## 1 Introduction  
Among statistical process control (SPC) tools, control charts are by far the most widely used method due to the simplicity of understanding them, while at the same time being efficient in detecting defects in production processes [1]. There are two types of control charts: variable or attribute control charts. According to [2], such classification is made according to the type of data being monitored. In variable control charts, the degree of data precision (usually defined by the number of decimal places) and continuous data, such as length, height, mass, time, among others, can be measured. For attribute control charts, data may or may not have some attributes, such as number of nonconforming items or number of nonconformities per lot, thus requiring the use of discrete variables that are countable. When human judgments and subjectivity significantly affect the definition of quality characteristics, traditional control charts should be used. In such a case, the theory of fuzzy sets developed by [3] should be used instead, since it enhances the flexibility of control charts and adds further information about process details, in addition to its performance improvement capability [4]. In scenarios containing several sources of uncertainty regarding the data under analysis, the type-2 fuzzy set approach proposed by [5] should be used, which was mathematically formulated by [6]. Measurement error is a concept related to the difference between a measured value and the reference value of a measurand. As measurement errors cannot be fully corrected, there will always be a portion of doubt associated with measurements, which is represented by uncertainty [7]. The theory of type-2 fuzzy sets is applied in order to model this uncertainty. Type-1 fuzzy logic makes use of uncertainties related to the meanings of words through precise membership functions. Such membership functions, when well defined, are capable of eliminating uncertainties arising from the meanings of words. A membership function of type-2 fuzzy sets, on the other hand, measures uncertainty through the so-called footprint of uncertainty (FOU), which allows working on a higher level of uncertainty. Therefore, if type-2 fuzzy pertinence functions are well defined, type-2 uncertainties are also eliminated and data are restored to type-1 fuzzy numbers [6]. Regarding the performance of fuzzy control charts, [8] presented type-1 fuzzy \(\overline{\text{X}}\)-\(R\) control charts for monitoring the mean and range of univariate processes. Through a performance analysis, the authors observed that fuzzy control charts achieved higher efficiency in detecting special causes compared to traditional control charts. \(\overline{\text{X}}\) and R control charts through the approach presented by [9] allowed implementing exponentially weighted moving average (EWMA) control charts using fuzzy numbers to monitor the average and range of processes. A performance analysis of their proposed control chart through ARL proved to be more efficient than traditional control charts. Furthermore, future research on the use of other performance metrics such as standard deviation of the run length (SDRL) and median of the run length (MDRL) has been suggested. Therefore, this paper proposes a performance analysis of \(\overline{\text{X}}\)-R control charts under the use of interval type-2 fuzzy sets in univariate processes through the average run length (ARL), SDRL and percentile of RL. Equations for control limits using triangular type-2 fuzzy numbers will be presented, and simulations were performed to show the values of ARL, SDRL and percentile of RL as functions of the variation in parameters \(\delta\) (shift), \(\lambda\) (disturbance) and the FOU. Finally, an illustrative example will be presented.