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Parameter estimation and design considerations in prospective applications of the X chart

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  • Subha Chakraborti

Abstract

The effects of parameter estimation on the in-control performance of the Shewhart X chart are studied in prospective (phase 2 or stage 2) applications via a thorough examination of the attained false alarm rate (AFAR), the conditional false alarm rate (CFAR), the conditional and the unconditional run-length distributions, some run-length characteristics such as the ARL, the conditional ARL (CARL), some selected percentiles including the median, and cumulative run-length probabilities. The examination involves both numerical evaluations and graphical displays. The effects of parameter estimation need to be accounted for in designing the chart. To this end, as an application of the exact formulations, chart constants are provided for a specified in-control average run-length of 370 and 500 for a number of subgroups and subgroup sizes. These will be useful in the implementation of the X chart in practice.

Suggested Citation

  • Subha Chakraborti, 2006. "Parameter estimation and design considerations in prospective applications of the X chart," Journal of Applied Statistics, Taylor & Francis Journals, vol. 33(4), pages 439-459.
    • Handle: RePEc:taf:japsta:v:33:y:2006:i:4:p:439-459
    DOI: 10.1080/02664760500163516
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    Citations

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    Cited by:

    1. Rob Goedhart & Michele M. da Silva & Marit Schoonhoven & Eugenio K. Epprecht & Subha Chakraborti & Ronald J. M. M. Does & Álvaro Veiga, 2017. "Shewhart control charts for dispersion adjusted for parameter estimation," IISE Transactions, Taylor & Francis Journals, vol. 49(8), pages 838-848, August.
    2. Tilottama Chakraborty & Mrinmoy Majumder, 2019. "Application of statistical charts, multi-criteria decision making and polynomial neural networks in monitoring energy utilization of wave energy converters," Environment, Development and Sustainability: A Multidisciplinary Approach to the Theory and Practice of Sustainable Development, Springer, vol. 21(1), pages 199-219, February.
    3. Johannssen, Arne & Chukhrova, Nataliya & Castagliola, Philippe, 2022. "The performance of the hypergeometric np chart with estimated parameter," European Journal of Operational Research, Elsevier, vol. 296(3), pages 873-899.

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