Control Chart Limits for Monitoring Process Mean Based on Downton's Estimator

Adeoti, Olatunde Adebayo; Olaomi, John Olutunji; Adekeye, Kayode S.

doi:10.1002/qre.1909

Cited by 6 publications

(7 citation statements)

References 14 publications

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“…For normally distributed processes, D is an unbiased estimator of

σ

. Control charts based on D showed superiority over R ‐ and S ‐based charts considering nonnormal processes 20,24 Mean absolute deviation ( MD ) based on absolute deviations from median: This is defined as

M D = \frac{1}{n} \sum_{i = 1}^{n} |x_{i} - \tilde{x}| .

…”

Section: Dispersion Estimatorsmentioning

confidence: 99%

Efficient homogeneously weighted dispersion control charts with an application to distillation process

Nassar

Aldosari

Adeoti

2021

Quality & Reliability Eng

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Monitoring disturbances in process dispersion using control chart is mostly based on the assumption that the quality characteristic follows normal distribution, which is not the case in many real‐life situations. This paper proposes a set of new dispersion charts based on the homogeneously weighted moving average (HWMA) scheme, for efficient detection of shifts in process standard deviation (σ). These charts are based on a variety of σ estimators and are investigated for normal as well as heavy tailed symmetric and skewed distributions. The shift detection ability of the charts is evaluated using different run length characteristics, such as average run length (ARL), extra quadratic loss (EQL), and relative ARL measures. The performance of the proposed HWMA control charts is also compared with the existing EWMA dispersion charts, using different design parameters. Furthermore, an illustrative example is presented to monitor the vapor pressure in a distillation process.

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“…For normally distributed processes, D is an unbiased estimator of

σ

M D = \frac{1}{n} \sum_{i = 1}^{n} |x_{i} - \tilde{x}| .

…”

Section: Dispersion Estimatorsmentioning

confidence: 99%

Efficient homogeneously weighted dispersion control charts with an application to distillation process

Nassar

Aldosari

Adeoti

2021

Quality & Reliability Eng

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“…The Downton's estimator was introduced by Downton 13 as an estimator for standard deviation of a normal population. Downton's statistic is an unbiased estimator of σ 9 and a very robust dispersion estimator that is not affected by departure from normality 1,7 . The Downton's statistic does not require coefficients of X ( i ) or divisors like d n and its asymptotic efficiency is 97.8% (Abu‐Shawiesh, 2000) 3…”

Section: Mad‐ and Amad‐based Control Chartsmentioning

confidence: 99%

Performance of median absolute deviation and some alternatives to median absolute deviation control charts for skewed and heavily tailed process

Adekeye

Adewara

Aako

et al. 2021

Quality & Reliability Eng

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In this paper, trueX¯ charts based on robust scale estimators (known as Sn and Qn estimators) are proposed, and the performance of control charts based on median absolute deviation (MAD) is compared with those based on some alternatives to MAD, which do not need any location estimate, for normal, skewed, and heavily tailed distributions. MAD is often used as a substitute for standard deviation in constructing control charts due to its robustness. Three alternatives to MAD namely the Sn, Qn, and Downton (D) are considered in this paper as location‐free estimators. A simulation study was carried out to appraise the performance of the control charts based on the MAD, Sn, Qn, and D estimators. The average run length (ARL), median run length (MRL), standard deviation run length (SDRL), and control limits interval (CLI) were used to assess the performance of the four control charts. The results showed that MAD, Sn, and D are suitable estimators for standard deviation for mean charts while Sn and Qn are suitable estimators for standard deviation for dispersion charts for skewed and heavily tailed distributions.

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“…In this section we describe the control chart limits for the process mean and variability, based on the Downton estimator (following the idea of Abbasi and Miller ([15], [16]), and Adeoti, Olaomi & Adekeye [17]). The knowledge of the control chart limits is used to derive the process capability index-based control chart.…”

Section: Design Of Proposed Control Chart With Specified Cpmentioning

confidence: 99%

“…The corresponding control chart limits for the mean derived by Adeoti, Olaomi & Adekeye [17] are given as . So an unbiased estimator of , defined by Abassi and Miller [15], is used in (1).…”

Section: Design Of Proposed Control Chart With Specified Cpmentioning

confidence: 99%

Process Capability Index-Based Control Chart for Variables

Adeoti¹,

Olaomi²

2017

SAJIE

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This paper proposes a process capability index-based control chart for variables using the Downton estimator with a specified Cp value. The proposed chart is able to address the issue of control and capability simultaneously. We also provide a control chart constant to construct the process capability index-based control chart. A numerical example is presented to demonstrate the application of the proposed chart, and the effect of non-normality is discussed. The result shows that the proposed control chart performs better in monitoring and assessing processes, and eliminates the usual twostage procedure reflected in the literature. OPSOMMING'n Prosesvermoë indeksgebaseerde beheerkaart word voorgestel vir veranderlikes met gebruik van die 'Downton' beramer met 'n gespesifiseerde Cp waarde. Die voorgestelde beheerkaart kan die kwessie rondom die beheer en vermoë gelyktydig aanspreek. 'n Beheerkaartkonstante word ook verskaf om die prosesvermoë indeksgebaseerde beheerkaart te skep. 'n Numeriese voorbeeld word voorgehou om die toepassing van die voorgestelde beheerkaart te illustreer. Die effek van nie-normaliteit word ook bespreek. Die resultaat toon dat die voorgestelde beheerkaart beter vertoon in die monitering en assessering van prosesse en dit elimineer die gewone twee stap prosedure wat in die literatuur gevind word.

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Control Chart Limits for Monitoring Process Mean Based on Downton's Estimator

Cited by 6 publications

References 14 publications

Efficient homogeneously weighted dispersion control charts with an application to distillation process

Efficient homogeneously weighted dispersion control charts with an application to distillation process

Performance of median absolute deviation and some alternatives to median absolute deviation control charts for skewed and heavily tailed process

Process Capability Index-Based Control Chart for Variables

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