Extended maximum generally weighted moving average control chart for monitoring process mean and variability

Methods in Ranking Fuzzy Numbers: A Unified Index and Comparative Reviews

“…Their subbranches have also been established; for example, fuzzy differential equations [6][7][8][9][10][11][12][13][14] and fuzzy integrodifferential equations [15][16][17][18][19][20][21][22] are of fuzzy mathematics while fuzzy-number ranking, the focus of this paper, is of fuzzy decision-making. Specifically, based on its feasible mathematical capacity for representing the imprecise information in practice, we have observed many successful cases spreading in disparate disciplines, such as robot selection [23], supplier selection [24], logistics center allocation [25], facility location determination [26], choosing mining methods [27], manufacturing process monitoring [1,2,[28][29][30][31], cutting force prediction [32], firm-environmental knowledge management [33,34], green supply-chain operation [35], and weapon procurement decision [36]. Apparently, to find their best alternative, those decisive problems are evaluated under resource constraints and with to some extent linguistic preference of multiattribute, which is realized from users' perspectives, as well as subjective quantification of multiple characteristics, which is assessed from decision-makers [2,3,[37][38][39].…”

Fuzzy MaxGWMA chart for identifying abnormal variations of on-line manufacturing processes with imprecise information

“…The EWMA chart is widely used to detect small shifts in process mean and it has successfully attracted the unceasing attention of many researchers as in the reviews by Xie (1999), Han and Tsung (2004), Eyvazian et al (2008), , Zhang et al (2010), Sheu et al (2012). In the sense of simultaneously monitoring the shifts of the process mean and variance, Chan et al (1990) introduced a single chart with the mean and variability plotted separately to identify the shifts; Domangue and Patch (1991) proposed an omnibus EWMA chart; Gan (1995) recommended a joint scheme consisting of a two-sided EWMA mean chart and a two-sided EWMA variance chart and found that it can perform well for several out-of-control circumstances; Chao and Cheng (1996) came up with a semicircle chart for joint monitoring the shifts of process mean and variance; Gan (1997) presented a two-dimensional chart with an elliptical incontrol region for the sample variance EWMA (s 2 -EWMA) against the sample mean EWMA ( x-EWMA).…”

“…Because MG i is non-negative, Sheu et al (2012) proposed using only upper control limit (UCL) to monitor the MG i . The UCL i for the ith subgroup is determined by…”

“…Sheu and Lin (2003) created the generally weighted moving average (GWMA) chart which can detect small shifts much quicker than the EWMA can. By combing the advantages of the MaxEWMA chart and GWMA chart, Sheu et al (2012) proposed a new chart called the maximum generally weighted moving average (Max-GWMA) chart which was found to be more sensitive under abnormal variations of on-line manufacturing processes than the MaxEWMA chart (Sheu et al, 2012). Therefore, in this paper, based on the fuzzy set theory, we develop a Fuzzy-MaxGWMA (F-MaxGWMA) chart, an extension of the MaxGWMA chart, to well adapt to the fuzzy environment where both the randomness and fuzziness of imprecise sample data (fuzzy numbers) are taken into consideration.…”

“…To further advance the surveillance performance of EWMA, several of its modified statistical schemes have been proposed (see Section 2 for detail). Amid those charting techniques, the latest proposed control chart called maximum generally weighted moving average (MaxGWMA) is found superior due to its outstanding diagnostic abilities at swiftly alerting abnormal variations in the manufacturing process (Sheu et al, 2012).…”