Advertisement

Metrika

, Volume 28, Issue 1, pp 211–236 | Cite as

Kostenoptimale Prüfpläne für die laufende Kontrolle eines normalverteilten Merkmals

  • E. v. Collani
Article

Summary

The process under consideration is assumed to start in control with mean μ and standard deviation σ. There is a single assignable cause of variation, which takes the form of a shift in the process mean from μ to μ+δσ or to μ−δσ. The time until the assignable cause occurs has an exponential distribution with parameter λ. To maintain current control 3 different strategies are compared.
  1. 1.

    no control at all,

     
  2. 2.

    in constant time intervals the process is stopped with a given probability and a search for the assignable cause and if necessary a repair is undertaken,

     
  3. 3.

    samples of sizen are drawn after constant time intervalls; if the sample mean\(\bar x\) exeeds the action limits\( \pm k\sigma /\sqrt n \) the process is stopped and a search for the assignable cause, and if necessary, a repair is undertaken.

     
When operating with \gm, the process derives a profit ofGI per item and when operating with mean \gm + \gd\gs or \gm\t-\gd\gs it derives a profit ofGII<GI per item. An expected time oft D hours and an average search cost ofK D are required if the assignable cause does not exist. If the assignable cause actually exists, it can always be discovered and eliminated but takes further average revision time oft R hours and a further average revision cost ofK R to restore the process. The process starts a-new with mean \gm after adjustment. The costs for maintaining the repair workshop are considered to bed R per time unit. Similar the costs for taking a sample are divided in current costsd P per time unit and the actual sampling costs, which are assumed to be proportional to the sample size. Generalized control plans are defined including all 3 strategies, and for the mean loss per item in the long run a loss function is derived. It is shown that there exists an optimal control plan and, suitable defined, that it is unique.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literaturverzeichnis

  1. Chiu, W.K.: The economic design of cusum charts for controlling normal means. Applied Statistics23, 1974, 420–433.CrossRefGoogle Scholar
  2. Chiu, W.K., andG.B. Wetherill: A simplified scheme for the economic design ofX-charts. J. Qual. Tech.6, 1974, 63–69.Google Scholar
  3. Collani, E.v.: Kostenoptimale Prüfpläne für die laufende Kontrolle eines normalverteilten Merkmals. Dissertation, Würzburg 1978.Google Scholar
  4. Duncan, A.J.: The economic design ofX-charts used to maintain current control of a process. J. Amer. Statist. Ass.51, 1956, 228–242.MATHGoogle Scholar

Copyright information

© Phydica-Verlag 1981

Authors and Affiliations

  • E. v. Collani
    • 1
  1. 1.Institut für Angewandte Mathematik und StatistikWürzburg

Personalised recommendations