X-MR control chart for autocorrelated fuzzy data using D p,q -distance

Abstract

A control chart is a tool for investigating whether the variation in a production process is random or assignable. X − MR control chart is a binary control chart on which average values of process and moving range between observations are used to discover the variability in the process. In an ordinary control chart, the data are crisp values but sometimes, the data are generated as vague and uncertain values because of some of environmental conditions and other factors. In such cases, fuzzy sets theory is a useful tool for analyzing data. On the other hand, the assumption of independence between observations cannot be accepted because the probability of false warning will increase if the data are autocorrelated and their correlation is ignored. In this article, we will discuss the construction of fuzzy control charts for autocorrelated fuzzy observations and employment of ranking method in order to find out whether the observations are in or out of control. In fact, by using defined D p,q -distance between fuzzy numbers, we calculate their variance, covariance, and autocorrelation coefficient. The autocorrelation coefficient is used in order to modify the limit of control chart. By using D p,q -distance, we present a new approach for constructing control charts.

Attribute Control Chart Construction Based on Fuzzy Score Number

“…In this case study, the parameters were set as . According to Formulas (6), (7), (11), and (12), we obtain the results shown in Table 1.…”

“…In this case study, the parameters were set as α = 0.8 and β = 0.3 in terms of Formulas (10) and (11). The upper and lower control limits, 6.2, 5.8 and 6.7, 5.3, were the right and left endpoints of α-cut and β-cut of process mean fuzzy number S (5, 6, 7), respectively, according to Formulas (12) and (13).…”

“…A sample size of 5 was taken randomly and the scoring triangular fuzzy numbers were S 1 (5.5, 6.3, 6.8), S 2 (4.6, 5.6, 6.6), S 3 (3, 6, 9), S 4 (3, 7, 8.5), and S 5 (6.5, 7.5, 8.5). According to Formulas (6), (7), (11), and (12), we obtain the results shown in Table 1. Step 4: Build a fuzzy control chart for control.…”

“…Some indirect approaches were also proposed to build different types of control charts, for example, Shu et al [10] constructed fuzzy and R control charts based on the fuzzy dominance between the fuzzy averages and variances, and Gildeh et al [11] used Dp,q-distance between fuzzy numbers to calculate their variance, covariance, and autocorrelation coefficient, and then used the autocorrelation coefficient to modify the limits of the control chart. Zarandi et al [12] constructed a fuzzy control chart for different process shifts by adjusting the membership function parameters.…”

Interval Type-2 Fuzzy c-Control Charts: An Application in a Food Company

“…Poongodi and Muthulakshmi (2015) used α-cut approach for analysing the fuzzy queueing model via fuzzy control charts in their paper. Gildeh and Shafiee (2015) investigated the effects of autocorrelation on fuzzy average and moving range control charts. Wang and Hyrnıewıcz (2015) considered a nonparametric Shewhart chart for fuzzy data.…”