The Speedway Clinical Laboratory is a scientific blood-testing facility that rec

Question

The Speedway Clinical Laboratory is a scientific blood-testing facility that receives 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 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: Determine the upper and lower control brats for p-chart to be used in assessing the quality of the service described above. On average, what is the expected number of incorrect tests per 100 samples? 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 the service? What recommendations can you suggest?

Explanation / Answer

(a) From the first table given on the left side, the proportion of corrcet diagnosis is p= 0.962, q = 0.038, n = 2000

Upper and Lower Control Limit for a p-chart assuming 3- limit, which covers 99.73 percent of the distribution

the UCL = p + 3* (pq/n) = 0.962+ 3*(0.962*0.038/2000) = 0.974826

and the LCL = p + 3* (pq/n) = 0.962 - 3*(0.962*0.038/2000) = 0.949174

(b) The probabilty of incorrect test is = 0.038 for the entire sample, so the number of incorrest test per 100 sample is = 0.038*100 = 3.8

(c) Later another sample of 100 is taken and found that 10 were found to be incorrectly analysed. So p = 10/100 = 0.1; q = 1-0.1 = 0.9 if total sample size is 2000

the UCL = p + 3* (pq/n) = 0.9+ 3*(0.9*0.1/2000) = 0.920125

and the LCL = p + 3* (pq/n) = 0.9 - 3*(0.9*0.1/2000) = 0.879875

Under the given condition, the probability that the test is correctly done lies between the limit 88% to 92%.

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