On designing a new control chart for Rayleigh distributed processes with an application to monitor glass fiber strength

Hossain, M. Pear; Omar, M. Hafidz; Riaz, Muhammad; Arafat, Sheikh Y.

doi:10.1080/03610918.2019.1710192

Cited by 17 publications

(20 citation statements)

References 22 publications

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“…Control chart designs rooted on mixture distribution models have also been proposed in [19], [20]. Assuming the Rayleigh distribution as an appropriate model for manufacturing variables, Hossain et al [21] has made further developments. While the existing Rayleigh design is developed to monitor the target parameter of the Rayleigh distributed processses.…”

Section: Consideringmentioning

confidence: 99%

“…In this study, a new design namely -control chart has been proposed for the scale parameter of the Rayleigh distributed processes. The design of chart [21] is veritably not based on an unbiased estimator of parameter and thus could not be utilized for monitoring the scale parameter of the Rayleigh distributed process.…”

Section: Consideringmentioning

confidence: 99%

“…In the existed structure of , it has been assumed that theoretical model for the observed quality characteristic is a single parameter Rayleigh distribution [21]. The quality characteristic is said to follow Rayleigh distribution with scale factor if it has the following probability density function (PDF) and cumulative distribution function (CDF) respectively:…”

Section: The Existing -Control Chartmentioning

confidence: 99%

“…We let the process is subject to assignable cause(s) that resulted in a shift in control value to . Thus the ability of -control chart for not detecting this shift can be described in terms of type-II error as: = ≤ ≤ | (23) where and are lower and upper probability limits of the proposed chart, defined in (21). Simplification of (23) provides = √2 − √2 (24) where is distribution function of the chi-distribution with 2n degree of freedom.…”

Section: Proposed Design Of Control Chartmentioning

confidence: 99%

“…implies to = ( ) (20) Following simplification,(20) can be written as: probability limits provided in(21) for the estimated value can be written as:…”

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confidence: 99%

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On Scale Parameter Monitoring of the Rayleigh Distributed Data Using a New Design

et al. 2020

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In recent years, many supplementary designs have been developed incorporating the assumption that data follow the particular non-normal distribution. The-control chart is one such design proposed to monitor the parameter of the single parameter Rayleigh distributed data. Commonly, in authentic situations, practitioners need to estimate the scale parameter in the observed processes instead of. However, the positive square root of the-statistic used in the existing design of-control chart is not an unbiased estimator of and thus could not be practiced to monitor the scale parameter of the Rayleigh distributed process. A new structure of the-control chart namely for monitoring the scale parameter of the Rayleigh distributed data has been originally developed in this study. The statistical basis of this newly design in terms of average run length (), characteristic function and power curve have been derived. The analytical results are utilized further to determine the parameters of-chart and in comparing the performance of the proposed control chart with existing competitors. Comparative results illustrate the effectiveness of the proposed design in view of statistical power. Finally, the computational procedure of this newly-chart has been demonstrated using simulated data and real data on the breaking strength of carbon fibers.

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Section: Consideringmentioning

confidence: 99%

Section: Consideringmentioning

confidence: 99%

Section: The Existing -Control Chartmentioning

confidence: 99%

Section: Proposed Design Of Control Chartmentioning

confidence: 99%

“…implies to = ( ) (20) Following simplification,(20) can be written as: probability limits provided in(21) for the estimated value can be written as:…”

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confidence: 99%

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