Question

Ten units were placed on stress for 1000 hours. At 250,500 , and 750 hours, 1 randomly chosen surviving unit was removed for physical analysis. There were five failure times observed at 41, 253, 441, 561, and 920 hours. At test end, two units survived. Using the Kaplan-Meier PLE, estimate the CDF at the observed failure times. Estimate the standard error of the CDF estimate using Greenwood's formula. Provide 90% pointwise confidence intervals at all failure times using the normal approximation. Redo the confidence interval estimates by applying the log and logistic transformations.

Answer 1

To estimate the CDF at observed failure times, use the Kaplan-Meier PLE and calculate the survival function. Estimate the standard error using Greenwood's formula. Calculate 90% pointwise confidence intervals using the normal approximation. Apply log and logistic transformations for alternative confidence interval estimates.

Step-by-step explanation:

The question is asking for the estimation of the CDF at the observed failure times using the Kaplan-Meier PLE. To estimate the CDF, we need to first calculate the survival function and then take its complement. The survival function is the product of the survival probabilities at each failure time. The survival probability at each failure time is calculated by dividing the number of surviving units at that time by the total number of units at the start.

Greenwood's formula is used to estimate the standard error of the CDF estimate. It takes into account the number of units at risk at each failure time and the number of observed failures at each time.

Pointwise confidence intervals can be calculated using the normal approximation. The mean of the normal distribution is the estimated CDF, and the standard deviation is the estimated standard error. For a 90% confidence interval, we can use the z-score of 1.645.

Applying log and logistic transformations to the confidence interval estimates can help with data transformation if the assumptions of normality are violated.