Journal of The Japanese Society for Quality Control
Online ISSN : 2432-1044
Print ISSN : 0386-8230
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Volume 10, Issue 4
Displaying 1-8 of 8 articles from this issue
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From Abroad
Contributed Paper
  • Sampling Inspection Plan by Variables （σ Unknown） Based on the Non-Central t Distribution and Consideration on Its A p proximation Formulae
    Takao ENKAWA
    Article type: Contributed Paper
    1980 Volume 10 Issue 4 Pages 36-44
    Published: October 15, 1980
    Released on J-STAGE: March 12, 2019
    DOIhttps://doi.org/10.20684/quality.10.4_36
    JOURNAL RESTRICTED ACCESS
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    In the case of σ unknown, sampling inspection plan by variables is based on a statistic having the non-central t distribution, which can be approximated by the normal distribution when sample size is sufficiently large. Existing sampling plans by variables use this normal approximation over all or most part of the tables. The followings are show in the present paper.
    (1) We examine the accuracy of designed values by the normal approximation. Furthur in the part of small sample sizes, the sampling table having desired operating characteristics is given, which is based on the non-central t distribution.
    (2) The approximate method utilizing the new formula E(s)=√<(3n-4)/(3n-3)ρ in the normal approximation of x + ks is proposed which converges more rapidly than existing methods and the procedure to obtain the sampling plan by the new method is shown.
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  • An Approximating the Binomial Confidence Limit
    Yoritake FUJlNO
    Article type: Contributed Paper
    1980 Volume 10 Issue 4 Pages 45-51
    Published: October 15, 1980
    Released on J-STAGE: March 12, 2019
    DOIhttps://doi.org/10.20684/quality.10.4_45
    JOURNAL RESTRICTED ACCESS
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    For obtaining approximate binomial confidence limits, the most commonly used is p±u_α√<p(1-p)/n>, where p=x/n, n is the sample size, x is the number of defectives, and u_α denotes the upper α point of the standard normal distribution. This approximation is simple and its meaning is intuitively clear, but its accuracy is too poor to meet practical requirements unless n is very large. To improve its accuracy, it is proposed to use p*=(x+d)/(n+e) instead of p=x/n, where two constants d and e are suitably chosen. Numerical investigations are made to compare the accuracy of the new method with those of other procedures.
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