Question 2.2: From the histogram in Figure 2.4: (a) Calculate the unreliab......

Reliability Engineering [1026554]

From the histogram in Figure 2.4

(a) Calculate the unreliability of the product at a time of 30 hours.

(b) Also calculate the reliability.

2.4

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(a) For the discrete data represented in this histogram, the unreliability is the sum of the failure probability density function values from t = 0 to t = 30. This sum, as a percentage, is 73.7%.

(b) The reliability is equal to 26.3% and can be read from column 5 of Table 2.2. The sum of reliability and unreliability must always be equal to 100%.

Operating time interval (hours)	Number of failures in the interval	Number of surviving products at the end of the interval	Relative frequency	Estimate of reliability at the end of the interval	Estimate of hazard rate in each interval (failures/hour)
0-10	105	146	0.418	0.582	0.042
11–20	52	94	0.207	0.375	0.036
21–30	28	66	0.112	0.263	0.03
31–40	17	49	0.068	0.195	0.026
41–50	12	37	0.048	0.147	0.024
51–60	8	29	0.032	0.116	0.022
61–70	6	23	0.024	0.092	0.021
71–80	4	19	0.016	0.076	0.017
81–90	3	16	0.012	0.064	0.016
91–100	3	13	0.012	0.052	0.019
101–110	2	11	0.008	0.044	0.015
111–120	3	8	0.012	0.032	0.027
121–130	3	5	0.012	0.02	0.038
131–140	4	1	0.016	0.004	0.08
Over 140	1	0	0.004	0	–

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