Q. 191 Explain the four terms with respect to Run Charts - Mixtures, Clusters, Oscillations and Trends. Does a run chart provide any advantage as compared to a control chart?

 

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We use run chart to see if there is any sign of special cause variation in our process data. It is graphical representation of the process performance plotted over time (hourly for Continuous Flow processing and most commonly in days or in months)

 

Most importantly, What is Run?

It is 1+ consecutive data points on the same side of Median (Either above median or below median)

 

Variations can be common cause or special cause.

Point to note:

Common cause variation is outcome in an Stable process that is predictable &

Special cause variations is outcome in an Unstable process that is not predictable

 

By using run chart, we will be able to find the trend and pattern in the process data set

 

Common patterns of non-randomness include:
Mixture Patterns
Cluster Patterns
Oscillating Patterns &
Trend Patterns

 

When we run control chart on Minitab, it detects whether above mentioned patterns are existing in the data

 

Sample data – Considered gold price/10 grams for the last 55 months 

Classification: Public

In the above chart we can witness, clustering and trends.

 

Cluster Pattern:
In general, it is set of points in one area of the chart, above or below the median line.
Thumb rule for cluster, 6+ continuous nearby points above/below the median line

We can also check out the P value to see if there is potential cluster in the data
Specifically, when P value is < 0.05, we could say possibly the data could indicate cluster.

In reference to the above Run chart, Approximate p-value for clustering is 0.000 which is less than 0.05, so reject null hypothesis.

Cluster can show sign of potential sampling or measurement issues.

 

Trend Pattern:
It is sustained drift in the data set; either upward trend or downward trend;
Thumb rule to conclude trend is 6+ consecutive points either higher than previous data in one continuous period or the other way, that is 6+ consecutive points lower than previous data points.

In the referred above chart we could observe an upward trend and P-value is also less than 0.05 to conclude potential trend.

 

Now as we know about Cluster and Trend, lets note the below points:
Opposite of Cluster is Mixture &
Opposite of Trend is Oscillation

 

Oscillation:
When the process is not stable, we get data points spread above and below the median line, looks like oscillation.
Thumb Rule: 14+ points in one continuous period increasing and then decreasing cyclically
For P value < 0.05, possible oscillation can be observed. 
 

                                                                     Classification: Public

Mixture:
When there are no points near the center line, with 14+ points upward and downward, increasing and decreasing over the median line and P value <0.05, we can have potential mixture in the data set.
 

Run Chart & Control Chart

In Control chart, along with the center line we have the upper and lower control limits.

Another major difference is in Control chart - Center line is median and in Run chart - Center line is Mean;  

 

Run chart does not give any detail on the statistical control limits.

 

We can see control chart as an Enhancement to Run Chart.

 

In control chart,

we will be able to check the stability - whether the process mean and variation are stable;  check whether any out of control.

We can check normality - data is normal or non normal;

But it does not provide view on patterns.

 

When we use control chart from assistant view in Minitab we get below output view: Stability Report

                            Classification: Public

It gives commonly used patterns for reference, however does not highlight the pattern in the output.

 

Control charts will be useful over an Run chart, when the focus in on the variation and to identify potential deviation.

However, downside of control charts is that it could have below limitations and can cause unnecessary wastage of time.

• False Alarms
• Incorrect Assumptions
• Incorrect Control Limits

Both - Run chart and Control charts has its own advantages and used for different purpose [Run - Trend & Patterns; Control - Stability] and are useful based on the required objective, situation and analysis.

Run Chart

A Run Chart is a line chart that visually displays data over a period of time.  It’s also known as a trend or time series chart.

Why Run Chart?

Run Charts help us to identify patterns that may exist in the data, and trends over time.  

When to use Run Chart?

You should use Run Charts whenever you want to understand how your process has performed over a certain period of time or when you want to see if your changes resulted in sustainable improvements.

In a Run Chart we can identify below non-random variations or patterns:

Clusters:

Cluster is one where we can see a group of data points in a particular area in the Run Chart.  We can also identify the clustering by looking at the probability value.  If the probability value for Clustering is less than 0.05, we will be having clustering of data in the Run Chart.

Mixtures:

If the data points frequently crosses the median line, it’s called Mixtures.  We can see than when we pool the data points from more than one population.  We can also identify the Mixtures by looking at the probability value.  If the probability value for Mixtures is less than 0.05, we will be having Mixture of data in the Run Chart.

Trends:

A trend is defined as a continued drift or float of data.  It can be either in the upward direction or downward direction.  This is an indication that the process may in near future go unstable.  This may cause due to replacement of operators, aspects such as dilapidated tools etc. Trends can be identified by looking at the probability value.  If the probability value for Trends is less than 0.05, we will be having Trends in data in the Run Chart.

Oscillations:

When data swings upwards and downwards, it’s called Oscillations.  This gives an warning that the underlying process is not stable.  Oscillations can be identified by looking at the probability value.  If the probability value for Oscillations is less than 0.05, there will be Oscillations in data in the Run Chart.

Comparison of Run Charts Vs. Control Charts:

Below are some comparisons between Run Charts and Control Charts:

Run Chart:

·         Run Chart is simple and can be created easily,

·         Can be quickly analyzed

·         A person looking at a Run Chart does not require statistical knowledge to read the chart

However, a run chart lacks the below advantages which a Control Chart possesses:

Control Charts:

·         A control chart will help us understand whether the process is stable or in control

·         Is the process in the correct track

Run Chart is a plot of the data points for a particular metric with respect to time. It is primarily used for following two purposes

 

1. Graphical representation of performance of the metric (without checking for any patterns in it). E.g. The scoring comparison in a cricket match. The runs are plotted on Y axis and X axis has overs (which is a substitute for time spent)

Source: The Telegraph

 

2. To check if the data from the process is random or if there is a particular pattern in it. These patterns could be one or more of the following

a. Clusters

b. Mixtures

c. Trends

d. Oscillations

 

Source: Minitab help section

 

Run chart if used for point number 2, performs following tests for randomness

- Test for number of runs about the median. This is used for checking Clusters and Mixtures.

Clusters are present if the actual number of runs about the median is less than the expected runs. This implies that there are data points in one part of the chart

Mixtures are present if the actual number of runs are more than expected runs. This implies that there are frequent crossings of the median line

- Test for number of runs up or down. This is used for checking Trends and Oscillations.

Trends are present if the actual number of runs is less than the expected runs. This implies that there is a sustainable drift in the process (either up or down)

Oscillations are present if the actual number of runs is more than the expected runs. This implies that the process is not steady

 

These are hypothetical cases with the below hypothesis

Ho - Data is random

Ha - Data is not random

p values are calculated for all the 4 patterns. A p value of less than 0.05 indicates acceptance of Ha implying that the particular pattern is present in the data set.

 

Absence of these patterns indicate that the process is random.

 

Advantages of Run chart over Control chart

Ideally control chart is a more advanced tool as compared to a run chart. However following situations warrant the use of run chart over a control chart

1. Run chart is preferred when we need a snapshot of the metric performance with time without taking into account the control limits or if the process is stable/unstable. E.g. like the scoring run rate comparison for cricket (refer the screenshot above)

2. One can start creating run chart without any prior data collection unlike in a control chart (where data is collected first to determine the control limits)

3. As a quick check to see if the process data is random or not. For doing such checks (clusters, mixtures, trends and oscillations) in a control chart, one would have to run all the Nelson tests (usually control charts are used with only one test i.e. any points outside 3 standard deviations and hence might not be able to detect such patterned data)

4. Apart from the above, it is easy to prepare and interpret a run chart in comparison to a control chart

1) A mixture represents more crossing at the center lines i.e. no points near the center line. It is used to indicate the mixture of data from 2 different groups.
2) Clusters indicates group of points above or below the center line
3) Oscillation occurs to fluctuation of data up and down:
4) A trend is a extended drift in the data

 

Run chart helps in determining the shifts, trends or patterns for a time period in a process. It can also help in understanding the common or special cause of variations. Supports in identifying on the pattern of changes in a process. Run chart is very simple to create and understand as compared to other charts. Sometimes setting up incorrect upper or lower control limit in a control chart can lead to incorrect outcome / analysis. There is no such distortion in the run chart is tries providing natural flow of data points over the time period

Benchmark Six Sigma Expert View by Venugopal R

People who are not trained or exposed to the principles of Control charts often find it difficult to understand the significance of the Control limits and their interpretation.

 

A good understanding of control charts starts with understanding data types. Then one has to understand some probability theory. Then the principle of Normal distribution. Good clarity on Special and Common causes. Then preferably an insight into Central Limit Theorem. Such a foundation prepares a person to have a good grasp of the underlying principles of Control Charts, their different types and application of each type of chart and so on.

 

Even with all this understanding, usually the control charts are used for the observing any points falling outside the control limits, though there are 8 rules defined to observe statistical instability. There still remains the confusion in the minds of some as to how the Control limits differ from the specification limits and some are not comfortable with out including the specification limits also on the control charts.

 

The run charts are much simpler and their understanding and interpretation do not require the extent of subject knowledge as above. Run charts do not have ‘Control limits’ much to the relief of those who had discomfort with control limits of control charts. Those who use Minitab to create run charts would have seen the chart has p values pertaining to the types of instability viz. Mixtures, Clusters, Oscillations and Trends. I am not explaining these terms here, since I am sure many respondents will do a good job there. However, if we go through the rules to detect instability as per the control chart, we can see that not only the four terms that are used for run charts are well covered by those rules, but additional ones as well.

 

One may choose to use Run charts or Control charts depending upon the situation and the ease of comprehension by stakeholders involved. In many instances, some of the instability observations will be quite evident on a run chart and one may proceed by taking decisions for improvement. 

Run Chart – It shows the trend/pattern in the process. However, we need to identify if there is Mixture Pattern, Cluster Pattern, Oscillation pattern or trend pattern. Variation can be due to normal cause or special cause. If there is common cause, data points will remain close to the mean, however, if any data point of very far or not in the specification limits that is possible due to special cause which needs to be identified and addressed.

 

Control Chart - It shows how your process is performing. In control chart we have a central line (Average) one UCL (Upper control Limit) and LCL (Lower control limit). If all the data points of process/activity falls near central line or within UCL and LCL, it means that process is in control & stable and if any data point is out of UCL or LCL, it mean that there is some special cause which needs to be identified and address. In some cases, if data point is beyond LCL, that means that may be due to special cause but your process is more perfect at that point and it could be a best practice to look at to sustain the same for improvement in the overall process.

 

Mixtures Pattern is said to be there when the frequent crossing of the center line. If p value of mixture is less than 0.05, the process has mixture pattern and the data is from 2 different processes

 

Cluster Pattern is said to be there when the several data points occurring on the one side of the center line and creating a group due to special cause variation. If p-value for cluster is less than 0.05 then you have cluster pattern in data

 

Trend Pattern is nothing but a sustained improvement or depletion in the process. It shows if there is improvement in the process or not. If the p-value for tends is less than 0.05, then you have trend pattern in your data.

 

Oscillation Pattern occurs when there is lot of fluctuations (up & down) in data points on run chart. It shows that the process is not stable. If the p-value for oscillation is less than 0.05, you have oscillation pattern in your data.

 

Control chart is the advance version of run chart which given you more insight then Run chart.

The chosen best answer is that of Natwar as he has explained all 4 terms - Trends, Oscillations, Mixtures and Clusters. He also clearly outlines when is Run Chart preferred over Control Charts.

 

Run Charts only indicate non randomness in data or existing patterns; if the desire is to check for common cause vs special cause variation, Control Charts should be used.