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

C++

Copy

[SerializableAttribute]
public class KaplanMeierECDF

<SerializableAttribute>
Public Class KaplanMeierECDF

[SerializableAttribute]
public ref class KaplanMeierECDF

[<SerializableAttribute>]
type KaplanMeierECDF =  class end

The KaplanMeierECDF type exposes the following members.

Constructors

	Name	Description
	KaplanMeierECDF	Constructor for KaplanMeierECDF.

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Methods

	Name	Description
	Equals	Determines whether the specified object is equal to the current object. (Inherited from Object.)
	EvaluateCDF	Computes the empirical CDF and returns the CDF values up to, but not including the time values returned by GetTimes.
	Finalize	Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object.)
	GetHashCode	Serves as a hash function for a particular type. (Inherited from Object.)
	GetTimes	Retrieves the time values where the step function CDF jumps to a greater value.
	GetType	Gets the Type of the current instance. (Inherited from Object.)
	MemberwiseClone	Creates a shallow copy of the current Object. (Inherited from Object.)
	SetCensor	Set flags to note right-censoring.
	SetFrequency	Sets the frequency for each entry in t.
	ToString	Returns a string that represents the current object. (Inherited from Object.)

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Properties

	Name	Description
	NumberOfPoints	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 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:

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

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 counts up to and including that failure time, but not after.

Reference

Imsl.Stat Namespace

Other Resources

Example