Q 496. What are rare event control charts (e.g. G Chart or T chart)? What advantage do they offer over traditional discrete data charts like a P or a U chart? 

 

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As the name suggests, the occurrence of event is rare. These events are rare in nature & are also spaced farther in time which makes us to have ineffective traditional attribute control charts with more zeros & with occasional spikes. There are 2 types of rare event control charts: G chart & T chart.

 

T chart is based on the amount of time since the last event occurred. A traditional P chart might show lot of zeros & an occasional spike. This makes us difficult to check if an improvement has helped to control the process. In contrast, a T chart can overcome this & help us in concluding if an improvement has helped or not.

 

On the other hand, a G chart is based on the number of events between rare events. This again prevents lot of zeros.

Rare event control charts are leveraged to study the processes where the data is generated from events that occur rarely. These events occur infrequently which a traditional chart will not be able to capture effectively. Thus the rare event control charts were developed keeping in mind the limitations in the traditional control charts.

 

There are two main types of rare event control charts i.e. G Chart & T Chart. Let us understand both these charts.

 

G Charts :

 

G chart is used to measure the number of events between rarely occurring incidents & this chart represents these rare events in a process over time. Here, each point on the chart represents the number of units of the rare event occurrences. One common example can be the medicine indent process in a hospital’s OPD where an expected server breakdown can occur. So, we can use G chart in order to plot the number of medicine indent entries done between events of server breakdown. Below is the visual representation of the G-chart for this example:-

 

 

Here, the points above the control limit indicate that the number of medicine indent entries has increased between server breakdown, thus it is a desirable to see if any point is above the upper control limit as the number of entries have increased which is favorable as far as patients in OPD are concerned.

 

T Chart :

 

T-chart measures the amount of time that is elapsed since the last event. Here, each point on the chart represents the number of time intervals that have been passed since the prior occurrence of a rare event. Let us take the same above example of medicine indent process in a hospital’s OPD & plot the days passed since the last server breakdown happened.

 

 

The above chart shows that there is an improvement in the days between server breakdown which is good sign for the process as the rate of server breakdown has decreased.

 

The traditional chart have their set of limitations when it comes to capturing rare event scenarios. Plotting rare events will result in lot of zeros or a spike or two. Let us understand this  through an example.

 

Let us say we are having a production process where we are capturing loss in production due to accidents in the shop floor. Let us plot this data on a P-chart:-

 

 

The above chart shows how many months there were no occurrences of lost production due to shop-floor accidents. Now, there are many months where there are no occurrences of lost production, now if there is an improvement in the process which resulted in a reduction in days lost production due to shop-floor accidents, this chart provides little or no insights.

 

Now let us consider the same data using a t-chart where instead of plotting the lost production per month, the days passed since the last instance of lost production.

 

 

Now on the t-chart, we can clearly see an increase in the days between two production losses due to shop-floor accident which was not evident on the p-chart earlier.

 

Thus we can clearly see that for capturing rare event, using rare even control charts such as G-Chart or T-Chart offer more advantage over the traditional charts such as P-Chart or U-Chart & are considered to be more robust & insightful.

 

 

The control chart, which is used to study the data of rarely occurring incidents/events is known as the “RARE EVENT CONTROL CHART”. Rare event charts provide insight into the processes that occur infrequently enough to track them using traditional control charts. Rare event charts offer two types they are, G Charts and T Charts. They differ from each other in the way it measures rare events, the G Chart measures the count of events between incidents and the T Chart measures the time intervals between incidents. 

 

 

G Charts,

It measures the number of events between errors or nonconformities which occurs rarely, each point on the chart represents the number of units between relative occurrences, E.g. In a production line materials are produced daily, and an unexpected line shutdown may happen we can use a G Chart to track the number of units produced between line shutdowns.

 

T Charts,

It measures the time elapsed (Interval) since the last event, each point on the chart represents several time intervals that have passed since a prior occurrence, E.g. In a production line materials are produced daily, and an unexpected line shutdown may happen we can use a T Chart to track the number days between line shutdowns.  A “T chart” can be used for numeric, nonnegative data, date/time data, and time-between data.

Understanding the rare control chart, the points that appear above the UCL indicates that the number of events between errors has increased. Which is a positive event. Hence, a point flagged as out of control above the limits is usually considered as the desired effect when we read G & T charts.

 

ADVANTAGES OF THE G CHART

Advantages of the Rare control chart, in addition to its easiness, this chart offers better statistical sensitivity for monitoring rare events than its traditional charts (P or U charts). Since rare events occur at very low frequencies, traditional control charts are naturally not effective in detecting the changes immediately. In addition to the difficult task of collecting more data, this creates the circumstance of having to wait longer to detect a shift in the process.

 

On the other hand, G / T charts do not require large quantities of data to effectively detect a shift in a rare events process. Another advantage of using the G / T chart to monitor rare events is that it does not require the collection and recording of data on the total number of opportunities.

 

Therefore, G or T Charts are more effective and quick in detecting the shift in rare events monitoring than the traditional P or U charts.

 

Rare event control charts are used for observations or events, when they occur rarely. Plotting such rare events on traditional discrete data charts, like C, U, NP & P charts, will not be effective primarily for two reasons as below:

1.     Since discrete control charts are time-series based and the probability of event occurring is so low that it’ll be a very time consuming and difficult to task to collect required number of events to plot on these chart to make statistical sense.

2.      Discrete control charts also require to collect total number of opportunities to calculate the control limits.

 

 Rare event control charts address both of these issues for rare events scenarios as they only require to record the number of events between rarely occurring events, when using G Chart, or the time elapsed between the rarely occurring events, when using T Chart.

 

How to read rare event control charts:

The logic is to look for points, shown in red in Minitab, which are above UCL. These points are the desirable points as these would mean a higher number of events/time elapsed between two rarely occurring undesirable events. And points below or near LCL are those which require attention as these mean lesser than usual number of events/time elapsed has happened between two rarely occurring undesirable events.

Among all the published answers, the best answer has been provided by Kaviraj. Well done!

 

P.S. There were some brilliant answers but they failed the plagiarism test. Requesting all respondents to be a little careful regarding plagiarism.