## What are Control Limits?

Control limits can be defined as a horizontal line that is drawn above and below the centerline. This line helps us to know whether a process is within or out of the control. Also known as natural process limits, these lines are drawn at a distance of + 3 standard deviations in a plotted statistic.

## Application of Control Limits

Control limits can be used as a detector of signals in the data process. This would further indicate that the process is not operating as per predictions. A signal can be defined as a point that exists in a single outside the control limits.

Control limits are generally based on the performance of the process & are considered as a representative of the processed voice. Apart from all these control limits also ensure that the time is not wasted unnecessarily in handling any issues.

## Differences Between Control and Specification Limits

Specification limits can be defined as targets that are set for a particular process or a product either by the customer or based on the performance of the market. In other words, it can also be defined as a result that is expected from a particular metric.

Control limits on the other hand help in indicating the changes which occur in the performance of a particular process. Control limits also provide the real-time value.

Control limits can be either UCL OR LCL which is the upper control limit or lower control limit. Similarly, specification limits can be either USL or LSL; upper specification limit and, lower specification limit.

This concept can be explained with the help of the following example.

There is an athlete who wants to take part in the Olympics in a 400-meter race. For guidance, the athlete approaches a coach to help him to win the race. The coach provides all the required information & also shows data about past records. The past records show that the target speed of the winners was 25-30 seconds speed & hence he advises the athlete to run at this speed to win the game. When the athlete starts his practice, he observes that his speed is at the range of 27-35 seconds (There is a 3 sigma deviation from the average performance). As the example shows, control limits help in knowing the differences in the performance.

## Control Charts

The control chart is a type of graph which helps to analyze the process change over a period of time. Data in the chart is plotted in the order of time. A control chart always has a central line, an upper control limit and, a lower control limit. With the help of these lines, a comparison can be made with the current data which helps in drawing a conclusion on whether a process is within or out of the control.

## Circumstances when Control Charts are Used

Control charts are used in the following situations:

- To know the stability of a particular process.
- When patterns of process variation are analyzed either from a special or common cause.
- When deciding whether the quality improvement projects must avoid problems of specific nature or to make any fundamental changes.
- When a prediction is made on the anticipated range of outcomes in a particular process.

Hence on the whole control charts whether everything is fine or if something is wrong. With the help of control charts, one can know the process behavior with the help of its position and scattering.

## Features of Control Charts

Following are some of the features of control charts:

- The control chart has a centerline which is nothing but the representation of the value of mean in the control process.
- A control chart usually starts with a time-series graph.
- Upper & lower control limits are calculated with the help of the available information & are usually placed at a distance that is equal to the central line. This can also be called process dispersion.
- A central line called X can be added as a reference for visual which helps in detecting the shifts or trends. This can also be called process location.

## Types of Control Charts

Control charts can be divided into three types namely x-bar and range chart, individual x-moving chart & x-bar and, standard deviation chart.

- Xbar and range chart: This is the most widely used chart in statistical process control. This chart is majorly used to monitor the data of a variable in which the samples at intervals regularly. This chart is more beneficial when the size of the sample is very small.
- Individual x-moving range chart: This chart is more suitable in the case where it is not possible to take many readings. This chart is also more suitable in situations where the data is very costly & also when more time is involved in samples.
- Xbar and standard deviation chart: This chart helps us to know the level of variation from the expected value. This chart is more useful for manufacturers, engineers, etc.

## Applications of Control Charts

The main purpose of the control chart is that it helps in detecting events that indicates the change in the actual process. Control charts are also beneficial statistically. It helps in identifying any bad changes & also helps in eliminating the cause of that change.

## Calculation of Control Limits

Control limits can be calculated by following the three simple steps:

- The first step would be to calculate the standard deviation of the given sample.
- The second step is to multiply the standard deviation value by 3.
- The final step is to add(3*SD to the average) in case of the upper control limit & subtracting the same in case of lower control limit.

## Context and Applications

This topic is significant in the professional exams for both undergraduate and graduate courses, especially for

- B.Tech
- M.Tech

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