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Estimation and Design of Sampling Plans for Monitoring Dependent Production Processes

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  • P. Vellaisamy

    (Indian Institute of Technology)

  • S. Sankar

    (Indian Institute of Technology)

  • M. Taniguchi

    (Osaka University, Toyonaka)

Abstract

We consider the problem of designing single and the double sampling plans for monitoring dependent production processes. Based on simulated samples from the process, Nelson proposed a new approach of estimating the characteristics of single sampling plans and, using these estimates, designing optimal plans. In this paper, we extend his approach to the design of optimal double sampling plans. We first propose a simple methodology for obtaining the unbiased estimators of various characteristics of single and double sampling plans. This is achieved by defining the various characteristics of sampling plans as explicit random variables. Some of the important properties of the double sampling plans are established. Using these results, an efficient algorithm is developed to obtain optimal double sampling plans. A comparison with a crude search shows that our algorithm leads to about 90% savings, on the average, in computational timings. The procedure is also explained through a suitable example for the ARMA(1,1) model. It is observed, for instance, that an optimal double sampling plan leads to about 23% reduction in average sample number, compared to an optimal single sampling plan. Tables for choosing the optimal plans for certain auto regressive moving average processes at some practically useful values of acceptable quality level and rejectable quality level are also presented.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metcap:v:5:y:2003:i:1:d:10.1023_a:1024129421819
    DOI: 10.1023/A:1024129421819
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    References listed on IDEAS

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    1. 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.
    2. 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.
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    1. 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.

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