samples from local hospitals and clinics. The blood samples are passed through several automated tests, and the results are printed through a central computer that reads and stores the information about each sample that is tested.

Management is concerned about the quality of the service it provides and wants to establish quality$-$control limits as a measure for the quality of its tests. Such managerial practice is viewed as significant, because incorrect analysis of a sample can lead to a wrong diagnosis by the physician, which in turn might cost the life of a patient. For this reason, $100$ blood samples were collected at random each day after they had gone through testing. After retesting was performed manually on this sample, the results were:

Designing the Service Enterprise

$\backslash$table$[[$Day$,$Incorrect Analysis,Day,Incorrect Analysis$],[1,8,11,4],[2,3,12,6],[3,1,13,5],[4,0,14,10],[5,4,15,2],[6,2,16,1],[7,9,17,0],[8,6,18,6],[9,3,19,3],[10,1,20,2]]$

a$.$ Construct a $p-$chart to be used in assessing the quality of the service described above.

b$.$ On average, what is the expected number of incorrect tests per $100$ samples?

c$.$ Later, another sample of $100$ was taken. After the accuracy of the tests was established, $10$ samples were found to have been analyzed incorrectly. What is your conclusion about the quality of this service?