An electronic missile guidance system at Mguide Inc. consists of components A, B, C, and D, which have reliabilities of 0.98, 0.99, 0.92, and 0.96, 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.

To compute the reliability of the entire missile guidance system at Mguide Inc., given that the components A, B, C, and D have reliabilities of 0.98, 0.99, 0.92, and 0.96 respectively, you'll follow these steps:

### Steps to Calculate System Reliability:

1. **Identify the Configuration**: 
   - **Series Configuration**: If the components are arranged in series, the overall reliability is the product of the individual reliabilities.
   - **Parallel Configuration**: If the components are arranged in parallel, the overall reliability is calculated using a different formula where the failure of all components is considered.

2. **Enter the Data**:
   - Enter the given reliabilities (0.98, 0.99, 0.92, and 0.96) into the yellow cells of the Excel template under the appropriate section (Series or Parallel).

### Calculating Reliability for a Series System:

If the components are connected in series, the reliability \( R_{system} \) is computed as:

\[
R_{system} = R_A \times R_B \times R_C \times R_D
\]

Where:
- \( R_A = 0.98 \)
- \( R_B = 0.99 \)
- \( R_C = 0.92 \)
- \( R_D = 0.96 \)

So,
\[
R_{system} = 0.98 \times 0.99 \times 0.92 \times 0.96
\]

Let's calculate this:

\[
R_{system} = 0.98 \times 0.99 \times 0.92 \times 0.96 \approx 0.8570
\]

### Final Answer:
The reliability of the entire system, rounded to four decimal places, is **0.8570**.

Would you like a more detailed explanation, or do you have any questions?

### Related Questions:

1. How would the reliability change if one of the components had a much lower reliability?
2. What is the system reliability if the components are arranged in a parallel configuration?
3. How does the reliability change if an additional redundant component is added in series?
4. What is the effect on overall reliability if one of the components is removed?
5. How can we calculate the reliability for a mixed configuration of series and parallel components?

### Tip:
When dealing with systems involving multiple components, always ensure you know the configuration (series or parallel) before proceeding with reliability calculations.

Learn how to compute the reliability of an electronic missile guidance system using the series configuration method. Given the reliabilities of components A (0.98), B (0.99), C (0.92), and D (0.96), calculate the overall reliability. Suitable for engineering students and professionals.

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