# A one-shot device can be used only once; after use, the device (e.g., a nuclear weapon, space

## Question:

a. Suppose the desired failure rate for a one-shot device is p = .10. Suppose also that designers will conduct n = 20 tests of the device and conclude that the device is performing to specifications if K = 1 (i.e., if 1 or no failure is observed in the sample). Find P(x ≤ pbc).

b. In reliability analysis, 1 – P(x ≤ K) is often called the level of confidence for concluding that the true failure rate is less than or equal to p. Find the level of confidence for the one-shot device described in part a. In your opinion, is this an acceptable level? Explain.

c. Demonstrate that the confidence level can be increased by either (1) increasing the sample size n or (2) decreasing the number K of failures allowed in the sample.

d. Typically, designers want a confidence level of .90, .95, or .99. Find the values of n and K to use so that the designers can conclude with at least 95% confidence that the failure rate for the one-shot device of part a is no greater than p = .10.

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