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Question 4.3: A collection of 60 laser diodes were tested, and 7 failures ...

A collection of 60 laser diodes were tested, and 7 failures occurred after 1000 h. The lifetimes obtained are tabulated below.

Rank number (i) Lifetime (h) F(t_{i})=(i-0.3)/(60+0.4)
1 181 0.012              (1.2%)
2 299 0.028             (2.8%)
3 389 0.045             (4.5%)
4 430 0.061              (6.1%)
5 535 0.078             (7.8%)
6 610 0.094             (9.4%)
7 805 0.111                (11.1%)

1. Plot the results in both Weibull and lognormal fashion.
2. What is the MTTF for each?
3. For the lognormal plot, what is the value of σ?
4. For the Weibull plot, what is α?

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  1. First, F(t_{i}) is calculated for n = 60 and i = 1, 2, 3,…, 7 and entered in the table.
    The F values are plotted versus log time on Weibull and lognormal paper as shown in Figure 4.17(a) and (b).
  2. At a value of F = 0.5, MTTF = 2170 h (Weibull) and 3600 h (lognormal).
  3. It was shown above that \sigma=\ln[t_{0.5}/t_{0.159}]. Substituting, \sigma =\ln[3600/980]=1.30.
  4. From Eqn (4.16) \ln[1-F(t)]=-(t/ \alpha)^{\beta} we note that when t = α ,\ln[1-F(t)]=-1.Thus,1-F(t)=0.368, and F(t)=0.632. At this value, which is noted on the ordinate axis, α = t = 2990 h.
4.17 a
4.17 b

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