Abstract
CUSUM-schemes with variable sampling intervals and sample sizes are introduced and investigated for situations where a production process switches at an unknown time from an in-control state to an out-of-control state. Suitable performance criteria are derived to compare CUSUM-schemes with this additional feature. The gain from this feature may be substantial. Without seriously affecting the run length properties under the out-of-control state it is possible to simultaneously reduce the average number of sampled items per time unit (25% to 50%) and to increase the average run length under the in-control state (40% to 50%). Furthermore it is shown that one may restrict to simple schemes that have only two different sample sizes and equally spaced tim-iintervals between the observations.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Khan, R.A., 1978: Wald's approximations to the average run length in CUSUM procedures, J. Statist. Plan. and Inf., 2, 63–77
Moustakides, G. V., 1986: Optimal Stopping Times for Detecting Changes in Distributions, Ann. Statist., 14, 1379–1387
Page, E. S., 1954, Continuous inspection schemes, Biometrika, 41, 100–114
Rendtel, U., 1986: Verallgemeinerte CUSUM-Kontrollkarten und ihre Anwendung auf die Annahmestichprobenprüfung, Dissertation am Fachbereich Wirtschaftswissenschaft der Freien Universität Berlin, Berlin
Rendtel, U., 1987: The Use of Generalized CUSUM-Schemes to Control the Percent Defective of a Continuous Production Process in Frontiers, in Statistical Quality Control 3, Lenz, Wetherill, Wilrich (eds.), Physica-Verlag, Heidelberg.
Reynolds, M.R., R.W. Amin, J.C. Arnold and J.A. Nachlas, 1988: X Charts With Variable Sampling Intervals, Technometrics, 30, 181–192
Waldmann, K.-H., 1986a: Bounds for the distribution of the run length of one-sided and two-sided CUSUM quality control schemes, Technometrics, 28, 61–67.
Waldmann, K.-H., 1986b: Bounds for the run length in general quality control schemes, Statistische Hefte, 27, 37–56.
Woodall, W. H., 1984: On the Markov Chain Approach to the Two Sided CUSUM Procedure, Technometrics, 24, 41–46
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Rendtel, U. Cusum-schemes with variable sampling intervals and sample sizes. Statistical Papers 31, 103–118 (1990). https://doi.org/10.1007/BF02924681
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02924681