To find the overall reliability of the product, we can use the concept of reliability in series. In this case, since all components must work for the product to function, we can multiply the reliabilities of each component to obtain the overall reliability.
Given:
Number of components (n) = 45
Reliability of each component (R) = 0.97
To calculate the overall reliability (R_total):
R_total = R^
R_total = 0.97^45
Using a calculator, we can evaluate this expression:
R_total ≈ 0.5429
Therefore, the overall reliability of the product is approximately 0.5429 when rounded to four decimal places.