Monitoring of Short Series of Dependent Observations Using a XWAM Control Chart

Hryniewicz, Olgierd; Kaczmarek-Majer, Katarzyna

doi:10.1007/978-3-319-75295-2_13

Cited by 4 publications

(20 citation statements)

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“…An interesting comparison of the behavior of the classical Shewhart X chart for individual observations and the Shewharl X chart for residuals has been presented in the recent paper of the authors of this paper [16] . They have performed an extensive simulation expe1iment in which N = 50000 (200000 in the case of independent observations) charts were designed, and for each of them NR = 5000 process runs of maximum MR= 500000 observations (curtailment value) were simulated.…”

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confidence: 99%

“…Below, we present the results of that comparison only for the case of the average rnn length (average time to the alarm signal) ARL. In Table 1 taken from [16] we present the comparison of the following characteristics of the probability distribution of ARL: average of the distribution of ARL's (AvgARL), standard deviation of the distribution of ARL's (StdARL), median the distribution of of ARL's (MedARL), skewness of the distribution of ARL's (SkewARL). All the presented results have been obtained for independent observations.…”

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confidence: 99%

“…In Tables 2-3, taken from [16], we present the results of similar simulation experiments for autocorrelated data when the autocorrelation is described by the autoregression model of the first order -AR(I) model. Four cases of the strength of dependence are considered, described by the autocorrelation coefficients equal to -0.9 , -0.5 , 0.5 , and 0.9, respectively.…”

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confidence: 99%

“…This paper presents further development of the ideas described in [15] and [16) . In particular, a new and much simpler method for the construction of the XWAM chart (with only one model that is alternative to the estimated one) has been proposed.…”

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confidence: 96%

“…Their algorithm appears to be highly competitive when compared to the best available algorithms used for the prediction in short time series. In their recent papers [15) and [ 16) they have adopt a similar approach for the construction of a new Shew hart-type control chart for residuals, named the XWAM chart.…”

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Monitoring Series of Dependent Observations Using the sXWAM Control Chart for Residuals

Hryniewicz

Kaczmarek-Majer

2018

Studies in Systems, Decision and Control

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Control charts for monitoring residuals are the main tools for statistical process control of autocorrelated streams of data. X chart for residuals calculated from a seties of individual observations is probably the most popular, but its statistical characteristics are not satisfactory, especially for charts designed using limited amount of data. In order to improve these characteristics Hryniewicz and Kaczmarek proposed a new chart for residuals, XWAM chart, using the concept of weighted model averaging. Unfortunately, the design of the XWAM chart is rather complicated, and requires significant computational effort. In this paper we propose its simplification, named sXWAM chart, which is simpler to design, and in some practically important cases has similar statistical properties. 1 Introduction Control charts are nowadays the most frequently used tool of Statistical Quality Control (SQC). They were introduced in the 1920th by Shewhart who at that time worked for an American company Western Electric. Since that time many statistical procedures which have their origins in Shewhart's works have been developed, and their usage in practice is known under a common name of Statistical Process Control (SPC). In the majority of applications control charts are used for monitoring production processes when long series of quality-related measurements are observed. In such a case a well grounded mathematical theory have been established. Later on, control charts have been also applied in cases of short production runs. In

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confidence: 99%

Section: (1)mentioning

confidence: 99%

Section: (1)mentioning

confidence: 99%

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confidence: 96%

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confidence: 99%

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