Unit 3: Statistical Process Control (SPC)

Statistical Process Control (SPC) is a set of statistical methods used to monitor and control a process. This helps ensure that the process operates efficiently, producing more specification-conforming products with less waste. Here are some key terms and vocabulary for Unit 3: Statistical Process Control (SPC) in the course Professional Certificate in Performance Management in Quality Control.

1. **Control Chart**: A graph used to study how a process changes over time. Data is plotted in time order. A control chart always has a center line for the average, an upper line for the upper control limit, and a lower line for the lower control limit. These lines are determined from historical data.

2. **Process Capability**: The ability of a process to produce output within specified limits. It is measured by the process capability index (Cp), which is the ratio of the tolerance to the process standard deviation. A Cp of 1.0 or greater is usually desired.

3. **Common Causes**: Conditions that are an inherent part of a process and cause variation. They are always present and cannot be eliminated. They are also known as random causes.

4. **Special Causes**: Conditions that occur occasionally and cause variation. They are not part of the normal process and can usually be identified and eliminated. They are also known as assignable causes.

5. **Upper Control Limit (UCL)**: The upper boundary of the control limits, defined by the upper line on a control chart. If the process is in control, nearly all of the points will fall between the control limits.

6. **Lower Control Limit (LCL)**: The lower boundary of the control limits, defined by the lower line on a control chart. If the process is in control, nearly all of the points will fall between the control limits.

7. **Average (X-bar) Chart**: A type of control chart that plots the average of samples taken from a process. It helps detect if the process mean has shifted from its target value.

8. **Range (R) Chart**: A type of control chart that plots the range of samples taken from a process. It helps detect if the process variability has changed.

9. **Standard Deviation (SD) Chart**: A type of control chart that plots the standard deviation of samples taken from a process. It helps detect if the process variability has changed.

10. **Numerical Tolerance**: The amount of variation allowed in a process, often expressed as a plus or minus value around a target.

11. **Process Mean**: The average value of a process over time.

12. **Process Standard Deviation**: The amount of variation in a process.

13. **Sample Size**: The number of observations in a sample.

14. **Subgroup**: A set of samples taken at the same time from the same process.

15. **Run**: A sequence of points in the same direction on a control chart.

16. **Shift**: A significant change in the process mean or variability.

17. **Zone Testing**: A method of interpreting control charts where certain patterns of points are considered evidence of a process shift.

18. **Capability Analysis**: A statistical method used to evaluate the ability of a process to produce output within specified limits.

19. **Histogram**: A graphical representation of data that shows the frequency of different values.

20. **Probability Plot**: A graph that plots data against theoretical distribution values, used to assess the normality of a process.

Challenge:

1. Plot a control chart for a process with the following data: 45, 47, 46, 48, 49, 50, 51, 52, 53, 54. Assume a target of 50 and a numerical tolerance of ±5. 2. Calculate the process capability index (Cp) for a process with a tolerance of 10 and a standard deviation of 2. 3. Identify the common and special causes for the following process data: 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80.

Example:

1. Control Chart:


The control limits are calculated as follows: UCL = Target + 3 \* SD = 50 + 3 \* 2.83 = 58.49 LCL = Target - 3 \* SD = 50 - 3 \* 2.83 = 41.51

Since all points are within the control limits, the process is in control.

2. Process Capability Index (Cp):

Cp = Tolerance / (2 \* Standard Deviation) = 10 / (2 \* 2) = 2.5

The process capability index is 2.5, indicating that the process is capable of producing output within the specified limits.

3. Common and Special Causes:

The process data shows a steady increase over time, which is likely due to a special cause. The first step in addressing this would be to identify and eliminate the special cause. Once the special cause has been eliminated, the process would be in control and any remaining variation would be due to common causes. Common causes are inherent in the process and cannot be eliminated, but they can be reduced through process improvements.