Question

1. A study of junction failures was conducted over a two week period. The junctions were repeatedly subjected to heat cycling until they failed. There were five test stations and failed units were immediately replaced during the test. The test ended at a predetermined time. The data below are failure times in hours. The values marked with an asterisk (*) are censored.

           23     278*     73      263*   156*   334

     22*     72       91        32      102       81*

115      121     105*    263       74       53*

1. Calculate a maximum-likelihood estimate of the mean lifetime, assuming the lifetimes are exponentially-distributed.
   
2. Calculate a 95% two-sided confidence interval for the true mean lifetime, assuming the lifetimes have an exponential distribution.

Answer 1

SOLUTION-

LET X BE THE FAILURE TIMES IN HOURS AND THE LIFETIMES ARE EXPONENTIALLY DISTRIBUTED.

SO, X ~ EXPONENTIAL()

A.) THE MAXIMUM-LIKELIHOOD ESTIMATED OF THE MEAN LIFETIME IS,

  

  

HENCE,

B.) A 95% TWO-SIDED CONFIDENCE INTERVAL FOR THE TRUE MEAN LIFETIME IS GIVEN BY,

NOW,

  

HENCE, THE 95% CONFIDENCE INTERVAL IS

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