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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.

No abstract

The control chart based on mean deviation (MD ) is customary used as a robust alternative to the existing Shewhart control charts for observing changes in dispersion parameter of the process. The existing model of MD control chart is rooted under the assumption that indeterminate observations are not included in measured quality characteristic. If, inspected quality data entail some indeterminate and vague information, typical design of the MD control chart could not be effectively employed. This study originally presents an appropriate generalized design namely neutrosophic mean deviation ( MD) control chart that could accommodate imprecise observations in collected quality characteristic variables. Under the neutrosophic situation, the related properties of this newly MD design have been derived. Using simulated data, performance of the MD control chart in terms of neutrosophic average run length ( ARL) is investigated. The performance of proposed MD control chart relative to existing competitor designs has been evaluated. The study reveals that proposed design of MD chart outperforms as to existing counterparts in terms of statistical power. To illustrate the efficacy of this new design, real data from a manufacturing company has been used to describe the control procedure of the proposed MD control chart.INDEX TERMS Fuzzy control charts, probability limits, mean deviation, neutrosophic data, variability control charts.