## Statistics

Statistics basically is a summary value calculated from the observed values in a product or sample. It is a branch of mathematics dealing with the collection, analysis, interpretation, and presentation of masses of numerical data. The word statistic has two generally accepted meanings: (1) a collection of quantitative analysis data (data collection) pertaining to any subject or group, especially when the data are systematically gathered and collated and (2) the science that deals with the collection, tabulation, analysis, interpretation, and presentation of quantitative data.

As an example of statistical analysis of products there is statistical process control (SPC). It is an important on-line method in real time by which a production process can be monitored and control plans can be initiated to keep quality standards within acceptable limits. Statistical quality control (SQC) provides off-line analysis of the big picture such as what was the impact of previous improvements. It is important to understand how SPC operates.

There are basically two possible approaches for real-time SPC. The first, done on-line, involves the rapid dimensional measurement of a part or a non-dimensional bulk parameter such as weight and is the more practical method. In the second approach, contrast to weight, other dimensional measurements of the precision needed for SPC are generally done off-line. Obtaining the final dimensional stability needed to measure a part may take time. As an example, amorphous injection molded plastic parts usually require at least a half-hour to stabilize.

The SPC system starts with the premise that the specifications for a product can he defined in terms of the product's (customer's) requirements, or that a product is or has been produced that will satisfy those needs. Generally a computer communicates with a series of process sensors and/or controllers that operate in individual data loops.

The computer sends set points (built on which performance characteristics of the product must have) to the process controller that constantly feeds back to the computer to signal whether or not the set of points are in fact maintained. The systems are programmed to act when key variables affecting product quality deviate beyond set limits.

To target for better yields, higher quality, and increased profits, fabricators should consider the SPC and SQC techniques as standard tools for understanding, validating, and improving processes in all areas of manufacture that includes product distribution, transportation, and accounting. Using on-line software, SPC provides the close-up view; using off-line software, SQC detects differences over time. These two techniques provide two different essential functions.

Prior to the widespread implementation of supervisory control and data acquisition (SCADA) and human-machine interface (HMI) systems, most SPC and SQC was performed by quality-control departments as an off-line process. Data was collected from test stations, laboratories, etc. and statistical analysis was performed later. SCADA/HMI systems, however, have made it feasible to provide plant-floor SPC charts using data collected in real time direcdy from the process. Fabricators that want to standardize SPC and SQC to increase their use find they need the two following functions: (1) provide the plant floor with SPC charts and (2) make data collected by SCADA systems available for off-line analysis. Available is SPC and SQC software to support these efforts. Recognize that the bulk of SPC's value is derived from process improvements developed from offline SQC analysis.

Virtually all-classical design equations assume single-valued, real numbers. Such numbers can be multiplied, divided, or otherwise subjected to real-number operations to yield a single-valued, real number solution. However, statistical materials selection, because it deals with the statistical nature of property values, relies on the algebra of random variables. Property values described by random variables will have a mean value, representing the most typical value, and a standard deviation that represents the distribution of values around the mean value.

This requires treating the mean values and standard deviations of particular property measurements according to a special set of laws for the algebra of random variables. Extensive information can be found in statistical text. The algebra of random variables shares many elements of structure in common with the algebra of real numbers, such as the associadve and cumulative laws, and the uniqueness of sum and product. In combinations of addition and multiplication, the distributive law holds true.

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