A new distribution-free generally weighted moving average monitoring scheme for detecting unknown shifts in the process location
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Cites methods from "A new distribution-free generally w..."
...To evaluate the performance of the proposed schemes from an overall performance perspective, the expected ATS (EATS) and the expected SDTS (ESDTS) are used because users tend not to know beforehand what exact shift value(s) is targeted – see for example, Khoo et al. (2019) and Mabude et al. (2020)....
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Cites background from "A new distribution-free generally w..."
...Additional works (Arun et al., 2019; Larkin & Privalov, 2019; Jimmy et al., 2020; Mabude et al., 2020; Uniyal et al., 2020) also investigated the impact of various product quality issues on manufacturing systems, fabrication planning, and supply-chain systems....
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References
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"A new distribution-free generally w..." refers background or methods in this paper
...Otherwise, it is said to be out-of-control (OOC), see for example Montgomery (2005). An efficient monitoring scheme should be sensitive enough to detect small shifts in any type of process as quickly as possible....
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...Illustrative example To illustrate the implementation and application of the proposed W-GWMA monitoring scheme, two sets of data on the inside diameters of piston rings manufactured by a forging process are used (Montgomery, 2005, page 223)....
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...Proposed monitoring schemes for the Montgomery (2005)’s piston ring data...
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...Otherwise, it is said to be out-of-control (OOC), see for example Montgomery (2005)....
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"A new distribution-free generally w..." refers methods in this paper
...In an effort to further improve the EWMA-based schemes to monitor the process mean, Sheu and Lin (2003) proposed the generally weighted moving average (GWMA) scheme (denoted as 𝑋-GWMA), which is a general version of both the EWMA scheme and the Shewhart-type scheme (this is shown in Section 2)....
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...Following a similar procedure as Sheu and Lin (2003) and Sheu and Hsieh (2009), it can be shown without loss of generality that the W-GWMA statistic in Eq....
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...The Proposed W-GWMA monitoring scheme Following Sheu and Lin (2003)’s idea, the charting statistic of the W-GWMA monitoring scheme, denoted 𝐺𝐸 , is given by 𝐺𝐸 = 𝑃(𝑀 = 1) 𝑊 + 𝑃(𝑀 = 2) 𝑊 + ⋯ + 𝑃(𝑀 = 𝑡) 𝑊 + 𝑃(𝑀 > 𝑡) 𝑊 , (3) with 𝑃(𝑀 = 𝑡) = 𝑞( ) − 𝑞 and 𝑃(𝑀 > 𝑡) = 𝑞 , where 𝑀 is the number of samples until the first occurrence of event 𝐴 since the previous occurrence of event 𝐴, 𝑃(𝑀 = 1) represents the weight value for the current sample, 𝑃(𝑀 = 2) is the weight value for the previous sample, 𝑃(𝑀 = 𝑡) is the weight value for the first sample and 𝑃(𝑀 > 𝑡) is the weight value for the target value of the process mean, which is considered to be the unconditional IC expectation of 𝑊 given by 𝑊 = 𝐸(𝑊 |𝐼𝐶) = 𝜇 ....
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...Following Sheu and Lin (2003)’s idea, the charting statistic of the W-GWMA monitoring scheme, denoted GE , is given by...
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...The Proposed W-GWMA monitoring scheme Following Sheu and Lin (2003)’s idea, the charting statistic of the W-GWMA monitoring scheme, denoted 𝐺𝐸 , is given by 𝐺𝐸 = 𝑃(𝑀 = 1) 𝑊 + 𝑃(𝑀 = 2) 𝑊 + ⋯ + 𝑃(𝑀 = 𝑡) 𝑊 + 𝑃(𝑀 > 𝑡) 𝑊 , (3) with 𝑃(𝑀 = 𝑡) = 𝑞( ) − 𝑞 and 𝑃(𝑀 > 𝑡) = 𝑞 , where…...
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121 citations
"A new distribution-free generally w..." refers background or methods in this paper
...Note that the proposed W-GWMA scheme is more flexible than the W-EWMA scheme because of the extra design parameter, 𝛼, which can be set according to the operator’s expectations....
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..., q = 1 − λ) and α = 1, the W-GWMA scheme is equivalent to Li et al. (2010)’s WEWMA scheme; however, when q = 0 and α = 1, the GWMA scheme is equivalent to the Shewhart WRS scheme (denoted as W-Shewhart)....
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...Conclusion and recommendations A new distribution-free GWMA monitoring scheme based on the WRS, 𝑊 statistic, has been proposed in order to improve and expand Li et al. (2010)’s W-EWMA scheme....
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...In Case E, we found 𝐿 = 2.9402 so that the W-GWMA (0.9, 1) and W-EWMA (0.1) yield an attained 𝐴𝑅𝐿 value of 501.26....
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...The above measures are very useful in the design and implementation of the W-GWMA monitoring scheme as well as Li et al. (2010)’s EWMA scheme....
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