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12 components were tested to failure. The (unordered) times to failure (in hours) 76, 86, 57, 49, 81, 19, 69, 16, 93, 68, 28,
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No. Time (Hours) Increment Order f/s Failure Frequency Cumulative Frequency F(t) ln(t) ln(ln(1/(1-F(1-t)))
1 15 1 1 f 1 1 0.06 2.71 -2.85
2 16 1 2 f 1 2 0.14 2.77 -1.91
3 19 1 3 f 1 3 0.22 2.94 -1.4
4 28 1 4 f 1 4 0.3 3.33 -1.04
5 49 1 5 f 1 5 0.38 3.89 -0.74
6 57 1 6 f 1 6 0.46 4.04 -0.49
7 68 1 7 f 1 7 0.54 4.22 -0.25
8 69 1 8 f 1 8 0.62 4.23 -0.03
9 76 1 9 f 1 9 0.7 4.33 0.19
10 81 1 10 f 1 10 0.78 4.39 0.42
11 86 1 11 f 1 11 0.86 4.45 0.69
12 93 1 12 f 1 12 0.94 4.53 1.06
Life units: Time (Hours), f/s: failure/suspension, F(t): cumulative probability of failure

parameters using the rank regression method

Parameter value
Shape parameter (β) 1.56
Characteristic life (η) 64.1

The reliability component is derived by following formula:

t\B R(t) e \.

The hazard function is given by :

f(t) h(t) Rt B(t)0-1) e h(t) e

putting the values of t=10,50 and 75 hours we get,

h(10)=0.0086

h(50)=0.0212

h(75)=0.0266

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