Template:Normal Distribution Probability Plotting Example - Revision history

Kate Racaza: Redirected page to Normal Distribution Probability Plotting Example

2012-08-15T06:47:05Z

Redirected page to Normal Distribution Probability Plotting Example

← Older revision		Revision as of 06:47, 15 August 2012
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	~~=== Normal Distribution Probability Plotting===~~		#REDIRECT[[Normal Distribution Probability Plotting Example]]
	Seven units are put on a life test and run until failure. The failure times are 85, 90, 95, 100, 105, 110, and 115 hours. Assuming a normal distribution, estimate the parameters using probability plotting.
	[[Normal Distribution Probability Plotting Example]]
	~~==== Solution====~~
	In order to plot the points for the probability plot, the appropriate unreliability estimate values must be obtained. These will be estimated through the use of median ranks, which can be obtained from statistical tables or the Quick Statistical Reference in Weibull++. The following table shows the times-to-failure and the appropriate median rank values for this example:


	~~<center><math>\begin{matrix}~~
	~~\text{Time-to-} & \text{Median} \\~~
	~~\text{Failure (hr)} & \text{Rank ( }\!\!%\!\!\text{ )} \\~~
	~~\text{85} & \text{ 9}\text{.43 }\!\!%\!\!\text{ } \\~~
	~~\text{90} & \text{22}\text{.85 }\!\!%\!\!\text{ } \\~~
	~~\text{95} & \text{36}\text{.41 }\!\!%\!\!\text{ } \\~~
	~~\text{100} & \text{50}\text{.00 }\!\!%\!\!\text{ } \\~~
	~~\text{105} & \text{63}\text{.59 }\!\!%\!\!\text{ } \\~~
	~~\text{110} & \text{77}\text{.15 }\!\!%\!\!\text{ } \\~~
	~~\text{115} & \text{90}\text{.57 }\!\!%\!\!\text{ } \\~~
	~~\end{matrix}</math></center>~~



	~~These points can now be plotted on normal probability plotting paper as shown in the next figure.~~

	~~[[Image:chp8PP.gif\|thumb\|center\|300px\| ]]~~


	Draw the best possible line through the plot points. The time values where this line intersects the 15.85%, 50%, and 84.15% unreliability values should be projected down to the abscissa, as shown in the following plot.

	~~[[Image:chp8PP2.gif\|thumb\|center\|300px\| ]]~~


	The estimate of <math>\mu </math> is determined from the time value at the 50% unreliability level, which in this case is 100 hours. The value of the estimator of <math>\sigma </math> is determined by Eqn. (sigplot):

	~~::<math>\begin{align}~~
	~~\widehat{\sigma }= & \frac{t(Q=84.15%)-t(Q=15.85%)}{2} \\~~
	~~\widehat{\sigma }= & \frac{112-88}{2}=\frac{24}{2} \\~~
	~~\widehat{\sigma }= & 12\text{ hours}~~
	~~\end{align}</math>~~

	Alternately, <math>\widehat{\sigma }</math> could be determined by measuring the distance from <math>t(Q=15.85%)</math> to <math>t(Q=50%)</math> , or <math>t(Q=50%)</math> to <math>t(Q=84.15%)</math> , as either of these two distances is equal to the value of one standard deviation.

Nicolette Young at 00:08, 22 March 2012

2012-03-22T00:08:18Z

← Older revision		Revision as of 00:08, 22 March 2012
Line 1:		Line 1:

	=== Normal Distribution Probability Plotting===		=== Normal Distribution Probability Plotting===
	Seven units are put on a life test and run until failure. The failure times are 85, 90, 95, 100, 105, 110, and 115 hours. Assuming a normal distribution, estimate the parameters using probability plotting.		Seven units are put on a life test and run until failure. The failure times are 85, 90, 95, 100, 105, 110, and 115 hours. Assuming a normal distribution, estimate the parameters using probability plotting.
			[[Normal Distribution Probability Plotting Example]]
	==== Solution====		==== Solution====
	In order to plot the points for the probability plot, the appropriate unreliability estimate values must be obtained. These will be estimated through the use of median ranks, which can be obtained from statistical tables or the Quick Statistical Reference in Weibull++. The following table shows the times-to-failure and the appropriate median rank values for this example:		In order to plot the points for the probability plot, the appropriate unreliability estimate values must be obtained. These will be estimated through the use of median ranks, which can be obtained from statistical tables or the Quick Statistical Reference in Weibull++. The following table shows the times-to-failure and the appropriate median rank values for this example:

Nicolette Young: Created page with ' === Normal Distribution Probability Plotting=== Seven units are put on a life test and run until failure. The failure times are 85, 90, 95, 100, 105, 110, and 115 hours. Assum…'

2012-02-07T20:53:54Z

Created page with ' === Normal Distribution Probability Plotting=== Seven units are put on a life test and run until failure. The failure times are 85, 90, 95, 100, 105, 110, and 115 hours. Assum…'

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=== Normal Distribution Probability Plotting===
Seven units are put on a life test and run until failure. The failure times are 85, 90, 95, 100, 105, 110, and 115 hours. Assuming a normal distribution, estimate the parameters using probability plotting.

==== Solution====
In order to plot the points for the probability plot, the appropriate unreliability estimate values must be obtained. These will be estimated through the use of median ranks, which can be obtained from statistical tables or the Quick Statistical Reference in Weibull++. The following table shows the times-to-failure and the appropriate median rank values for this example:

<center><math>\begin{matrix}
\text{Time-to-} & \text{Median} \\
\text{Failure (hr)} & \text{Rank ( }\!\!%\!\!\text{ )} \\
\text{85} & \text{ 9}\text{.43 }\!\!%\!\!\text{ } \\
\text{90} & \text{22}\text{.85 }\!\!%\!\!\text{ } \\
\text{95} & \text{36}\text{.41 }\!\!%\!\!\text{ } \\
\text{100} & \text{50}\text{.00 }\!\!%\!\!\text{ } \\
\text{105} & \text{63}\text{.59 }\!\!%\!\!\text{ } \\
\text{110} & \text{77}\text{.15 }\!\!%\!\!\text{ } \\
\text{115} & \text{90}\text{.57 }\!\!%\!\!\text{ } \\
\end{matrix}</math></center>

These points can now be plotted on normal probability plotting paper as shown in the next figure.

[[Image:chp8PP.gif|thumb|center|300px| ]]

Draw the best possible line through the plot points. The time values where this line intersects the 15.85%, 50%, and 84.15% unreliability values should be projected down to the abscissa, as shown in the following plot.

[[Image:chp8PP2.gif|thumb|center|300px| ]]

The estimate of <math>\mu </math> is determined from the time value at the 50% unreliability level, which in this case is 100 hours. The value of the estimator of <math>\sigma </math> is determined by Eqn. (sigplot):

::<math>\begin{align}
\widehat{\sigma }= & \frac{t(Q=84.15%)-t(Q=15.85%)}{2} \\
\widehat{\sigma }= & \frac{112-88}{2}=\frac{24}{2} \\
\widehat{\sigma }= & 12\text{ hours}
\end{align}</math>

Alternately, <math>\widehat{\sigma }</math> could be determined by measuring the distance from <math>t(Q=15.85%)</math> to <math>t(Q=50%)</math> , or <math>t(Q=50%)</math> to <math>t(Q=84.15%)</math> , as either of these two distances is equal to the value of one standard deviation.