Library standards have been the source of considerable controversy, whereas many problems are involved in developing stardard for university library collections. For evaluation purposes, standards should be precise, quantifiable and measurable. In the United States, however, standards for academic libraries are limited to qualitative statements and principles. Quantitative standards, when given, are ususally related to the number of population in the institution being served, or the prescribed quantitative objectives are often arbitrarily formulated by value judgements. The study in this paper attempts to explain the problems involved in developing quantitative standard for academic library collections. Two problems facing in the formulation of the optimal size of collection are identified. One is the theoretically faulty concept of adequacy of collection to meet the situations of diversity of university libraies, and the other is the difficulties in quantification and measurement, along with the lack of concept of adequacy of collection. However, quantification of adequate size of collection is proved to be useful on the pratical level, even though not valid theoretically. ACRL, Clapp/Jordan and Voigt developed formulas or models for setting the optimal size of a library collection for any particular university library. The main purpose of this study is the analysis of the above formulas. ACRL standard was drawn from obervation and analysis of statistcs in leading library collections. In academic field, this judgement appears to have been based on the assumption that a high-grade institution would be apt to have a good library collection. This study criticizes ACRL standard for its failure to include some determinants of measurements, and points out the limitations of the standard. In contrast. Clapp/Jordan developed a formula rather scientifically based upon bibliographical sources. This is similarly empirical but has the advantage of bringing into play the elements which make universities diverse in nature. Both ACRL and Clapp/Jordan formulas share two major defects. (1) the specific subject needs of the collection are not indiacted directly, and (2) percentage rate of growth is an indicator in measuring the potential utility of a collection. Thus both formulas failed to provide a basis for meaningful evaluation. Voigt further developed a model for determining acquisition rates for currently published materials based on bibliographic technique. Voigt model encourages experimentation with different programs and different allocations of input resources, designed to meet the needs of the library's particular population. Standard for university library collections can be formulated in terms of input(traditional indicator), or additionally, in terms of output(cost-effectiveness). Cost effectiveness is expressed as user satisfaction, ability to provide wanted materials within a reasonable time period. Thus simple quantitative method does not cover all the situations of diversity of university library collections, nor measures the effectiveness of collections. Valid standard could not be established without further research.