A Reference Population-Based Conformance Proportion

• Published in: Journal of Agricultural, Biological and Environmental Statistics Vol. 21; no. 4; pp. 684 - 697
• Main Authors: Lee, Hsin-I, Chen, Hungyen, Kishino, Hirohisa, Liao, Chen-Tuo
• Format: Journal Article
• Language: English
• Published: New York Springer Science+Business Media, LLC 01.12.2016; Springer Science and Business Media LLC; Springer US; Springer; Springer Nature B.V
• Subjects: Agriculture; Biostatistics; Computer simulation; Confidence interval; Confidence intervals; Confidence limits; Data analysis; Data processing; Degrees of freedom; Gaussian distributions; Health Sciences; Inference; Mathematics and Statistics; Medicine; Monitoring/Environmental Analysis; Population (statistical); population ecology; Proportions; Sample size; Simulations; statistical analysis; Statistical inference; statistical models; Statistics; Statistics for Life Sciences; Transgenic plants; Environmental assessment; Agricultural management; Generalized pivotal quantity; Variance component; Tolerance interval
• DOI: 10.1007/s13253-016-0268-z
• ISSN: 1085-7117

Conformance proportion is a useful index in agricultural, biological, and environmental applications, which is defined as the proportion that a characteristic of interest falls in an acceptance region of a specification. In practice, however, the acceptance region may not be available when employing the regular conformance proportion. In this article, we propose a new index in which the acceptance region is obtained from a reference population. Furthermore, we develop approaches to constructing confidence limits for the proposed conformance proportion using the concept of a fiducial generalized pivotal quantity. We first consider the simple situation that the characteristic is assumed to be a univariate normal random variable. Then we extend it to the one-way random effects model. The proposed method is evaluated through simulation study and real data analysis. It is shown that our proposed new index and its statistical inference are easy to implement and reasonably satisfactory for most applications. Supplementary materials accompanying this paper appear on-line.