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.
R_s = R_1 \times R_2 \times R_3 \times . . . \times R_n (17-1)
SOLUTION \blacktriangleright The reliability of the loan process is:
R_s = R_1 \times R_2 \times R_3 = (.90)(.80)(.99) = .713, or 71.3%
INSIGHT \blacktriangleright 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 \blacktriangleright 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 \blacktriangleright 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.