finally, research conclusions and recommendations for future research are made.