# Busn603 - Statistical Process Control

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Statistical Process Control

Sascha Johnson, Logan Kreider, Sheyna Marshall, Sean Olaughlin, Margaret Poulsen

American Military University

Quantitative Analysis

BUSN603

Chander Sekar

April 7, 2019

Statistical Process Control

Many businesses and organizations use statistical process control (SPC) to monitor the production of goods and services.  SPC involves setting standards, monitoring said standards, taking measurements and implementing measures to correct abnormalities while products and services are being produced (Render, Stair, Hanna, Hale, 2015).  Using SPC, businesses are able to determine whether a process is in control or out of control through the use of control charts.  A control chart uses data of a specific process or function and visually presents that data over time.  There are four main types of control charts: X-bar charts, R-charts, p-charts, and c-charts.  Each of these different charts compares various aspects of the samples to determine averages and acceptable limits away from the average using standard deviation.  This information is then used to analyze the samples and maintain quality control within a process.

Central Limit Theorem

The Central Limit Theorem (CLT) is an essential part of the business equation, in being that it is considered the basis for multiple business related statistical procedures.  Within SPC, or quality control, CLT is one way to set the standards for goods or services.  In order to fully understand the CLT we must understand exactly what the “mean” is. The mean of an equation is the average of the data that is collected and being used to determine normal distributions within a company (Colburn, 2009).  What makes CLT stand out is that results will hold no matter what the original population distribution would have been.  This occurs because as more random samples are taken, the calculated mean has a slightly different result.  If this continues, and many different samples are taken and means are formed we then will begin to see their own form of distribution develop.  This is referred to as “sampling distribution” as it represents estimates of distribution across the repeated sampling that had taken place.  When a graph is made with these estimates we will end up seeing a bell curve (Albright, 2015).  This means that the CLT method results in statistics that are correct and usable.  CLT provides a way for that business to use mathematics and gathered data to get to the mean and properly use it in distribution (Bruner, 2018).

The mean-value developed from CLT, along with standard deviation, are used to develop the X-bar chart.  The X-bar chart is a control chart that allows for production managers to view how a group of samples is comparing to the average, or expected, value.  This use of CLT is extremely useful in quality control when there is a measurable value, as in weight or size.  The upper and lower limits are based on standard deviations from that mean.  By setting those limits at three standard deviations, one can be 99.7% certain that if the sample value lies outside of those limits, then there is an assignable cause for it (Render, Stair, Hanna, Hale, 2015).  The purpose of SPC is to find those outliers, investigate to find the assignable variation, and create a solution.  CLT provides a way to develop the X-bar charts in order to identify those outliers so that the control process can be fixed.

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