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KaplanMeierECDF Class
Computes the Kaplan-Meier reliability function estimates or the CDF based on failure data that may be multi-censored.
Inheritance Hierarchy
SystemObject
  Imsl.StatKaplanMeierECDF

Namespace: Imsl.Stat
Assembly: ImslCS (in ImslCS.dll) Version: 6.5.2.0
Syntax
[SerializableAttribute]
public class KaplanMeierECDF

The KaplanMeierECDF type exposes the following members.

Constructors
  NameDescription
Public methodKaplanMeierECDF
Constructor for KaplanMeierECDF.
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Methods
  NameDescription
Public methodEquals
Determines whether the specified object is equal to the current object.
(Inherited from Object.)
Public methodEvaluateCDF
Computes the empirical CDF and returns the CDF values up to, but not including the time values returned by GetTimes.
Protected methodFinalize
Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection.
(Inherited from Object.)
Public methodGetHashCode
Serves as a hash function for a particular type.
(Inherited from Object.)
Public methodGetTimes
Retrieves the time values where the step function CDF jumps to a greater value.
Public methodGetType
Gets the Type of the current instance.
(Inherited from Object.)
Protected methodMemberwiseClone
Creates a shallow copy of the current Object.
(Inherited from Object.)
Public methodSetCensor
Set flags to note right-censoring.
Public methodSetFrequency
Sets the frequency for each entry in t.
Public methodToString
Returns a string that represents the current object.
(Inherited from Object.)
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Properties
  NameDescription
Public propertyNumberOfPoints
The number of points in the empirical CDF.
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Remarks

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

Reference

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