Reliability, Maintainability and Risk, 9th Edition

Appendix 8

Answers to Exercises

Chapter 2

(a)	(b)
1. 114	1.1
2. 0.99	0.42 (0.12* )
3. 10–5	10–3
4. 2.2 × 10–3	0.18 (0.22* )
5. Negligible	Negligible
6. Unavailability × 2	Unavailability × approx 2

^* Beware the approximation. λt is large (i.e. 0.876). Furthermore, if the 10 000 hr per year approximation were used, then λt = 1.

Chapter 5

1. Accumulated time T = 50 × 100 = 5000 hr. Since the test was time truncated n = 2(k + 1).

Therefore,

(a) n = 6, T = 5000, α = 0.4. From Appendix 2, χ² = 6.21

$\text{MTB}{\text{F}}_{60\%}=\frac{2T}{{\mathrm{\chi }}^2}=\frac{10000}{6.21}=1610\text{hr}$

(b) n = 2, T = 5000, α = 0.4. From Appendix 2, χ² = 1.83

$\text{MTB}{\text{F}}_{60\%}=\frac{2T}{{\mathrm{\chi }}^2}=\frac{10000}{1.83}=5464$