Template:Example: Kaplan-Meier Example - Revision history

Lisa Hacker: Redirected page to Non-Parametric Life Data Analysis

2012-08-10T08:10:47Z

Redirected page to Non-Parametric Life Data Analysis

← Older revision		Revision as of 08:10, 10 August 2012
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	[[~~Category: For Deletion~~]]		#REDIRECT [[Non-Parametric_Life_Data_Analysis]]

Kate Racaza: Replaced content with 'Category: For Deletion'

2012-07-24T07:36:24Z

Replaced content with 'Category: For Deletion'

← Older revision		Revision as of 07:36, 24 July 2012
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	~~'''Kaplan-Meier Example'''~~		[[Category: For Deletion]]

	~~A group of 20 units are put on a life test with the following results.~~
	~~<center><math>\begin{matrix}~~
	~~Number & State & State \\~~
	~~in State & (F or S) & End Time \\~~
	~~3 & F & 9 \\~~
	~~1 & S & 9 \\~~
	~~1 & F & 11 \\~~
	~~1 & S & 12 \\~~
	~~1 & F & 13 \\~~
	~~1 & S & 13 \\~~
	~~1 & S & 15 \\~~
	~~1 & F & 17 \\~~
	~~1 & F & 21 \\~~
	~~1 & S & 22 \\~~
	~~1 & S & 24 \\~~
	~~1 & S & 26 \\~~
	~~1 & F & 28 \\~~
	~~1 & F & 30 \\~~
	~~1 & S & 32 \\~~
	~~2 & S & 35 \\~~
	~~1 & S & 39 \\~~
	~~1 & S & 41 \\~~
	~~\end{matrix}</math></center>~~
	~~Use the Kaplan-Meier estimator to determine the reliability estimates for each failure time.~~

	~~<br>'''Solution'''~~

	~~Using the data and the reliability equation of the Kaplan-Meier estimator, the following table can be constructed~~:
	~~<center><math>\begin{matrix}~~
	~~State & Number of & Number of & Available & {} & {} \\~~
	~~End Time & Failures, {{r}_{i}} & Suspensions, {{s}_{i}} & Units, {{n}_{i}} & \tfrac{{{n}_{i}}-{{r}_{i}}}{{{n}_{i}}} & \mathop{}_{}^{}\prod\tfrac{{{n}_{i}}-{{r}_{i}}}{{{n}_{i}}} \\~~
	~~9 & 3 & 1 & 20 & 0.850 & 0.850 \\~~
	~~11 & 1 & 0 & 16 & 0.938 & 0.797 \\~~
	~~12 & 0 & 1 & 15 & 1.000 & 0.797 \\~~
	~~13 & 1 & 1 & 14 & 0.929 & 0.740 \\~~
	~~15 & 0 & 1 & 12 & 1.000 & 0.740 \\~~
	~~17 & 1 & 0 & 11 & 0.909 & 0.673 \\~~
	~~21 & 1 & 0 & 10 & 0.900 & 0.605 \\~~
	~~22 & 0 & 1 & 9 & 1.000 & 0.605 \\~~
	~~24 & 0 & 1 & 8 & 1.000 & 0.605 \\~~
	~~26 & 0 & 1 & 7 & 1.000 & 0.605 \\~~
	~~28 & 1 & 0 & 6 & 0.833 & 0.505 \\~~
	~~30 & 1 & 0 & 5 & 0.800 & 0.404 \\~~
	~~32 & 0 & 1 & 4 & 1.000 & 0.404 \\~~
	~~35 & 0 & 1 & 3 & 1.000 & 0.404 \\~~
	~~39 & 0 & 1 & 2 & 1.000 & 0.404 \\~~
	~~41 & 0 & 1 & 1 & 1.000 & 0.404 \\~~
	~~\end{matrix}</math></center>~~
	~~As can be determined from the preceding table, the reliability estimates for the failure times are:~~
	~~<center><math>\begin{matrix}~~
	~~Failure Time & Reliability Est. \\~~
	~~9 & 85.0% \\~~
	~~11 & 79.7% \\~~
	~~13 & 74.0% \\~~
	~~17 & 67.3% \\~~
	~~21 & 60.5% \\~~
	~~28 & 50.5% \\~~
	~~30 & 40.4% \\~~
	~~\end{matrix}</math></center>~~

Kate Racaza at 22:08, 9 March 2012

2012-03-09T22:08:30Z

← Older revision		Revision as of 22:08, 9 March 2012
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	'''Kaplan-Meier Example'''		'''Kaplan-Meier Example'''

	~~A group of 20 units are put on a life test with the following results.~~

			A group of 20 units are put on a life test with the following results.
	<center><math>\begin{matrix}		<center><math>\begin{matrix}
	Number & State & State \\		Number & State & State \\
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	1 & S & 41 \\		1 & S & 41 \\
	\end{matrix}</math></center>		\end{matrix}</math></center>
			Use the Kaplan-Meier estimator to determine the reliability estimates for each failure time.

	~~Use the Kaplan-Meier estimator to determine the reliability estimates for each failure time.~~		<br>'''Solution'''


	'''Solution'''

	~~Using the data and the reliability equation of the Kaplan-Meier estimator , the following table can be constructed:~~

			Using the data and the reliability equation of the Kaplan-Meier estimator, the following table can be constructed:
	<center><math>\begin{matrix}		<center><math>\begin{matrix}
	State & Number of & Number of & Available & {} & {} \\		State & Number of & Number of & Available & {} & {} \\
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	41 & 0 & 1 & 1 & 1.000 & 0.404 \\		41 & 0 & 1 & 1 & 1.000 & 0.404 \\
	\end{matrix}</math></center>		\end{matrix}</math></center>
			As can be determined from the preceding table, the reliability estimates for the failure times are:
	As can be determined from the preceding table, the reliability estimates for the failure times are:

	<center><math>\begin{matrix}		<center><math>\begin{matrix}
	Failure Time & Reliability Est. \\		Failure Time & Reliability Est. \\

Harry Guo at 23:26, 5 March 2012

2012-03-05T23:26:44Z

← Older revision		Revision as of 23:26, 5 March 2012
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	<center><math>\begin{matrix}		<center><math>\begin{matrix}
	State & Number of & Number of & Available & {} & {} \\		State & Number of & Number of & Available & {} & {} \\
	End Time & Failures, {{r}_{i}} & Suspensions, {{s}_{i}} & Units, {{n}_{i}} & \tfrac{{{n}_{i}}-{{r}_{i}}}{{{n}_{i}}} & \mathop{}_{}^{}\tfrac{{{n}_{i}}-{{r}_{i}}}{{~~\prod~~{n}_{i}}} \\		End Time & Failures, {{r}_{i}} & Suspensions, {{s}_{i}} & Units, {{n}_{i}} & \tfrac{{{n}_{i}}-{{r}_{i}}}{{{n}_{i}}} & \mathop{}_{}^{}\prod\tfrac{{{n}_{i}}-{{r}_{i}}}{{{n}_{i}}} \\
	9 & 3 & 1 & 20 & 0.850 & 0.850 \\		9 & 3 & 1 & 20 & 0.850 & 0.850 \\
	11 & 1 & 0 & 16 & 0.938 & 0.797 \\		11 & 1 & 0 & 16 & 0.938 & 0.797 \\

Harry Guo at 23:26, 5 March 2012

2012-03-05T23:26:12Z

← Older revision		Revision as of 23:26, 5 March 2012
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	<center><math>\begin{matrix}		<center><math>\begin{matrix}
	State & Number of & Number of & Available & {} & {} \\		State & Number of & Number of & Available & {} & {} \\
	End Time & Failures, {{r}_{i}} & Suspensions, {{s}_{i}} & Units, {{n}_{i}} & \tfrac{{{n}_{i}}-{{r}_{i}}}{{{n}_{i}}} & \mathop{}_{}^{}\tfrac{{{n}_{i}}-{{r}_{i}}}{{{n}_{i}}} \\		End Time & Failures, {{r}_{i}} & Suspensions, {{s}_{i}} & Units, {{n}_{i}} & \tfrac{{{n}_{i}}-{{r}_{i}}}{{{n}_{i}}} & \mathop{}_{}^{}\tfrac{{{n}_{i}}-{{r}_{i}}}{{\prod{n}_{i}}} \\
	9 & 3 & 1 & 20 & 0.850 & 0.850 \\		9 & 3 & 1 & 20 & 0.850 & 0.850 \\
	11 & 1 & 0 & 16 & 0.938 & 0.797 \\		11 & 1 & 0 & 16 & 0.938 & 0.797 \\

Harry Guo at 20:44, 20 February 2012

2012-02-20T20:44:59Z

← Older revision		Revision as of 20:44, 20 February 2012
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	'''Solution'''		'''Solution'''

	Using the data and ~~Eqn. (kapmeier)~~, the following table can be constructed:		Using the data and the reliability equation of the Kaplan-Meier estimator , the following table can be constructed:

	<center><math>\begin{matrix}		<center><math>\begin{matrix}

Harry Guo: Created page with ''''Kaplan-Meier Example''' A group of 20 units are put on a life test with the following results. $\begin{matrix} Number & State & State \\ in State & (F or…'$

2012-02-20T18:57:02Z

Created page with ''''Kaplan-Meier Example''' A group of 20 units are put on a life test with the following results. <center><math>\begin{matrix} Number & State & State \\ in State & (F or…'

New page

'''Kaplan-Meier Example'''

A group of 20 units are put on a life test with the following results.

<center><math>\begin{matrix}
Number & State & State \\
in State & (F or S) & End Time \\
3 & F & 9 \\
1 & S & 9 \\
1 & F & 11 \\
1 & S & 12 \\
1 & F & 13 \\
1 & S & 13 \\
1 & S & 15 \\
1 & F & 17 \\
1 & F & 21 \\
1 & S & 22 \\
1 & S & 24 \\
1 & S & 26 \\
1 & F & 28 \\
1 & F & 30 \\
1 & S & 32 \\
2 & S & 35 \\
1 & S & 39 \\
1 & S & 41 \\
\end{matrix}</math></center>

Use the Kaplan-Meier estimator to determine the reliability estimates for each failure time.

'''Solution'''

Using the data and Eqn. (kapmeier), the following table can be constructed:

<center><math>\begin{matrix}
State & Number of & Number of & Available & {} & {} \\
End Time & Failures, {{r}_{i}} & Suspensions, {{s}_{i}} & Units, {{n}_{i}} & \tfrac{{{n}_{i}}-{{r}_{i}}}{{{n}_{i}}} & \mathop{}_{}^{}\tfrac{{{n}_{i}}-{{r}_{i}}}{{{n}_{i}}} \\
9 & 3 & 1 & 20 & 0.850 & 0.850 \\
11 & 1 & 0 & 16 & 0.938 & 0.797 \\
12 & 0 & 1 & 15 & 1.000 & 0.797 \\
13 & 1 & 1 & 14 & 0.929 & 0.740 \\
15 & 0 & 1 & 12 & 1.000 & 0.740 \\
17 & 1 & 0 & 11 & 0.909 & 0.673 \\
21 & 1 & 0 & 10 & 0.900 & 0.605 \\
22 & 0 & 1 & 9 & 1.000 & 0.605 \\
24 & 0 & 1 & 8 & 1.000 & 0.605 \\
26 & 0 & 1 & 7 & 1.000 & 0.605 \\
28 & 1 & 0 & 6 & 0.833 & 0.505 \\
30 & 1 & 0 & 5 & 0.800 & 0.404 \\
32 & 0 & 1 & 4 & 1.000 & 0.404 \\
35 & 0 & 1 & 3 & 1.000 & 0.404 \\
39 & 0 & 1 & 2 & 1.000 & 0.404 \\
41 & 0 & 1 & 1 & 1.000 & 0.404 \\
\end{matrix}</math></center>

As can be determined from the preceding table, the reliability estimates for the failure times are:

<center><math>\begin{matrix}
Failure Time & Reliability Est. \\
9 & 85.0% \\
11 & 79.7% \\
13 & 74.0% \\
17 & 67.3% \\
21 & 60.5% \\
28 & 50.5% \\
30 & 40.4% \\
\end{matrix}</math></center>

Template:Example: Kaplan-Meier Example - Revision history

Lisa Hacker: Redirected page to Non-Parametric Life Data Analysis

Kate Racaza: Replaced content with 'Category: For Deletion'

Kate Racaza at 22:08, 9 March 2012

Harry Guo at 23:26, 5 March 2012

Harry Guo at 23:26, 5 March 2012

Harry Guo at 20:44, 20 February 2012

Harry Guo: Created page with ''''Kaplan-Meier Example''' A group of 20 units are put on a life test with the following results. \begin{matrix} Number & State & State \\ in State & (F or…'

Harry Guo: Created page with ''''Kaplan-Meier Example''' A group of 20 units are put on a life test with the following results. $\begin{matrix} Number & State & State \\ in State & (F or…'$