# Statistical Quality Control

Statistical quality control, as the name hints, is the use of mathematical techniques to control the quality of a process. It is mostly used in the manufacturing industry to measure, monitor, and analyze the variation in different processes with the intent of keeping the quality of processes under control. Essentially, statistical control processes will not enhance the quality or reliability of a poorly designed product but can help maintain the consistency and steadiness of how the product is manufactured.

## Dimensions of quality control

There are several ways through which the quality of a given product can be evaluated and described. They include:

### Performance:

Potential customers usually analyze a product to find out if it will serve the desired purpose and how well it will actually do that. For instance, one could evaluate two data analysis programs to see which one outperforms the other perhaps in terms of execution speed, a larger library of functions, etc.

### Reliability:

This will be measured in terms of how often a product fails. Complex products like airplanes, automobiles, or appliances will usually need some repair over time. An automobile, for example, will require occasional repair, but if the repairs become too frequent, then it becomes unreliable.

### Durability:

Customers will always go for products that serve them satisfactorily over a long time. The automobile and electrical appliance industries are good examples of businesses where durability is a major factor when it comes to deciding the quality of a product.

### Aesthetics:

The visual appearance of a product is also a factor for some customers, often putting into consideration elements like color, style, shape, tactile characteristics, packaging alternatives, and other features. For instance, manufacturers of soft drinks rely on the appearance of their packaging to distinguish the product from their competitors.

### Features:

If a product has some features that are beyond the standard performance of the competition, it will always draw more customers. For instance, you may consider a smartphone that has more built-in features to be of superior quality than its competitors.

## Techniques used in statistical quality control

Statistical quality control employs sampling and other statistical methods to evaluate and monitor the quality of a process that is ongoing such as the production of goods. A visual display known as a control chart is used to illustrate whether variations in the process output are a result of common causes or out-of-the-ordinary assignable occurrences. If the variations are caused by assignable events, then a decision is made to alter the process so that the output can be brought back to the acceptable levels of quality. Control charts can be categorized based on the type of data they carry. For example, an x̄-chart is used in instances where the sample mean has been employed in measuring the output quality. This chart can be used to measure and monitor quantitative data such as temperature, weight, and length. The variability of a process can be measured using an R-chart and in situations where the output quality is monitored in terms of the proportion or number of defectives in a given sample, a p-chart or np-chart can be used.

## Design of a statistical control chart

All control charts have a similar structure. For instance, the middle line of an x̄-chart usually matches the process mean when the process being examined is under control and giving out an output of satisfactory quality. The y-axis shows the measurement scale for the variable being studied. The upper control limit of the control chart (upper horizontal line) and the lower control limit (lower horizontal line) are selected such that when the process of interest is under control, there is a high likelihood that the sample mean value falls exactly at the center of the two main horizontal lines. To obtain the best results, the horizontal lines should be set at three standard deviations below and above the mean of the process. The process being examined can also be sampled periodically. When selecting each sample, however, the sample means value should be displayed on the control chart. The quality level of the process will only be considered acceptable if the sample mean value falls within the two horizontal lines. If the sample mean value doesn’t fall within the horizontal lines, the process is considered out of control, and suggestions are made to bring it back to satisfactory quality levels.