RELIABILITY IN A SERIES. The National Bank of Greeley, Colorado, processes loan applications through three clerks (each checking different sections of the application in series), with reliabilities of .90, .80, and .99. It wants to find the system reliability.
APPROACH $\blacktriangleright$ Apply Equation (17-1) to solve for $R_s$ .

Question

RELIABILITY IN A SERIES. The National Bank of Greeley, Colorado, processes loan applications through three clerks (each checking different sections of the application in series), with reliabilities of .90, .80, and .99. It wants to find the system reliability.
APPROACH [latex]\blacktriangleright[/latex] Apply Equation (17-1) to solve for [latex]R_s[/latex].

[latex]R_s = R_1 imes R_2 imes R_3 imes . . . imes R_n[/latex] (17-1)

Accepted Answer

SOLUTION [latex]\blacktriangleright[/latex] The reliability of the loan process is:
[latex]R_s = R_1 imes R_2 imes R_3[/latex] = (.90)(.80)(.99) = .713, or 71.3%
INSIGHT [latex]\blacktriangleright[/latex] Because each clerk in the series is less than perfect, the error probabilities are cumulative and the resulting reliability for this series is .713, which is less than any one clerk.
LEARNING EXERCISE [latex]\blacktriangleright[/latex] If the lowest-performing clerk (.80) is replaced by a clerk performing at .95 reliability, what is the new expected reliability? [Answer: .846.]
RELATED PROBLEMS [latex]\blacktriangleright[/latex] 17.1, 17.2, 17.3, 17.9 (17.16 and 17.17 are available in MyOMLab)
ACTIVE MODEL 17.1 This example is further illustrated in Active Model 17.1 in MyOMLab.
EXCEL OM Data File Ch17Ex1.xls can be found in MyOMLab.

Question 17.EX.1: RELIABILITY IN A SERIES. The National Bank of Greeley, Color...

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