Question

Give your example. Compare and contrast the consideration/use of power versus average run length for the design of a control chart. Is one a more meaningful measure of performance than the other? What information (if any) does the average run length convey that power does not?

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Answer 1

Reducing process variability is presently an area of much interest in manufacturing organizations. It is the responsibility of all individuals from top to bottom (including operators, engineers and management) must continuously seek to improve manufacturing process output and reduce the variability. Statistical Process Control (SPC) charts are one of the very effective instruments of reducing the variability in the manufacturing process. The primary purposes of SPC charts are to achieve process stability and reduce variability.The performance measure of control chart techniques is usually evaluated by the Average Run Length (ARL) in literature. ARL has the function of determining how many samples are necessary so that control chart presents the indicative signal to detect the change of out of control in the probability distribution. When a process is out-of-control, the users want the control chart to signal quickly, i.e., to have a small out-of-control average run length. Conversely when the process is in control, the users want the chart to produce fewer false alarms, i.e., to have a large in-control average run length.

If this were a hypothesis test, we could measure the α (Type I) and β (Type II) error. This method can’t be used for control charts because control charts are a series of sample by sample hypothesis tests. Instead of the traditional α and β error that is used for hypothesis tests, the Average Run Length (ARL) is typically used to measure the performance of control charts.

Run Length is the number of samples (subgroups) taken before there is a signal (point beyond the control limits). In the image on the left, the run length is four because there were four samples taken before a point went beyond the upper control limit. Run length is a random variable that can only take on integer values. We need to use the expected value or Average Run Length to measure performance. ARL (Average Run Length) is the expected value of the run length,

The traditional control chart signal rule is to declare a production process to be not in a state of statistical control if the last plotted point breaches any of the control limits. As long as points are within the control limits, the process is deemed to be in a state of control. Since the run length random variable is the number of plotted points to an out-of-control signal, the underlying assumption behind the concept of ARL is that of infinite production length.

How to measure the performance of a control chart? One could the α error and b error, the same as for evaluating any hypothesis test. But a control chart is actually a series of sample by sample hypothesis tests, could we develop something more intuitive and that measure the performance of a chart more directly? For that, people like to use the average run length as a performance measure of control charts.

Benefits of using a Control Chart

• To monitor and control the ongoing process by recognizing the issues that arise.

• To predict the expected ranges of outcomes from the process.

• To determine the stability of a process.

• To analyze the patterns of the process variation from the special causes (non-routine events) or common causes (built into the process).

• To determine the areas where the quality needs to be improved in the project in order to increase the productivity.

Comparison :

• The major differences between these two methods are that run charts have a center line that represents the middle point of the measurement that is being tracked, while control charts have a center line that represents the average of the measurement that is being tracked.

• Both these charts are drawn by plotting the data within a particular period. However, the control chart consists with an upper and a lower control limit lines with a center line. (As indicated in the above figure)

• Control charts are designed to;

1) Make the necessary improvements within the process and

2) Prevent the errors occurred in the process.

• Run charts do not provide any support with the statistical control limits. Therefore, when it is required to make changes in the process, it may be useful to add more variations to the process rather than reducing the variations.

Based on the goals of the project, the most suitable chart can be chosen. Usually control charts provide more specific information and insight to the process, compared to the run chart.