Costello Labs supplies 500- cc bottles of treated Elixir plasma solution to Mercy Hospital. Several factors are important in assessing plasma quality, such as purity, absence of AIDS or hepatitis virus, and bacterial count. The most important quality characteristic, however, is protein concentration. Protein concentration is measured by a sophisticated electronic process known as electrophoresis. American Medical Association (AMA) standards specify that a 500- cc plasma bottle should contain between 30 and 35 grams of protein. Both concentrations under and over this range may be hazardous to a patient's health. Hospital administrators have instructed Costello Labs to straighten out its plasma production operation and to demonstrate evidence of tighter process controls prior to the renewal of its supply contract. Costello's plasma production equipment consists of a protein injector and a mixer that determine protein concentration in each bottle. Process capability depends on the precision of these pieces of equipment.
a. Suppose that the hospital and the lab have agreed that at least 98% of the plasma bottles supplied by Costello should conform to AMA specifications
(i. e., should contain between 30 and 35 grams of protein). Determine the following:
• The precision of Costello's protein injector as measured by
• The standard deviation of the amount of protein that it must inject into each bottle in order to produce 98% of process output within the specifications Also compute the corresponding process capabil-ity ratio Cp.
b. Costello Labs production manager Phil Abbott wants to establish statistical process control charts to monitor the plasma- injection process. Set up these control charts based on average protein readings taken from randomly selected samples of 12 bottles from each batch.