What is Control Charts?
A control chart is an SPC tool used to determine whether a process is stable and predictable or unstable and unpredictable. It is used to control the quality of a process. If a process is stable at an accepted level of output, then the process quality of the process is under control. However, if the process is unstable, then the organization needs to increase the level of control over the process.
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Control charts were introduced by the quality guru, Walter A. Shewart, and therefore are also known as Shewart charts. You can use a control chart to represent variations in a process in a graphical manner. These charts show variations as well as their causes.
Some of the reasons for using control charts are as follows:
- They help to improve the productivity of a process
- They identify defects in a process
- They help to determine the kind of process adjustments required
- They help to determine whether a process is under control
A control chart is represented by three lines that depict the control limits, which are:
- The Upper Line: known as the Upper Control Limit (UCL)
- The Middle Line: known as the center line or average line
- The Lower Line: known as the Lower Control Limit (LCL)
The UCL and LCL are used to show the boundaries of a process. The points within these control limits determine the status of the process. Any point that deviates outside the UCL or LCL is considered to be an abnormal cause of variation.
In Figure, the control charts have three lines: UCL, center line, and LCL. The crooked line along the center line shows the normal variation pattern in the process. This pattern does not go out of the UCL and LCL, showing that this is a stable process.
To understand control charts in a real-life context, consider that the Figure shows the percentage of marks obtained by a student from primary school to senior secondary school. In the control chart of the student, the crooked line represents the percentage of marks obtained by the student throughout his/her school years.
UCL represents the student obtaining the highest marks in a class, whereas LCL represents the student obtaining the lowest marks in the class. Based on this control chart, this particular student has been an average performer, scoring neither the highest marks nor the lowest marks in a class.
Types of Control Charts
Control charts are classified according to the data used for analyzing the quality characteristic of a process. Data can be of the following two types:
- Attribute Data: Refers to the data that is used to determine the presence or absence of quality characteristics. It does not include any mathematical techniques. Examples of attribute data can be whether you have passed or failed and whether you have paid your mobile phone bill. (Yes/No), whether you have checked or crossed a field in a document, etc.
- Variable Data: Refers to the data that can be measured and can be assigned with a number. This means that a variable has a numeric value, which is measurable and mathematically applicable. Examples of variable parameters include the age, weight, and height of a student.
Control charts can be prepared for both types of data. There are two types of control charts:
- Control charts for attributes
- Control charts for variables
Control Charts for Attributes
Control charts for attributes monitor qualitative characteristics of products that are assessed with the discrete response, such as pass/ fail, yes/no, good/bad, and defective/non-defective. The control charts used for attributes are p-charts and c-charts.
P-charts
Assume that p is the population charts used to measure the proportion of defective items in a sample. The center line is the average proportion of defective items in the population.
Suppose you inspect 10 samples of an item of size 50. The table shows the number of defective items in each sample:
| Sample No. | No. of Defectives |
|---|---|
| 1 | 2 |
| 2 | 3 |
| 3 | 2 |
| 4 | 0 |
| 5 | 2 |
| 6 | 3 |
| 7 | 2 |
| 8 | 1 |
| 9 | 2 |
| 10 | 3 |
Next, you can calculate the fraction defectives (p) in each sample, as shown in Table:
| Sample No | No. of Defective Items | Fraction Defectives (p) = No. of Defectives/ Sample Size |
|---|---|---|
| 1 | 2 | .04 |
| 2 | 3 | .06 |
| 3 | 2 | .04 |
| 4 | 0 | 0 |
| 5 | 2 | .04 |
| 6 | 3 | .06 |
| 7 | 2 | .04 |
| 8 | 1 | .02 |
| 9 | 2 | .04 |
| 10 | 3 | .06 |
| .40 |
C-charts
c-charts count the actual number of defects and not the proportion of defects. A control chart helps in monitoring the number of defects per unit.
Control Charts for Variables
Control charts for variables monitor quantitative characteristics of products that can be measured on a continuous scale, such as height, weight, and volume. For example, a beverage company measures the amount of liquid in bottles and a candle-making company measures the height of candles.
Control charts for variables include control charts of averages ( x ) and ranges (R). These charts are used to examine a scale and measurement.
Mean ( x ) Charts
Mean ( x ) charts monitor changes in the mean of a process. Here, you take different samples (4 to 5 observations) and calculate their mean. The total average of sample means is calculated as follows:
