Machinery's Handbook, 31st Edition
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STATISTICAL ANALYSIS STATISTICAL ANALYSIS OF MANUFACTURING DATA Statistics Theory in Brief
High-volume manufacturing production, unlike prototype design work, typically in- volves repeating machining operations and processes hundreds, thousands, or even mil- lions of times during a given product or product family’s production run. Understand ing the failure mechanisms in a product’s tooling and improving the efficiency of these operations by adjusting manufacturing parameters brings many essential benefits to the manufacturing process. Seeing where failure and inefficiency occur can save on tool wear of indexable inserts, milling cutters, reamers, twist drills, etc.; improve speed, feeds, and power consumption profiles; reduce machine tool accuracy drift; and reduce lubrication and other maintenance-related failures. Improving these and other related process, even by a tiny amount, can result in huge cost savings in large production run environments. To begin this process, measurements and other production process values must be col- lected so that patterns can be found. This is the collection of raw (or source ) data . The information is put into tables (tabular form), to be processed (usually) by a computer pro- gram that analyzes and interprets it by rigorous statistical analysis . Without statistics theory, it would be impossible to know whether or not the testing was comprehensive enough to offer valid experimental conclusions that can then be used to make manufac- turing process changes. Probability.— In commercial enterprises, predictions about a particular outcome or event are made regularly to determine best practices and to minimize risk. Predictions are formed by observing events and collecting data, which is then interpreted using statistical analysis, based on concepts of probability theory . Probability is the likelihood of an event happening randomly among all possible events. Simple experiments, such as observing the number of times heads or tails turn up in a coin toss, and complex ones, like locating the position of an electron in an atom, are studied using probability. Data analysis enables development of a detailed statistical picture of the event being studied, and probability quantifies how likely the particular event is. In industry, statistical analysis is used to investigate data to evaluate the success and/or efficiency of a manufacturing process. Statistical methods are described in this section using these terms: Experiment: A well-defined action that is repeatable. Data: Information collected during an experiment. Trial: A particular performance of an experiment. Set: A collection of events (or elements), such as may occur in an experiment. Sample space: The set of all possible outcomes. Event: Any subset of the sample space; one outcome or a collection of outcomes. Probability of an event: Ratio of number of outcomes of a particular event to total number of outcomes possible in the sample space of events. The probability of an event can be expressed as a decimal between 0 and 1, as a fraction , or as a percent between 0 and 100. The sum of all probabilities for outcomes of a particu- lar experiment is 1; that is, it is 100% likely that one of the outcomes will occur. In the coin toss example, each toss is a trial, and there are two possible outcomes: heads or tails (as long as the coin is fair, that is, both sides have an equal chance of turning up). So the probability of tossing a head is 1 ⁄ 2 or 0.5 (50%). As another example with two out- comes, consider a water treatment plant with 34 female workers (set A) and 36 male work- ers (set B); the universal set is 34 + 36 = 70 workers. The probability that a female worker is chosen at random from the universal set is 34/70, or approximately 0.486 (48.6%). In manufacturing parts, the probability of a defective part occurring in a production run would be the number of parts found to be defective (the “event”) in relation to the total number of parts in the run (the “trials”); defective parts ought to be far fewer than accept- able ones. So, to say there is a 3% probability of a defect means that for every 100 parts that are produced, on average, 3 will be defective and the other 97 will be acceptable. In other words, the predicted defect rate is 3% and the yield of acceptable parts is 97%.
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