Question

spreadsheet an electronic missile guidance system at mguide inc. consists of components a, b, c, and d, which have reliabilities of 0.96, 0.93, 0.90, and 0.91, respectively (see the following diagram). use the excel template systems reliability to compute the reliability of the entire system. round your answer to four decimal places.

Explanation:

Step1: Analyze the system structure

The system has components A and B in series, then a parallel subsystem of two C components, then component D in series. For series components, reliability is the product of individual reliabilities. For parallel components, reliability is \(1 - (1 - R)^n\) where \(R\) is the reliability of one component and \(n\) is the number of parallel components.

Step2: Calculate reliability of A and B (series)

Reliability of A and B in series: \(R_{AB}=R_A\times R_B = 0.96\times0.93\)
\(R_{AB}=0.8928\)

Step3: Calculate reliability of parallel C components

There are 2 C components in parallel. \(R_C = 0.90\), so reliability of parallel C: \(R_{parallel\ C}=1-(1 - 0.90)^2=1 - 0.1^2=1 - 0.01 = 0.99\)

Step4: Calculate reliability of D (single component)

\(R_D = 0.91\)

Step5: Calculate total system reliability (series of AB, parallel C, D)

Total reliability \(R_{total}=R_{AB}\times R_{parallel\ C}\times R_D\)
Substitute the values: \(R_{total}=0.8928\times0.99\times0.91\)
First, \(0.8928\times0.99 = 0.883872\)
Then, \(0.883872\times0.91=0.80432352\)
Round to four decimal places: \(0.8043\)

Answer:

\(0.8043\)