## Statistical Process Control (SPC) in Quality Improvement

#### Non Standard X-Bar Charts

There are many applications where normal X-Bar Charts will not work. The X-Bar Chart as proposed by Walter Shewhart is based on within subgroup variation.

#### Modified Control Charts for Individuals Charts

Modified Control Charts are normally used for data with subgroup size greater than 1, say 5.

#### Modified Control Charts for Individuals Charts for Six Sigma Processes

Once a process is in control and variability well within specification limits, e.g. Cp>3, it maybe be reasonable to allow the process to drift a little within specification limits, without any noticeable effect, whilst appreciating that there is a cost in unnecessary tight control.

#### Zone Charts

Standard control charts consist of outer control limits and sometimes warning limits. Some analysts will enhance these charts with run and trend tests to increase the sensitivity to detecting variation due to assignable causes.

#### U (Average Number of Defects per unit) Chart

U Charts are used to control the number of defects. Defects must not be confused with defectives. A defective part has one or more defects.

#### Statistical Process Control Charts

SPC Charts were formally introduced over 100 hundred years ago by engineers and statisticians, such as Walter Shewhart, a self-taught statistician. These pioneers recognized and understood the concept of variability.

#### Percent P (Percent of Defectives) Chart

Percent Charts are used for the same applications that P Charts are used i.e. to control the fraction of non-conforming products, although they can be used to also control fraction conforming (yield).

#### P (Proportion Defective) Chart

P Charts are used to control the fraction of non-conforming products, although they can be used to also control fraction conforming (yield). Control limits are based on the binomial distribution.

#### NP (Number of Defectives) Chart

NP Charts are used for the same applications that P Charts are used i.e. to control the fraction of non-conforming products, although they can be used to also control fraction conforming (yield).

#### Modified Control Charts

Once a process is in control and variability well within specification limits, e.g. Cp>3, it maybe be reasonable to allow the process to drift a little within specification limits, without any noticeable effect, whilst appreciating that there is a cost in unnecessary tight control.

#### Modified Control Charts for Six Sigma Process

A six sigma process that is centered at target has a Cp and Cpk index of 2.0. A six sigma process assumes that a shift in process average as high as 1.5 standard deviations from target will not cause perceivable problems.

#### Exponentially Weighted Moving Average (EWMA) and Range/Sd Control Charts

The EWMA chart has the same application that the moving average chart has. It is an alternative to the Shewhart X-Bar or Individuals chart when it is important to detect relatively small changes in the process mean.

#### Tabular Cusum Chart for the Average and Hawkins Statistic for Variability

The Cusum chart is arguably the most sensitive classical control chart for detecting shifts in the process mean. Whereas a Shewhart X Bar chart can take a one standard error change a Cusum chart only takes 9 points on average.

#### C (Number of Defects) Chart

C Charts are used to control the number of defects. Defects must not be confused with defectives. A defective part has one or more defects.

#### X-bar and Sd (Standard Deviation) Control Charts

Because it is so easy to calculate and understand the range, over the standard deviation, the X-bar and Range chart is often preferred over the X-Bar and S control chart.

#### X-bar and Range Control Charts

Because it is so easy to calculate the range, the X-bar and Range chart is often preferred over the XBar and S control chart. However, it is recommended that the subgroup size is less than 10.

#### Moving Average and Range/Sd Control Charts

The moving average chart is used as an alternative to the Shewhart X-Bar or Individuals chart when it is important to detect relatively small changes in the process mean.