Refer to given Example and the data for the nitrogen content in a certain fertilizer mix. Ifit is desired that the proportion nonconforming be within 0.5% and the level of type I error be limited to 0.025, find the modified control limits for the process mean.
Example
The nitrogen content of a certain fertilizer mix is a characteristic of interest. Random samples of size 5 are selected, and the percentage of nitrogen content is found for each. The sample mean and range R are shown for 20 samples in given Table. The specification limits allow values from 12 to 33%. A process nonconformance rate of more than 1% is unacceptable. We want to construct 3σmodified control limits: that is, limits with a type I error rate α of 0.0026.
