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A Unified Approach for Modeling and Designing Attribute Sampling Plans for Monitoring Dependent Production Processes

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  • P. Vellaisamy

    (Indian Institute of Technology)

  • S. Sankar

    (Indian Institute of Technology)

Abstract

In this paper, we consider a probabilistic model to represent some general dependent production processes and present a unified approach for designing attribute sampling plans for monitoring the ongoing production process. This model includes the classical iid model, independent model, Markov-dependent model and previous-sum dependent model, to mention a few. Some important properties of this model are established. We derive the recurrence relations for the probability distribution of the sum of n consecutive characteristics observed from the process. Using these recurrence relations, we present efficient algorithms for designing optimal single and double sampling plans for attributes, for monitoring the ongoing production process. Our algorithmic approach, which uses effectively the recurrence relations, yields a direct and an exact method, unlike many approximate methods adopted in the literature. Several interesting examples concerning specific models are discussed and a few tables for some special cases are also presented. It is demonstrated that the optimal double sampling plans lead to about 42% reduction in average sample number over the single sampling plans for process monitoring.

Suggested Citation

  • P. Vellaisamy & S. Sankar, 2005. "A Unified Approach for Modeling and Designing Attribute Sampling Plans for Monitoring Dependent Production Processes," Methodology and Computing in Applied Probability, Springer, vol. 7(3), pages 307-323, September.
    • Handle: RePEc:spr:metcap:v:7:y:2005:i:3:d:10.1007_s11009-005-4519-7
    DOI: 10.1007/s11009-005-4519-7
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    References listed on IDEAS

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    1. Layth C. Alwan & Harry V. Roberts, 1995. "The Problem of Misplaced Control Limits," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 44(3), pages 269-278, September.
    2. P. Vellaisamy & S. Sankar & M. Taniguchi, 2003. "Estimation and Design of Sampling Plans for Monitoring Dependent Production Processes," Methodology and Computing in Applied Probability, Springer, vol. 5(1), pages 85-108, March.
    3. P. Vellaisamy & S. Sankar, 2001. "Sequential and systematic sampling plans for the Markov‐dependent production process," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(6), pages 451-467, September.
    4. 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.
    5. V. S. Sampath Kumar & M. B. Rajarshi, 1987. "Continuous sampling plans for markov‐dependent production processes," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(5), pages 629-644, October.
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    Cited by:

    1. Vellaisamy, P. & Upadhye, N.S., 2007. "On the negative binomial distribution and its generalizations," Statistics & Probability Letters, Elsevier, vol. 77(2), pages 173-180, January.

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