On the misleading signals in simultaneous schemes for the mean vector and covariance matrix of multivariate i.i.d. output

Ramos, Patrícia Ferreira; Morais, Manuel Cabral; Pacheco, Antònio; Schmid, Wolfgang

doi:10.1007/s00362-015-0663-5

Cited by 7 publications

(13 citation statements)

References 29 publications

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“…When it comes to out‐of‐control scenarios, we follow Ramos et al and Morais et al, and assume that the magnitude of the shifts in each component of the mean vector is the same, ie,

boldδ = {false[δ_{i} false]}_{i = 1, . . ., p} = {false[δ false]}_{i = 1, . . ., p}

; all the in‐control variances

σ_{0, i i}

false(i = 1, \dots, p false)

and all the in‐control covariances

σ_{0, i j}

false(i, j = 1, \dots, p, i \neq j false)

are equal to

σ_{0}^{2}

and

σ_{0}^{2} ρ_{0}

(respectively), where

ρ_{0}

stands for the target value of the common correlation coefficient.…”

Section: Comparative Studymentioning

confidence: 99%

“…We did not study the scenarios considered by Ramos et al and Morais et al where (c) all the variances increase from

σ_{0}^{2}

σ^{2}

and the correlation coefficients shift from

ρ_{0}

ρ = 0

; (d) the in‐control covariance matrix is equal to the identity matrix, all the variances increase from

σ_{0}^{2} = 1

σ^{2}

, and all the correlations shift from

ρ_{0} = 0

ρ

. The decision of not including these two out‐of‐control scenarios has also to do with the fact that they seem less realistic than (a) and (b).…”

Section: Comparative Studymentioning

confidence: 99%

“…Another possibility for future work is to investigate how the adoption of exponentially weighted moving average (EWMA) charts may impact on the values of the PMS of types III and IV. Keep in mind that, according to Ramos et al, the joint scheme resulting from the adoption of EWMA control statistics based on

T^{false(1 false)}

and

U^{false(1 false)}

does not perform necessarily (resp. does perform) better than its Shewhart‐type counterpart, the joint scheme 1, when it comes to the frequency of MS of type III (resp.…”

Section: Final Remarksmentioning

confidence: 99%

“…There are fundamentally two types of joint schemes for

bold-italicμ

and

𝚺

. On the one hand, the schemes make use of a single control chart to monitor both parameters; see, for example, Spiring and Cheng, Chen et al, Khoo, Chen and Thaga, Yeh and Lin, Zhang et al On the other hand, the most popular joint schemes that result from running simultaneously two individual charts, one for

bold-italicμ

and another one for

𝚺

, such as the ones discussed by Chen and Thaga, Reynolds and Cho, Hawkins and Maboudou‐Tchao, Machado and Costa, Reynolds and Stoumbos, Zhang and Chang, Costa and Machado, Reynolds and Cho, Ramos et al, Ramos, Ramos et al, Morais et al…”

Section: Introductionmentioning

confidence: 99%

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Misleading signals in joint schemes for the mean vector and covariance matrix

Morais

Schmid

Ramos

et al. 2020

Quality & Reliability Eng

Self Cite

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In multivariate statistical process control, it is recommendable to run two individual charts: one for the process mean vector and another one for the covariance matrix. The resulting joint scheme provides a way to satisfy Shewhart's dictum that proper process control implies monitoring both process location and spread. The multivariate quality characteristic is deemed to be out of control whenever a signal is triggered by either individual chart of the joint scheme. Consequently, a shift in the mean vector can be misinterpreted as a shift in the covariance matrix and vice versa. Compelling results are provided to give the quality control practitioner an idea of how joint schemes for the mean vector and covariance matrix are prone to trigger misleading signals that will likely lead to a incorrect diagnostic of which parameter has changed.

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“…When it comes to out‐of‐control scenarios, we follow Ramos et al and Morais et al, and assume that the magnitude of the shifts in each component of the mean vector is the same, ie,

boldδ = {false[δ_{i} false]}_{i = 1, . . ., p} = {false[δ false]}_{i = 1, . . ., p}

; all the in‐control variances

σ_{0, i i}

false(i = 1, \dots, p false)

and all the in‐control covariances

σ_{0, i j}

false(i, j = 1, \dots, p, i \neq j false)

are equal to

σ_{0}^{2}

and

σ_{0}^{2} ρ_{0}

(respectively), where

ρ_{0}

stands for the target value of the common correlation coefficient.…”

Section: Comparative Studymentioning

confidence: 99%

“…We did not study the scenarios considered by Ramos et al and Morais et al where (c) all the variances increase from

σ_{0}^{2}

σ^{2}

and the correlation coefficients shift from

ρ_{0}

ρ = 0

; (d) the in‐control covariance matrix is equal to the identity matrix, all the variances increase from

σ_{0}^{2} = 1

σ^{2}

, and all the correlations shift from

ρ_{0} = 0

ρ

. The decision of not including these two out‐of‐control scenarios has also to do with the fact that they seem less realistic than (a) and (b).…”

Section: Comparative Studymentioning

confidence: 99%

T^{false(1 false)}

and

U^{false(1 false)}

does not perform necessarily (resp. does perform) better than its Shewhart‐type counterpart, the joint scheme 1, when it comes to the frequency of MS of type III (resp.…”

Section: Final Remarksmentioning

confidence: 99%

“…There are fundamentally two types of joint schemes for

bold-italicμ

and

𝚺

bold-italicμ

and another one for

𝚺

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Misleading signals in joint schemes for the mean vector and covariance matrix

Morais

Schmid

Ramos

et al. 2020

Quality & Reliability Eng

Self Cite

View full text Add to dashboard Cite

show abstract

“…output (eg, see the works of Ramos et al); and multivariate normal i.i.d. processes . As far as one has investigated, the PUNS have only been addressed by Ralha et al for univariate and bivariate normal i.i.d.…”

Section: Misleading and Unambiguous Signalsmentioning

confidence: 99%

GARCH processes and the phenomenon of misleading and unambiguous signals

Sousa

Morais

Okhrin

et al. 2018

Appl Stoch Models Bus & Ind

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In finance, it is quite usual to assume that a process behaves according to a previously specified target generalized autoregressive conditionally heteroscedastic process. The impact of rumors or other events on this process can be frequently described by an outlier responsible for a short‐lived shift in the process mean or by a sustained change in the process variance. This calls for the use of joint schemes for the process mean and variance. Since changes in the mean and in the variance require different actions from the traders/brokers, this paper provides an account on the probabilities of misleading and unambiguous signals of those joint schemes, thus adding insights on their out‐of‐control performance.

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Effect of Measurement Error on Joint Monitoring of Process Mean and Variability under Ranked Set Sampling

Ghashghaei

Bashiri

Amiri

et al. 2016

Quality & Reliability Eng

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In this paper first we apply ranked set sampling (RSS) procedure in joint monitoring of both process mean and variance. Then, we study the effect of measurement error on joint monitoring of process mean and variance when simple random sampling (SRS) as well as RSS procedure is used. The results prove that the measurement error can seriously deteriorate the ability of the control chart in detecting all out-of-control scenarios. The results also represent that using RSS procedure can improve the ability of the monitoring scheme in detecting mean shifts, variance shifts as well as joint shifts either measurement error exists or not. In other words, RSS procedure can reduce the adverse effect of measurement error on detecting ability of joint monitoring scheme. After that, we utilize multiple measurements at each sample point when both SRS and RSS procedures are used. We investigate the effect of parameters in the covariate model thorough a sensitivity analysis. Finally, the applicability of the proposed control charts is illustrated using a real case of the piston rings in an automotive engine manufactured by a forging process.

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On the misleading signals in simultaneous schemes for the mean vector and covariance matrix of multivariate i.i.d. output

Cited by 7 publications

References 29 publications

Misleading signals in joint schemes for the mean vector and covariance matrix

Misleading signals in joint schemes for the mean vector and covariance matrix

GARCH processes and the phenomenon of misleading and unambiguous signals

Effect of Measurement Error on Joint Monitoring of Process Mean and Variability under Ranked Set Sampling

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