We observe 11 components, starting from time t = 0. The component life times are independent. Observation ends immediately following the 9th failure, which occurs at time t = 13.48. Give (correct to 2 decimal places) an appropriate estimate for F(13.48), using the Mean ranking metho
Question
We observe 11 components, starting from time t = 0. The component life times are independent. Observation ends immediately following the 9th failure, which occurs at time t = 13.48. Give (correct to 2 decimal places) an appropriate estimate for F(13.48), using the Mean ranking metho
Solution
The Mean Ranking Method is a non-parametric method used to estimate the cumulative distribution function (CDF) F(t) of a random variable. In the context of reliability analysis, it is used to estimate the unreliability (or failure probability) at a given time.
The Mean Ranking Method uses the order statistics of the observed data. In this case, the order statistics are the ordered failure times. The estimate for F(t) at the ith failure time is given by:
F(t_i) = i / (n+1)
where n is the total number of components observed.
In this case, the 9th failure occurs at t = 13.48, and we have observed a total of 11 components. Therefore, the estimate for F(13.48) is:
F(13.48) = 9 / (11+1) = 0.75
Therefore, an appropriate estimate for F(13.48) is 0.75 (correct to 2 decimal places).
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