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Importance of central limit theorem

Why is the central limit theorem so important in SQC?

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No matter how carefully a production process is controlled, these quality measurements will vary from item to item, and there will be a probability distribution associated with the population of such measurements.
If all important sources of variations are under control in a production process, then the slight variations among the quality measurements usually cause no serious problems.
Such a process should produce the same distribution of quality measurements no matter when it is sampled, thus this is a "stable system."

Objective of quality control is to develop a scheme for sampling a process, making a quality measurement of interest on sample items, and then making a decision as to whether or not the process is in the stable state, or "in control."
If the sample data suggests that the process is "out of control," a cause is for the abnormality is sought.
A common method for making these decisions involves the use of control charts.
These are very important and widely used techniques in industry, and everyone in the industry, even if not directly related to quality control, should be aware of these.
Attributes - A performance characteristics that is either present or absent in the product or service under consideration.

Examples: Order is either complete or incomplete; an invoice can have one, two, or more errors.
Attributes data are discrete and tell whether the characteristics conforms to specifications.
Attributes measurements typically represented as proportions or rates. e.g. rate of errors per opportunity.
Typically measured by "Go-No Go" gauges.

Statistical process control
Methodology for monitoring a process to identify special causes of variation and signaling the need to take corrective action.
When special causes are present, the system said to be statistically out of control.
If the variations are due to common causes alone, the process is said to be in statistical control.
SPC relies heavily on control chart A typical quality control plan requires sampling one or more items from a production process periodically, and making the appropriate quality measurements.
Usually more than one item is measured each time to increase accuracy and measure variability.
The chart helps the quality control person decide whether the center (or average, or the location of central tendency) ...

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