# Blog 13: Implementation and Interpretation of Control Chart

## Introduction:

Control chart are very popular and commonly used in quality control techniques, Six Sigma also plays an important role in defining process capacity and production fluctuations. This tool also helps identify how well the manufacturing process meets customer expectations.

Control charts are graphs used to show the performance of a process over time. This is basically a statistical chart that helps you determine if an industrial process is controlled and can meet customer-defined specification limits. Subgroups of data points are collected and merged in a short period of time. The average of the data points in the subgroup is represented as a single point on the control chart. The amount of variation present in the sample dataset is the standard deviation and is used to determine the control limits. A process is said to be unmanageable if the subgroup is outside the control limits or shows certain patterns or trends.

The control chart is also known as the Shewhart control chart, named after Walter A. Shewhart. The real purpose of the control chart is to determine if the process is running stably under the current conditions.

In the control chart, the relationship between data and time is plotted on the x-axis. The control chart always has a centerline (average or mean), an upper limit for control, and a lower limit for control. These lines are calculated from historical data collected. By comparing actual data with these lines, experts can identify whether process variability is consistent (during control, affected by common causes of variability) or unpredictable (out of control, can be influenced by the special cause of variability). This helps to distinguish between common and special causes of variability. Control charts predict process performance, understand different production patterns, and investigate how processes change over time or deviate from normally established control limits.

## What are control charts useful for?

The use of Control charts can be used for a variety of purposes. Some of its basic uses

• Determine if the process is stable
• Monitor the process and learn how to improve it
• Used to predict the performance of the manufacturing process
• Identify the confusion in the process or the specific cause of the confusion
• Identify trends such as errors and process failures.

## The purpose of control chart

Control charts provide an overview of the history of process data to help distinguish between special cause deviations and common cause deviations.

• Common cause: Unknown malfunction. They change the process with a random distribution, but never significantly above or below control limits.
• Special cause: The special cause is a known malfunction. They cause major failures and defects in the long run. Data typically goes above and below control limits.

## How to make a control chart:

• Determine the type of control chart: Decide and determine which type of control chart is to be made whether production data, defects data, process variation, etc. Also, decide the period of time for which the control chart is to be made.
• Collect the data: After deciding which type of control chart is to be made start collecting the actual data over a period of time.
• Determine the subgroups: Subgroups can be calculated using the formula:

N= (Ζ α/2+ Ζ β)2 * σ2 / D2

where

n = subgroup size required

Ζ α/2 = the number of standard deviations above zero on the standard normal distribution such that the area in the tail of the distribution is α/2 (α is the type I error probability and is typically 0.0027 for control chart applications. In this case, Ζ 0.00135 =3).

Ζ β = the number of standard deviations above zero on the standard normal distribution such that the area in the tail of the distribution is β (β is the type II error probability).

σ = the standard deviation of the characteristic being charted.

D = the difference we are trying to detect.

• Determine overall average: After collecting the data for a certain amount period calculate its average. This will be the centerline for data.
• Calculate the range: To calculate the range we must use the following formula:

UCL (X-bar) = X-bar-bar + (A2 x R-bar)

LCL(X-bar) = X-bar-bar – (A2 x R-bar)

• Compute the average of the range: Average range can be calculated using the formula:

UCL (R) = R-bar x D4

LCL(R) = R-bar x D3

• Calculate the control limit: Using the data of the X bar and R bar calculate the control limit for the specific graph.
• Plot the data in the graph: After all limits are calculated to draw the graph and then plot the data on the graph.
• Interpret the graph: Interpret the data to check the behavior of the data to find whether the behavior is within the limit or outside limit.

## Interpretation of control chart:

Following are the rules for the interpretation of the control chart:

• Rule 1: One point beyond the 3 σ control limit is termed an unstable point.
• Rule 2: Eight or more points on one side of the centerline without crossing then it is a prominent shift.
• Rule 3: Four out of five points in zone B or beyond this is considered a small shift.
• Rule 4: Six points or more in a row steadily increasing or decreasing this shows a trend of working.
• Rule 5: Two out of three points in zone A is considered a large shift.
• Rule 6: 14 points in a row alternating up and down is considered out of control.
• Rule 7: Any noticeable/predictable pattern, cycle, or trend