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About Change Analysis - A modern alternative to Shewhart Control Charts

The BIS.Net Team BIS.Net Team

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 power of the technology can be seen in a cigarette industry case study. Several years were spent, trying to identify reasons for drops in cigarette firmness after manufacture. The drop in firmness was compensated for by adding more tobacco, which was costly. Change analysis was applied 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 content 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 by the other two volatiles, causing overcorrection for moisture and hence the drop in firmness after the volatiles dissipated into the atmosphere. Considerable money was thus wasted compensating for a firmness drop that did not exist.

Change Analysis is a modern alternative to the Shewhart Control Chart. The Shewhart Control chart technology which, in essence, consists of no more than two lines placed at locations within which the natural variation of the process is expected to fall, was a reflection of the times, where there was no modern computing power available. Through modern computing power Change Analysis offers a number of significant advantages over Shewhart Charts.

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. The analyst cannot be certain that the out-of-control point was due to an enduring change in the process mean, or a one-off instance of an assignable cause acting. For example, Figure 1 shows an out-of-control point for a Phase I control chart. Operators would search for an assignable cause at around the time where the out-of-control point occurred.

Shewhart chart demonstrating the issues with spc theory Figure 1 Phase I X-bar Chart

Figure 2 shows a Phase II control chart, using the same data. In this instance the Control Limits are fixed, based on a stable process during Phase I (not the same data)

Shewhart chart demonstrating the issues with spc theory Figure 2 Phase I X-bar Chart using the same data

Now there are several out of-control points. Operators may search at four points in time for assignable causes. The difference between the two charts is because for the first, limits were placed around the process average which were affected by the assignable cause. Excluding the points, in calculations for the process mean had little effect as is seen in Figure 3, which still only had one out-of-control point. The reason is that the process was not just out-of-control for one instance but much longer, to be shown below.

Shewhart chart demonstrating the issues with spc theory Figure 3 Figure 1 data excluding out-of-control points from calculations

Figure 4 shows a Change Analysis chart on the same data, which is more informative and accurate.

Shewhart chart demonstrating the issues with spc theory Figure 4 Change Analysis on the same data.

The Change Analysis shows where the changes are most likely to have occurred. Due to random sampling there is no guarantee that the exact times are identified. This depends on the magnitude, specified sensitivity and duration of the change, but as Figure 4 demonstrates Change Analysis is designed to show the onset, duration and magnitude of a change. The Shewhart chart is not. This makes it difficult to search for assignable causes. Knowing the estimate of the onset and duration of a change makes it easier to identify the cause.

Change analysis can also be used to identify one point in time instances of assignable causes, however, hybrid Change Analysis found in the hybrid app is a better alternative.

Another benefit is that Change Analysis detects small changes much faster than X-Bar chart, in a level comparable to Cusum charts, though Cusums are the recommended option if the objective is to detect a change from target and then reset the process.

Change Analysis is robust to non-normality when compared to x-bar charts. Figure 5 shows an x-bar chart of an in-control highly skewed process.

Shewhart chart demonstrating the issues with spc theory Figure 5 Standard X-bar chart applied to highly skewed data with subgroup size of 5 incorrectly showing the process to be out-of-control

Although the process was out-of-control, even though many scholars assert that the Shewhart X-bar chart is robust to non-normality, the reality, evidenced by Figure 5 is different. Distribution optimized charts do however work as is shown in Figure 6,

Shewhart chart demonstrating the issues with spc theory Figure 6 Distribution Optimized Chart correctly showing the non-normal process to be in control

Change Analysis also works as is shown in Figure 7. False alarm rate is very low (0)

Shewhart chart demonstrating the issues with spc theory Figure 7 Change Analysis Chart correctly showing the non-normal process to be in control

The difference between Distribution Optimized X-bar charts and Change Analysis is that x-bar charts, whether standard or machine powered distribution optimized charts are not designed to identify the onset, magnitude and duration of a change. Figure 8 shows a small change with a highly skewed non-normal distribution using Change Analysis. Figure 9 uses a Distribution Optimized X-bar chart.

Shewhart chart demonstrating the issues with spc theory Figure 8 Change Analysis output of a non-normal process with a small magnitude change.
Shewhart chart demonstrating the issues with spc theory Figure 9 Distribution Optimized X-bar chart is ineffective in showing the change for the same non-normal process

Change Analysis is more effective as it is more sensitive to picking small changes and shows the magnitude, onset and duration of a change. Figure 10 shows that the standard x-bar chart fails completely

Shewhart chart demonstrating the issues with spc theory Figure 10 The standard x-bar chart fails completely

In summary, Change Analysis is designed to show the onset, duration and magnitude of a process change, the standard x-bar and distribution optimized x-bar chart are not. The standard x-bar chart is not robust to non-normality, Change Analysis and distribution optimized x-bar charts are. Change Analysis can be used to detect spikes equally effective as x-bar charts, but hybrid change analysis is a better option. Change Analysis detects small changes better than x-bar charts and has comparable false alarm rates. The analyst has more control over the performance of change analysis compared to Shewhart Charts. The analyst can alter sensitivity, minimum duration, whereas for a Shewhart chart only sensitivity can be altered.

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

  • Step Changes
  • Sd Changes
  • Slope Changes
  • Target charts
  • Sd Charts
  • D-Charts
  • Finger Print Analysis

Reality Check

Change analysis cannot perfectly detect changes at exactly the correct time, nor can it perfectly estimate the magnitude of changes. Onset and duration and magnitude of changes are estimates only depending on the way the numbers fall. These estimates become unreliable when there are small changes in magnitude and duration. No control chart technology performs well with small changes, due to sampling noise. For medium to large changes Change Analysis out performs standard control charts introduced at a time when modern competing power was non-existent.

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