Statistical process control is used to monitor and then manage the process being monitored. For complex systems, it may be necessary to generate a model to determine how the SPC chart will look given specific variable states. This also allows management to calculate a mean and expected deviation to create an SPC control chart for specific input variables, instead of having to let the system run and create a new chart each time the process inputs change.

## Overview of Statistical Process Control

SPC collects a series of values on the characteristics (height, weight, dimensions) being observed. These values are charted. The process mean is calculated. This is used as the center line of the SPC chart. Then, the standard deviation is calculated. An upper and lower control limit are determined and then placed on the chart. The SPC chart is then monitored. Any trends are recorded. Any trends that approach the upper or lower control limits will result in corrective action.

## Time-Series Modeling

Time series modeling measures a process at specific time intervals. A series of trend lines or curves is then calculated for the existing time series data. The trend line is a simple algebraic equation. A time series model can then forecast what that trend line will be in the future. A trend line can be flat, trending up or trending down.

## Multivariate Modeling

Multivariate means many variables. A multivariate model has several variables, all with their own associated equations. These variables can include time, process speed, material variations and any other process variable. A multivariate model is created based on taking all of these factors into account. A multivariate model for the statistical process control chart will then be created by entering different times. This model can then show how the SPC chart should look over time for different variable values.

## Stochastic Models

Stochastic processes are essentially random. These processes are modeled by assigning a probability to each possible outcome. The model is then created by running the equation many times to generate a most likely outcome and probabilities of other outcomes. Stochastic models are also called Monte Carlo simulations.

## Artificial Neural Networks

This type of statistical process control model is abbreviated to ANNs. ANNs are the most complex form of statistical process control models. They simulate processes with multiple inputs that can vary, intermediate steps that can vary, and different resulting outputs. The ANN will then give the resulting outcomes. If the process has any stochastic processes along with variables defined by linear equations, the ANN can give a range of outcomes. If run many times, this will give the most likely and thus “mean” outcome for an SPC chart for such a complex process.

#### References

- “Statistical Process Control in Automated Manufacturing”; John Bert Keats, Norma Faris Hubele; 1988
- “Statistical Models and Control Charts for High-Quality Processes”; Min Xie, Thong Ngee Goh, Vellaisamy Kuralmani; 2002
- “Statistical Applications in Process Control”; John Keats, Douglas Montgomery; 1996
- “Instrument Engineers' Handbook: Process Control and Optimization”; Bela Liptak; 2005

#### Photo Credits

- statistic image by Soja Andrzej from Fotolia.com