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### P AND NP CONTROL CHARTS

With data of type attributes, np and p charts (np chart vs p chart) can be used. These charts are used to monitor the percentage (p chart), or number (np cart) of defective items within a subgroup.

This type of data has only two possible outcomes. Either the item is defective, or it isn’t defective. Let’s say you use a p control table to track the percentage (or percent) of hospital admissions with incorrect insurance information each week. One of two outcomes is possible: the admission had correct insurance information, or the admission did not have correct insurance information. This data type is known as “yes/no data”. It meets a predetermined specification (yes), or it doesn’t meet that specification (no). Each week, you would collect data on hospital admissions (n), the subgroup size, and the number of patients with incorrect or incomplete insurance information (np), the number defective. You calculate the fraction defective (p) each week, equal to np/n. Over time, the values of p can be plotted. Once you have enough data, you can calculate the average (p bar), and control limits (LCLp or UCLp).

The np control charts can be replaced by the p control charts if the subgroup size remains constant. This will show the time-averaged number of defective items (np). Once enough data has been collected, the average (np) and control limits are calculated.

• Both charts include counts. You are counting items. The counts must meet the following conditions in order to use a p/np control chart:
• You are counting n items. np is the number n items fail to conform with specification.

Let’s say that p’ represents the likelihood that an item will not conform to the specification. Each of the n items must have the same value for p’. np chart vs p chart.

These two conditions can be met to determine the binomial distribution. The p and np control charts may be used to calculate the distribution of counts. You should be careful as condition 2 may not always hold. Some people use the p control charts to track on-time delivery on an ongoing basis. If the probability that all shipments will arrive on time during a month is equal, this chart is invalid. Customers with large orders often have priority. Because of this, the probability that their orders will arrive on time is higher than for customers with smaller orders. The p control chart cannot be used.