Package com.imsl.stat

Class KaplanMeierECDF

java.lang.Object
com.imsl.stat.KaplanMeierECDF
All Implemented Interfaces:
Serializable, Cloneable
public class KaplanMeierECDF extends Object implements Serializable, Cloneable
Computes the Kaplan-Meier reliability function estimates or the CDF based on failure data that may be multi-censored.

The Kaplan-Meier (K-M) Product Limit procedure provides simple estimates of the reliability function or the CDF based on failure data that may be multi-censored. No underlying probability model is assumed; K-M estimation is an empirical (non-parametric) procedure. Exact times of failure are required.

Consider a situation in which we are reliability testing n (non-repairable) units taken randomly from a population. We are investigating the population to determine if its failure rate is acceptable. In the typical test scenario, we have a fixed time T to run the units to see if they survive or fail. The data obtained are called Censored Type I data.

During the T hours of test we observe r failures (where r can be any number from 0 to n). The failure times are \( t_1,t_2,\ldots,t_r\), and there are \((n-r)\) units that survived the entire T-hour test without failing. Note that T is fixed in advance, and r is an output of the testing, since we don't know how many failures will occur until the test is run. Note that we assume the exact times of failure are recorded when they occur.

This type of data is also called "right censored" data since the times of failure to the right (i.e., larger than T) are missing. The steps for calculating K-M estimates are the following:

  1. Order the actual failure times from \(t_1\) through \(t_r\), where there are r failures
  2. Corresponding to each \(t_i\), associate the number \(n_i\) with \(n_i\) = the number of operating units just before the ith failure occurred at time \(t_i\)
  3. First estimate the survival \(R(t_1)=(n_1-1)/n_1\)
  4. Estimate each ensuing survival \(R(t_i)=R(t_{i-1})(n_i-1)/n_1 \), \(i>1\)
  5. Estimate the CDF \(F(t_i)=1-R(t_i)\), \(i=1, 2,\ldots\)

Note that non-failed units taken off testing (i.e., right-censored) only count up to the last actual failure time before they were removed. They are included in the \(n_i\) counts up to and including that failure time, but not after.

See Also:

  • Constructor Summary

    Constructors
    Constructor
    Description
    KaplanMeierECDF(double[] t)
    Constructor for KaplanMeierECDF.

  • Method Summary

    Modifier and Type
    Method
    Description
    double[]
    evaluateCDF()
    Computes the empirical CDF and returns the CDF values up to, but not including the time values returned by getTimes.
    int
    getNumberOfPoints()
    Retrieves the number of points in the empirical CDF
    double[]
    getTimes()
    Retrieves the time values where the step function CDF jumps to a greater value.
    void
    setCensor(int[] censor)
    Set flags to note right-censoring
    void
    setFrequency(int[] freq)
    Sets the frequency for each entry in t

    Methods inherited from class java.lang.Object

    clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

  • Constructor Details

    • KaplanMeierECDF

      public KaplanMeierECDF(double[] t)
      Constructor for KaplanMeierECDF.
      Parameters:
      t - a double array containing the failure times.

  • Method Details

    • setFrequency

      public void setFrequency(int[] freq)
      Sets the frequency for each entry in t
      Parameters:
      freq - a double array containing the repeat count for each entry in t.

    • setCensor

      public void setCensor(int[] censor)
      Set flags to note right-censoring
      Parameters:
      censor - an int array of 0 or 1 flags to note right-censoring. Values of 0 = continue to use datum and 1 = remove datum. If this method is not called, no data is right-censored.

    • getTimes

      public double[] getTimes()
      Retrieves the time values where the step function CDF jumps to a greater value. This array has right-censored values of t removed.
      Returns:
      a double array of time values.
      Throws:
      IllegalStateException - is thrown if the CDF has not been evaluated.

    • getNumberOfPoints

      public int getNumberOfPoints()
      Retrieves the number of points in the empirical CDF
      Returns:
      an int containing the number of points in the empirical CDF.
      Throws:
      IllegalStateException - is thrown if the CDF has not been evaluated.

    • evaluateCDF

      public double[] evaluateCDF()
      Computes the empirical CDF and returns the CDF values up to, but not including the time values returned by getTimes.
      Returns:
      a double array of CDF values.