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Problems associated with defining normal forms of relational tables relevant to statistical processing are discussed. The concepts of derived identifier, class identifier, derived class-counts, count domains, compact domains, and uniform domains for statistical relational tables are introduced. The structures of the first and the second statistical-normal forms and the relational decompositions needed to achieve them are also discussed. It is shown that the statistical-normal form can be an important method to determine whether the usual statistical analysis techniques are valid. Some suggestions are presented for extending the structured query language (SQL) statements to achieve these operations on statistical relational tables. Some results linking Codd's normal forms with statistical normal forms are discussed. Relational statistical abnormalities, called outlyers, are also discussed.>

The problem is discussed of defining numerical operations on a relational database to accommodate the statistical analyses associated with a bivariate frequency table. An attempt has been made to extend Codd's relational algebra to include simple bivariate statistical operations preserving the closure of Codd's algebra. This extended algebra is applied to bivariate relational data structures needed for real-time automatic statistical quality control of a manufacturing process. Also discussed are some new category-numeric operations on relational tables.>

Statistical processing of data has been around for a long time. In biblical times people were concerned with census data for tax collection purposes. The history of usage of statistics data prior to the eighteenth century is not well documented. In the eighteenth century mathematicians, like Pascal, when they invented probability theory, found the use of statistical data for estimating probabilities. The use of relative frequencies for estimating probabilities of events, can be considered as the first attempt of data engineering for intelligent inference. Of course, data engineering did not surface until the invention of computers, which was another two centuries later. In these two centuries Statistics developed as a science, specially in the later part of the nineteenth and the first half of the twentieth century. The age of computers followed the maturity of the science of statistics.

As advanced applications become more and more demanding, the use of the data on hand becomes more and more sophisticated. In applications such as the kind in commercial banking environment, the search for data is rather simple and precise; the time constraints are not severe; statistical applications are not often used; history data is not so important; and estimates are not performed. In short, the demand to have an intelligent DB is at best minimal.

This paper deals with statistical reduction of the large volume of data that are generated by modern computerized testing in manufacturing environment. Two statistical algorithms have been developed to reduce dynamically, in real time, the amount of manufacturing testing, while maintaining the quality level, thus reducing the volume of data generated. In algorithm 1, homogeneous clusters of tests are formed based on statistical correlation coefficients, and then a subset of tests from each cluster are executed. In algorithm 2, the correlation coefficients arc used to derive statistical prediction equations, which are then used to decide if certain test are to be performed on an item. A method and algorithm for statistically discarding manufacturing test data (associated with an item) is given in algorithm 3. Algorithm 4, deals with computerized stratification and sample selection of manufacturing test data. An method for computerized sampling based on test values, for retaining a subset of the data, is provided in the algorithm 5.

E.F. Codd's (1970) relational view is extended to represent statistical data and to achieve its analysis. A new view called a statistical relational table is presented to meet the needs of statisticians, and some of Codd's relational operators are extended to statistical relational tables. New operators based on these tables are introduced for communicating requests for statistical analysis. A new query language called the query-by-statistical-relational-table (which has some similarities to query-by-example) is introduced. Extensions of the SQL language for processing the commands of the new query language are also discussed. Creation and storage of metadata for fast statistical analysis are considered. Some problems related to privacy in statistical databases are also examined.

This paper discusses some applications of statistical and database techniques for integrating tests in manufacturing products. It shows how statistical databases can be used for automatically controlling a manufacturing process in real time. Some new statistical methods of manufacturing testing, e. g., test-compression, testing-by-sampling, testing-by-factorial-design, are discussed. All these techniques are possible because of the availability of a statistical database.

This paper discusses some applications of statistical and database techniques for integrating tests in manufacturing products. It shows how statistical databases can be used for automatically controlling a manufacturing process in real time. Some new statistical methods of manufacturing testing, e.g., test-compression, testing-by-sampling, testing-by-factorial-design, are discussed. All these techniques are possible because of statistical database.

EXPRESS is an experimental prototype data translation system which can access a wide variety of data and restructure it for new uses. The system is driven by two very high level nonprocedural languages: DEFINE for data description and CONVERT for data restructuring. Program generation and cooperating process techniques are used to achieve efficient operation. This paper describes the design and implementation of EXPRESS. DEFINE and CONVERT are summarized and the implementation architecture presented. The DEFINE description is compiled into a customized PL/1 program for accessing source data. The restructuring specified in CONVERT is compiled into a set of customized PL/1 procedures to derive multiple target files from multiple input files. Job steps and job control statements are generated automatically. During execution, the generated procedures run under control of a process supervisor, which coordinates buffer management and handles file allocation, deallocation, and all input/output requests. The architecture of EXPRESS allows efficiency in execution by avoiding unnecessary secondary storage references while at the same time allowing the individual procedures to be independent of each other. Its modular structure permits the system to be extended or transferred to another environment easily.

The problem of distributing a data base (with logical associations between segment types) on a computer network such that multiple segment types satisfying a query can be retrieved in paralel from different nodes has been introduced. Properties of such distributions without redundancy and with redundancy have been discussed. Lower bounds on the number of nodes needed for such distributions have been given. Algorithms for constructing such distributions have also been given. Distributions of data bases for queries whose target segments form a combinatorial set have been studied in detail. Closed form expressions for redundancy have been obtained for such query sets.

A statistical design of an experiment for modeling the performance (access time) of a data base (DB) system in a controlled environment has been outlined. A three-factor pilot experiment with retrieval sequence, logical view (combined with access method), and target segment type as factors was designed and the results analyzed for a specific IMS batch DB. It was found that: 1) the variation of sequences of DB retrieval calls in the application program did not have any signifilcant effect on the access time, whereas the other two factors did have significant effect; 2) the variability in access time is not completely explained by these three factors; and 3) the distribution of the residual error is "nonnormal," with a large positive skew.

The construction of a hierarchy of indexes (the indexed sequential access method) is one means of providing rapid random access to sequential files. An examination is made of the consequences of partially or completely replacing one or more index levels by linear interpolation procedures. For all possible configurations of the several types of key distributions investigated, linear interpolation on the average provides significant performance improvements. Typically, the two accesses required to obtain track index and data are reduced to 1.1 to 1.7 accesses per record. Extremely unusual key distribution will, however, raise the number of accesses required above 2.