RELIABILITY WITH BACKUP. The National Bank is disturbed that its loan-application process has a reliability of only .713 (see Example 1) and would like to improve this situation.
APPROACH \blacktriangleright The bank decides to provide redundancy for the two least reliable clerks, with clerks of equal competence.
SOLUTION \blacktriangleright This procedure results in the following system:
R_1 R_2 R_30.90 0.80
↓ ↓
0.90 → 0.80 → 0.90
R_s = [.9 + .9(1 – .9)] × [.8 + .8(1 – .8)] × .99
= [.9 + (.9)(.1)] × [.8 + (.8)(.2)] × .99
= .99 × .96 × .99 = .94
INSIGHT \blacktriangleright By providing redundancy for two clerks, National Bank has increased reliability of the loan process from .713 to .94.
LEARNING EXERCISE \blacktriangleright What happens when the bank replaces both R_2 clerks with one new clerk who has a reliability of .90? [Answer: R_s = .88.]
RELATED PROBLEMS \blacktriangleright 17.7, 17.10, 17.12, 17.13, 17.14, 17.15
ACTIVE MODEL 17.2 This example is further illustrated in Active Model 17.2 in MyOMLab.
EXCEL OM Data File Ch17Ex3.xls can be found in MyOMLab.