Search theory of the defective apparatus for feeding cocoon end

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Other Title
  • 不良緒の探索理論
  • 不良緒の探索理論 II : 接緒の分布関数について
  • フリョウ ショ ノ タンサク リロン 2 セツショ ノ ブンプ カンスウ ニ
  • II. 接緒の分布関数について
  • II. On the distribution function of the number of feeding ends

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The probability in which the variation of feeding ends including the event missed taking a cocoon in a marked end feeder, P(Z=k), is generally given as follows.<br>P(Z=k)=a1p(a1+a0q)k<br>where p is the available efficiency of feeding ends (ratio) and q is 1-p, a1 is the taking out cocoons efficiency (ratio) and a0 is 1-a1, k is the number of feeding ends repeated k times over till the success event occurs. The distribution of the feeding ends efficiency (1-λ), λ=a1p, is given by f(λ)<br>f(λ)=(α+β+1)!λα(1-λ)β/α!β!<br>where α and β are the parameters of the distribution, the mean value of λ is (α+1)/(α+β+2) and the variance is (α+1)(β+1)/(α+β+2)2(α+β+3). And the distribution of feeding ends over the all end feeders in the factory is shown by the P(U=k)<br>P(U=k)=(α+β+1)!(α+k)!(β+1)/α!(α+β+k+2)!<br>where α, β and k are the above mentioned parameters, respectively. U is the random variable of the feeding ends. Then the mean value of U is (α+1)/β, the variance is (α+1)(β+1) (α+β+1)/β2(β-1).

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