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.

Question

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 [latex]\blacktriangleright[/latex] The bank decides to provide redundancy for the two least reliable clerks, with clerks of equal competence.

Accepted Answer

SOLUTION [latex]\blacktriangleright[/latex] This procedure results in the following system:

[latex]R_1 R_2 R_3[/latex]

0.90 0.80

[latex] ↓ ↓[/latex]
0.90 → 0.80 → 0.90

[latex]R_s[/latex] = [.9 + .9(1 - .9)] × [.8 + .8(1 - .8)] × .99
= [.9 + (.9)(.1)] × [.8 + (.8)(.2)] × .99
= .99 × .96 × .99 = .94

INSIGHT [latex]\blacktriangleright[/latex] By providing redundancy for two clerks, National Bank has increased reliability of the loan process from .713 to .94.

LEARNING EXERCISE [latex]\blacktriangleright[/latex] What happens when the bank replaces both [latex]R_2[/latex] clerks with one new clerk who has a reliability of .90? [Answer: [latex]R_s[/latex] = .88.]

RELATED PROBLEMS [latex]\blacktriangleright[/latex] 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.

Question 17.EX.3: RELIABILITY WITH BACKUP. The National Bank is disturbed that...

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