To calculate the system reliability with only one machine at each stage and no backup machines, we simply multiply the reliability of each individual machine in the system.

The formula for system reliability $R_{\text{system}}$ when machines are in series (one after the other) is:

$R_{\text{system}} = R_A \times R_B \times R_C$

Where:

• $R_A = 0.85$ (reliability of machine A)
• $R_B = 0.92$ (reliability of machine B)
• $R_C = 0.90$ (reliability of machine C)

Now, let's compute this:

$R_{\text{system}} = 0.85 \times 0.92 \times 0.90 = 0.7014$

So, the system reliability is approximately 0.7014 when rounded to four decimal places.

Would you like more details on how this calculation works or have any questions on the topic?

Further Questions:

1. How would the system reliability change if machine A's reliability were increased to 0.95?
2. How can the reliability of a system with machines in parallel be calculated?
3. What if one of the machines fails? How would you modify the system reliability?
4. What are the implications of a system having a low reliability value?
5. How does the reliability of a system relate to its expected lifespan or failure rate?

Tip: When calculating system reliability, always remember that for series systems, reliability is the product of individual reliabilities, while for parallel systems, it involves a different formula.