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Max-Chart for Autocorrelated Processes

Author

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  • Thaga K.

    (Department of Statistics, University of Botswana, Private Bag UB00705 Gaborone, Botswana)

  • Kgosi P. M.

    (Department of Statistics, University of Botswana, Private Bag UB00705 Gaborone, Botswana)

  • Gabaitiri L.

    (Department of Statistics, University of Botswana, Private Bag UB00705 Gaborone, Botswana)

Abstract

Statistical process control procedures are usually implemented under the assumption that the observations from a process are independent over time. However, this assumption is often violated. Therefore, we propose a single Shewhart-type control chart for autocorrelated process by fitting a time series model into the process and monitoring the residuals from the forecast values of a fitted time series model. Numerical results illustrate the ARL of the AR(1) plus random error model, for the cases of step changes in the mean and/or standard deviation. Compared to other charts that monitor autocorrelated processes, this chart quickly detects shifts in the process location and spread particularly for large shifts.

Suggested Citation

  • Thaga K. & Kgosi P. M. & Gabaitiri L., 2007. "Max-Chart for Autocorrelated Processes," Stochastics and Quality Control, De Gruyter, vol. 22(1), pages 87-105, January.
    • Handle: RePEc:bpj:ecqcon:v:22:y:2007:i:1:p:87-105:n:10
    DOI: 10.1515/EQC.2007.87
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    References listed on IDEAS

    as
    1. Alwan, Layth C & Roberts, Harry V, 1988. "Time-Series Modeling for Statistical Process Control," Journal of Business & Economic Statistics, American Statistical Association, vol. 6(1), pages 87-95, January.
    2. E. Collani, 1999. "Control of production processes subjectto random shocks," Annals of Operations Research, Springer, vol. 91(0), pages 289-304, January.
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    Cited by:

    1. Thaga Keoagile, 2008. "Control Chart for Autocorrelated Processes with Heavy Tailed Distributions," Stochastics and Quality Control, De Gruyter, vol. 23(2), pages 197-206, January.

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