ARTICLES
# About Change Analysis

#### Step Changes in the Mean

#### Step Changes in the Standard Deviation

#### Changes in the Slope

#### Target Charts

#### D Charts

**Change Analysis is used to detect changes in chronological ordered data**. Using machine power algorithms, combined with statistical significance testing, changes in the process average, standard deviation and slopes can be rapidly detected.

The technology was first applied in the cigarette industry to identify reasons for changes in cigarette firmness by comparing changes between cigarette firmness with changes in other variables. Such change comparisons are called fingerprint analysis. The fingerprint analysis showed that changes in moisture content corresponded to changes in cigarette firmness. The fact that moisture lowers cigarette firmness was expected, however cigarette firmness results were corrected for moisture and there should thus not have been a correlation. The initial reason for the correlation was thought to be due to inadequate moisture correction but extensive testing showed that the correction formulae used were correct. Further fingerprint analysis showed that there was a relationship between moisture contents and two volatile materials used in the tobacco expansion process. Because moisture content was measured by the oven volatile method the measured moisture content was inflated causing overcorrection for moisture and hence the change relationship.

Change Analysis is a better alternative to Shewhart Control charts as a Statistical Process Control tool to improve quality. Shewhart control charts without additional tests only show when individual points fall outside two limits determined statistically. If a point falls outside control limits the process is deemed to be out-of-control. This is inefficient and provides little information for the analyst. Change Analysis is more effective as it is more sensitive to picking small changes and shows the magnitude, onset and duration of a change.

Change analysis has many applications. Outside manufacturing it can be used to quantify the effect of medication on blood pressure, help manage diabetes, reduce obesity, detect water leaks, identify cannibalism by competing brands, show changes in power consumption, detect changes in sales and relate these to promotions and competitor behavior, plus virtually unlimited other applications such as global warming.

The algorithms are complex relying on machine power to search for changes in the process mean, standard deviation and slopes. Changes once found are statistically validated. This itself is a complicated process because changes in standard deviation effect significance testing for means and slopes. These in turn affect standard deviation.

There are five major types of change analysis that can be performed.

The is the most common change analysis performed. An example is shown below. Most changes can be modeled as steps and hence the popularity. Applications are countless including all the above mentioned examples.

Change Analysis - Step Changes in the Mean

Although step changes in the standard deviation are less popular, they should be of equal importance and in some instances even more important. In manufacturing standard deviation affects process capability and thus non-conformance. For health the average blood pressure alone is insufficient to make medication decisions. A sudden increase in standard deviation can indicate extreme fluctuation in stress levels and may require alternative treatment to medication.

Increases in standard deviations can be reflected in increases of the mean, if lower values are bounded. For weights and measures control, depending on the legislation, increases in standard deviation due to a faulty filling process will require increasing ‘give-away’ to ensure weights and measures legislation is met.

Change Analysis - Step Changes in the Standard Deviation

Standard deviations for Sd SPC charts are the subgroup standard deviations if sub groups are greater than one. If the subgroups are equal to one, moving standard deviations are computed. For Change Analysis of Standard Deviation, the calculations are similar, but for subgroup size equal to one requires first removing changes in the process mean, as these would inflate the moving standard deviations.

There are many applications where detecting changes in the slope is important. One example is for sales forecasting where we need to see if a plateau has been reached, or if there is a downward trend requiring a new marketing campaign. Another application is for dieting where it is important to detect plateaus requiring a change in diet, or too slow or rapid weight losses.

Changes in slopes are detected using a powerful regression switching detection algorithm.

Change Analysis - Changes in the Slope

Target charts are based on step chart change analysis. Each step is statistically compared to the specified target. If there is no significant difference the average for the step is deemed to be on target. Steps that are on target are color coded green and those that are off target are color coded red.

These charts have a wide range of application including weights and measures control to minimize ‘overfill’, hypertension and diabetes management, financial budget control, body weight management.

Target Charts

D-Charts are an advanced form of Change Analysis. They combine changes in both the average and standard deviation over time and display this information in a manner that enables the analyst to see the contribution to non-conformance. Applications are in quality assurance, process control, health and fitness and in genera any application which must fall inside specification limits.

To visualize the effect of changes in the average and standard deviation, color coded ‘D’s are used, as shown in the image below. Th effect of the instability can then be easily seen.

D-Charts