# Six Sigma

Introduction to Six Sigma

Homework 1

Page 48

1. An insurance firm has set a standard that policy applications be processed within three days of receipt. If, out of a sample of 1,000 applications, 50 fail to meet this requirement, at what sigma level is this process operating? DPMO= (Number of Defects Discovered/Opportunities for Error) x 1,000,000 DPMO= (50/1000) x 1,000,000= 50,000

=NORMSINV(1- Number of Defects/ Number of Opportunities) + Shift

=NORMSINV(1-50000/1000000)+1.5=3.144854 Between 3 and 3.5 Sigma Level

2. During one month, 35 preflight inspections were performed on a military aircraft. Eighteen nonconformance’s were noted. Each inspection checks 60 items. What sigma level does this correspond to? 35 x 60= 2100

18/2100 x 1,000,000= 8571.43

=NORMSINV(1-8571.43/1000000)+1.5=3.883629 Between 3.5 and 4 Sigma Level

3. Over the last year 1,054 injections were administered at a clinic. Quality is measured by the proper amount of dosage as well as the correct drug. In two instances, the incorrect amount was given, and in one case, the wrong drug was given. At what sigma level is this process? 3/1054 x 1,000,000= 2846.30

=NORMSINV(1-2846.30/1000000)+1.5=4.26498 Between 4 and 4.5 Sigma Level 6. As noted in the text, a typical hospital has 225 medication errors per year. Approximately 35 percent of these are a result of the prescription, 30 percent from dispensing, and the remaining from administration. Suppose that a hospital has 9,000 annual admissions, and that the average patient receives five prescriptions during a hospital stay. Patients stay an average of 5.3 days, and each ordered medication is dispensed daily. The average patient receives 12 medications per day. Compute the average dpmo for each of the three categories of medications errors. To what Sigma levels do these values correspond? Prescription:

35% X 225= 78.75

(78.75/9000) X 1,000,000= 8750

=NORMSINV(1-8750/1000000)+1.5= 3.876031 Around 4 Sigma Level...

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