What is statistical process control ? How is it different from acceptance sampling? When is a process said to be out of control ? How can control-charts be of use in identifying out of control process? Explain.

What is Statistical Process Control (SPC)?

Statistical Process Control (SPC) is the application of statistical methods to monitor and control a process. It involves collecting data from a process, plotting it on a control chart, and analyzing the patterns to determine if the process is stable and predictable. The core principle is to distinguish between ‘common cause’ variation (inherent to the process) and ‘special cause’ variation (attributable to specific identifiable factors). SPC aims to eliminate special cause variation to bring the process into a state of statistical control.

SPC vs. Acceptance Sampling

While both SPC and acceptance sampling aim to ensure quality, they differ fundamentally in their approach. Here’s a comparative overview:

Feature	Statistical Process Control (SPC)	Acceptance Sampling
Focus	Preventing defects by controlling the process	Detecting defects in a batch of products
Timing	Continuous monitoring during production	Inspection at the end of production
Data Usage	All data points from the process	Sample data from a batch
Goal	Process improvement and stability	Accept or reject a batch
Cost	Lower long-term costs due to defect prevention	Higher risk of shipping defective products; potentially lower initial cost

Acceptance sampling is often used when continuous monitoring is impractical or too costly. However, it only identifies defects *after* they have occurred, whereas SPC aims to prevent them in the first place.

When is a Process Said to be Out of Control?

A process is considered ‘out of control’ when it exhibits variation beyond the expected range of common cause variation. This is indicated by the presence of ‘special cause’ variation. Specifically, a process is out of control if any of the following conditions are met:

• Points outside control limits: A data point falls above the upper control limit (UCL) or below the lower control limit (LCL).
• Runs: A series of consecutive points (e.g., 7 or more) on the same side of the center line.
• Trends: A consistent upward or downward movement of points.
• Cycles: A repeating pattern of points.
• Non-random patterns: Any other unusual pattern that suggests a special cause is affecting the process.

How Control Charts Identify Out-of-Control Processes

Control charts are graphical tools used to monitor process variation over time. They consist of a center line (representing the average of the process), an upper control limit (UCL), and a lower control limit (LCL). These limits are typically set at ±3 standard deviations from the center line. Different types of control charts are used depending on the type of data being collected:

• X-bar and R charts: Used for continuous data (e.g., length, weight) to monitor the average and range of samples.
• Individuals and Moving Range charts: Used for continuous data when sample sizes are small (n=1).
• p-charts: Used for attribute data (e.g., number of defects) to monitor the proportion of defective items.
• c-charts: Used for attribute data to monitor the number of defects per unit.

By plotting data on a control chart, it becomes visually apparent when a process is out of control. The rules mentioned above (points outside limits, runs, trends, cycles, non-random patterns) can be easily identified. Once an out-of-control condition is detected, investigation is required to identify and eliminate the special cause of variation. For example, if an X-bar chart shows a sudden shift in the average, it might indicate a change in raw materials, a machine malfunction, or operator error.

Example: A manufacturing company producing bolts uses an X-bar and R chart to monitor the diameter of the bolts. If a point falls above the UCL, it indicates that the bolts are too large, prompting an investigation into the machine settings or tooling.