Question

Suggest a use for an attribute chart in the Education field. Provide the metric and how it is calculated along with how this information would be tracked and interpreted.

Answer 1

Attribute Charts

Attribute Charts are a set of control charts specifically designed for Attributes data. Attribute charts monitor the process location and variation over time in a single chart.

The family of Attribute Charts include the:

Np-Chart: for monitoring the number of times a condition occurs, relative to a constant sample size, when each sample can either have this condition, or not have this condition

p-Chart: for monitoring the percent of samples having the condition, relative to either a fixed or varying sample size, when each sample can either have this condition, or not have this condition

c-Chart: for monitoring the number of times a condition occurs, relative to a constant sample size, when each sample can have more than one instance of the condition.

u-Chart: for monitoring the percent of samples having the condition, relative to either a fixed or varying sample size, when each sample can have more than one instance of the condition.

When to Use an Attribute Chart

Only Attributes data can be applied to an Attributes control chart.

To illustrate the differences between various attribute charts, consider an example of the errors in an accounting process, where each month we process a certain number of transactions.

The Np-Chart monitors the number of times a condition occurs, relative to a constant sample size, when each sample can either have this condition, or not have this condition. For our example using this type of attribute chart, we would sample a set number of transactions each month from all the transactions that occurred, and from this sample count the number of transactions that had one or more errors. We would then track on the attribute control chart the number of transactions with errors per month.

The p-Chart monitors the percent of samples having the condition, relative to either a fixed or varying sample size, when each sample can either have this condition, or not have this condition. For our example using this type of attribute chart, we might choose to look at all the transactions in the month (since that would vary from month to month), or a set number of samples, whichever we prefer. From this sample, we would count the number of transactions that had one or more errors. We would then track on the attribute control chart the percent of transactions with errors per month.

The c-Chart monitors the number of times a condition occurs, relative to a constant sample size. In this case, a given sample can have more than one instance of the condition, in which case we count all the times it occurs in the sample. For our example using this type of attribute chart, we would sample a set number of transactions each month from all the transactions that occurred, and from this sample count the total number of errors in all the transactions. We would then track on the attribute control chart the number of errors in all the sampled transactions per month.

The u-Chart monitors the percent of samples having the condition, relative to either a fixed or varying sample size. In this case, a given sample can have more than one instance of the condition, in which case we count all the times it occurs in the sample. For our example using this type of attribute chart, we might choose to look at all the transactions in the month (since that would vary month to month), or a set number of samples, whichever we prefer. From this sample, we count the total number of errors in all the transactions. We would then track on the attribute control chart the number of errors per transactions per month.

Each attribute control chart includes statistically determined upper and lower control limits, indicating the bounds of expected process behavior. The fluctuation of the points between the control limits is due to the variation that is intrinsic (built in) to the process. We say that this variation is due to "common causes" that influence the process. Any points outside the control limits can be attributed to a special cause implying a shift in the process. When a process is influenced by only common causes, then it is stable, and can be predicted. Thus, a key value of the control chart is to identify the occurrence of special causes, so that they can be removed, with a reduction in overall process variation. Then, the process can be further improved by either relocating the process to an optimal average level, or decreasing the variation due to common causes.

Attribute control charts are fairly simple to interpret: merely look for out of control points. The control limits may vary on the P chart and the U chart, based on the different sample sizes used for each plotted point. If the sample size does not vary by more than 10 or 15%, then you can use the average sample size on these charts to determine common control limits for all samples. This is often an option on your SPC software

If there are special causes, they must be understood. Brainstorm and conduct Designed Experiments to find those process elements that contribute to sporadic changes in process location. Remove the statistical bias of the out of control points by dropping them from the calculations of the process center line and its control limits. (This can be done automatically using the Auto Drop feature in our SPC software).

Remember that the variation within control limits is due to the inherent variation in sampling from the process. (Think of the Deming Red Bead experiment: the proportion of red beads never changed in the bucket, yet each sample had a varying count of red beads). The bottom line is: React first to special cause variation. Once the process is in statistical control, then work to reduce variation and improve the location of the process through fundamental changes to the system.