Journal of The Japanese Society for Quality Control
Online ISSN : 2432-1044
Print ISSN : 0386-8230
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Volume 11, Issue 4
Displaying 1-7 of 7 articles from this issue
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Contributed Paper
  • The Estimation of the Characteristics of the Lognormal Distribution Using Probability Paper
    Takashi ICHIDA
    Article type: Contributed Paper
    1981 Volume 11 Issue 4 Pages 31-40
    Published: October 15, 1981
    Released on J-STAGE: March 09, 2019
    DOIhttps://doi.org/10.20684/quality.11.4_31
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    The purpose of this paper is to present the estimation procedures of characteristics of the lognormal distribution using probability paper and todiscuss the bias and efflciency of the estimates. The characteristics are the mode, median and k th root of moment of order k about the origin. These characteristics are in the same units as the variate. The estimation procedure described in this paper is completed with simple geometical operations on the probability paper. The obtained estimate of the characteristics of population, ξ is expressed as ξ=exp(μ+α(σ)2). Assigning α successively the values α=-1, 0, k/2, we obtain the estimates of the mode,median and k th root of moment of order k where μ^^^ and σ are the constants proportional to the interception and the inclination of the reglession line on the probability paper. To compute E(ξ)/ξ and Var(ξ)+(E(ξ)-ξ)^2 considering ξ as an estimator, following assumptions are made.
    (1) In the best case, the estimates μ and σ equal to the best linear unbiased estimates of mean and standard deviation of normal distribution by ranking the observations of a sample and taking linear combination of them.
    (2) In the worst case, the estimates μ and σ equal to the mean and range estimate with two observations of a sample.
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  • Comparison of Practical Procedures of Population Mean Estimation With Small Samples （ I ）
    Yoshikazu Ojima
    Article type: Contributed Paper
    1981 Volume 11 Issue 4 Pages 41-55
    Published: October 15, 1981
    Released on J-STAGE: March 09, 2019
    DOIhttps://doi.org/10.20684/quality.11.4_41
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    In chemical analysis or physical testing, presence of a discordant value in a small number of data (n≧2) is checked quite often by using the permissible tolerance. There are several procedures for such checking, and even in ISO standards, plural procedures are adopted. In this paper, simulation was carried out on the five procedures mentioned below, and comparison was made on the following three aspects :
    (1) Unbiasedness and dispersion of the final values;
    (2) Cost involved in the application ;
    (3) Simplicity in the statistical examination.
    The five procedures compared are :
    Procedure I ・・・・・・・・・・・・Procedure in ISO 4686;
    Procedure II・・・・・・・・・・・・Sequential application of permissible tolerances;
    Procedure III-1・・・・・・・・・Procedure in ISO 3271;
    Procedure III-2・・・・・・・・・Procedure in ISO 3087;
    Procedure IV ・・・・・・・・・・・・In JIS Z 8402-1974, clause 3. 3. 2 (1. 2. 2).
    The following two models were used for data generation :
    (1) Model-1 ・・・・・・・・・The second data is biased;
    (2) Model-2・・・・・・・・・The variance of data is greater than the specified average variance within a laboratory.
    Collectively for both of Model_<-1> and Model _<-2>, the procedure in ISO 3087 was proven to be the most recommendable procedure, the procedure in ISO 3271 being the second. However, when there is a limitation in the cost involved in the application of the procedure, the procedure of JIS Z 8402 in clause 3. 3. 2 (1. 2. 2) was proven to be the most recommendable.
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