Template:Standard actuarial method - Revision history

Kate Racaza: Redirected page to Non-Parametric Life Data Analysis

2012-06-29T07:35:35Z

Redirected page to Non-Parametric Life Data Analysis

← Older revision		Revision as of 07:35, 29 June 2012
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	~~== Actuarial~~-~~Standard Method ==~~		#REDIRECT [[Non-Parametric Life Data Analysis]]

	The actuarial-standard model is a variation of the actuarial-simple model. In the actuarial-simple method, the suspensions in a time period or interval are assumed to occur at the end of that interval, after the failures have occurred. The actuarial-standard model assumes that the suspensions occur in the middle of the interval, which has the effect of reducing the number of available units in the interval by half of the suspensions in that interval or:

	~~::<math>n_{i}^{\prime }={{n}_{i}}-\frac{{{s}_{i}}}{2}</math>~~

	~~With this adjustment, the calculations are carried out just as they were for the actuarial-simple model or:~~

	~~::<math>\widehat{R}({{t}_{i}})=\underset{j=1}{\overset{i}{\mathop \prod }}\,\left( 1-\frac{{{r}_{j}}}{n_{j}^{\prime }} \right),\text{ }i=1,...,m</math>~~

	~~<br>'''Example 3:''' {{Example: Standard Actuarial Example}}~~

Kate Racaza at 22:17, 9 March 2012

2012-03-09T22:17:06Z

← Older revision		Revision as of 22:17, 9 March 2012
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	==Standard ~~Actuarial~~ Method==		== Actuarial-Standard Method ==
	The standard ~~actuarial~~ model is a variation of the simple ~~actuarial~~ model ~~that involves adjusting~~ the ~~value for the number of operating units in an interval. The Kaplan~~-~~Meier and~~ simple ~~actuarial methods assume that~~ the suspensions in a time period or interval occur at the end of that interval, after the failures have occurred. The standard ~~actuarial~~ model assumes that the suspensions occur in the middle of the interval, which has the effect of reducing the number of available units in the interval by half of the suspensions in that interval or:
			The actuarial-standard model is a variation of the actuarial-simple model. In the actuarial-simple method, the suspensions in a time period or interval are assumed to occur at the end of that interval, after the failures have occurred. The actuarial-standard model assumes that the suspensions occur in the middle of the interval, which has the effect of reducing the number of available units in the interval by half of the suspensions in that interval or:

	::<math>n_{i}^{\prime }={{n}_{i}}-\frac{{{s}_{i}}}{2}</math>		::<math>n_{i}^{\prime }={{n}_{i}}-\frac{{{s}_{i}}}{2}</math>

	With this adjustment, the calculations are carried out just as they were for the simple ~~actuarial~~ model or:		With this adjustment, the calculations are carried out just as they were for the actuarial-simple model or:

	::<math>\widehat{R}({{t}_{i}})=\underset{j=1}{\overset{i}{\mathop \prod }}\,\left( 1-\frac{{{r}_{j}}}{n_{j}^{\prime }} \right),\text{ }i=1,...,m</math>		::<math>\widehat{R}({{t}_{i}})=\underset{j=1}{\overset{i}{\mathop \prod }}\,\left( 1-\frac{{{r}_{j}}}{n_{j}^{\prime }} \right),\text{ }i=1,...,m</math>

			<br>'''Example 3:''' {{Example: Standard Actuarial Example}}
	'''Example 3:'''
	{{Example: Standard Actuarial Example}}

Harry Guo: /* Standard Actuarial Method */

2012-02-20T23:55:19Z

Standard Actuarial Method

← Older revision		Revision as of 23:55, 20 February 2012
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	==Standard Actuarial Method==		==Standard Actuarial Method==
	The standard actuarial model is a variation of the simple actuarial model that involves adjusting the value for the number of operating units in an interval. The Kaplan-Meier and simple actuarial methods assume that the suspensions in a time period or interval occur at the end of that interval, after the failures have occurred. The standard actuarial model assumes that the suspensions occur in the middle of the interval, which has the effect of reducing the number of available units in the interval by half of the suspensions in that interval or:		The standard actuarial model is a variation of the simple actuarial model that involves adjusting the value for the number of operating units in an interval. The Kaplan-Meier and simple actuarial methods assume that the suspensions in a time period or interval occur at the end of that interval, after the failures have occurred. The standard actuarial model assumes that the suspensions occur in the middle of the interval, which has the effect of reducing the number of available units in the interval by half of the suspensions in that interval or:


	::<math>n_{i}^{\prime }={{n}_{i}}-\frac{{{s}_{i}}}{2}</math>		::<math>n_{i}^{\prime }={{n}_{i}}-\frac{{{s}_{i}}}{2}</math>

	With this adjustment, the calculations are carried out just as they were for the simple actuarial model or:		With this adjustment, the calculations are carried out just as they were for the simple actuarial model or:


	::<math>\widehat{R}({{t}_{i}})=\underset{j=1}{\overset{i}{\mathop \prod }}\,\left( 1-\frac{{{r}_{j}}}{n_{j}^{\prime }} \right),\text{ }i=1,...,m</math>		::<math>\widehat{R}({{t}_{i}})=\underset{j=1}{\overset{i}{\mathop \prod }}\,\left( 1-\frac{{{r}_{j}}}{n_{j}^{\prime }} \right),\text{ }i=1,...,m</math>

Harry Guo: /* Standard Actuarial Method */

2012-02-20T23:44:19Z

Standard Actuarial Method

← Older revision		Revision as of 23:44, 20 February 2012
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	::<math>n_{i}^{\prime }={{n}_{i}}-\frac{{{s}_{i}}}{2}</math>		::<math>n_{i}^{\prime }={{n}_{i}}-\frac{{{s}_{i}}}{2}</math>

	With this adjustment, the calculations are carried out just as they were for the simple actuarial model ~~in Eqn. (simpact)~~ or:		With this adjustment, the calculations are carried out just as they were for the simple actuarial model or:

Harry Guo: /* Standard Actuarial Method */

2012-02-20T19:06:53Z

Standard Actuarial Method

← Older revision		Revision as of 19:06, 20 February 2012
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	::<math>\widehat{R}({{t}_{i}})=\underset{j=1}{\overset{i}{\mathop \prod }}\,\left( 1-\frac{{{r}_{j}}}{n_{j}^{\prime }} \right),\text{ }i=1,...,m</math>		::<math>\widehat{R}({{t}_{i}})=\underset{j=1}{\overset{i}{\mathop \prod }}\,\left( 1-\frac{{{r}_{j}}}{n_{j}^{\prime }} \right),\text{ }i=1,...,m</math>

	'''Example 3:''
			'''Example 3:'''
	{{Example: Standard Actuarial Example}}		{{Example: Standard Actuarial Example}}

Harry Guo: /* Standard Actuarial Method */

2012-02-20T19:03:02Z

Standard Actuarial Method

@@ Line 10: / Line 10: @@
 ::<math>\widehat{R}({{t}_{i}})=\underset{j=1}{\overset{i}{\mathop \prod }}\,\left( 1-\frac{{{r}_{j}}}{n_{j}^{\prime }} \right),\text{ }i=1,...,m</math>
+'''Example 3:''
-====Example 11====
+{{Example: Standard Actuarial Example}}

Harry Guo at 18:49, 20 February 2012

2012-02-20T18:49:05Z

← Older revision		Revision as of 18:49, 20 February 2012
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	===Standard Actuarial Method===		==Standard Actuarial Method==
	The standard actuarial model is a variation of the simple actuarial model that involves adjusting the value for the number of operating units in an interval. The Kaplan-Meier and simple actuarial methods assume that the suspensions in a time period or interval occur at the end of that interval, after the failures have occurred. The standard actuarial model assumes that the suspensions occur in the middle of the interval, which has the effect of reducing the number of available units in the interval by half of the suspensions in that interval or:		The standard actuarial model is a variation of the simple actuarial model that involves adjusting the value for the number of operating units in an interval. The Kaplan-Meier and simple actuarial methods assume that the suspensions in a time period or interval occur at the end of that interval, after the failures have occurred. The standard actuarial model assumes that the suspensions occur in the middle of the interval, which has the effect of reducing the number of available units in the interval by half of the suspensions in that interval or:

Nicolette Young: Created page with '===Standard Actuarial Method=== The standard actuarial model is a variation of the simple actuarial model that involves adjusting the value for the number of operating units in a…'

2012-01-05T00:02:35Z

Created page with '===Standard Actuarial Method=== The standard actuarial model is a variation of the simple actuarial model that involves adjusting the value for the number of operating units in a…'

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===Standard Actuarial Method===
The standard actuarial model is a variation of the simple actuarial model that involves adjusting the value for the number of operating units in an interval. The Kaplan-Meier and simple actuarial methods assume that the suspensions in a time period or interval occur at the end of that interval, after the failures have occurred. The standard actuarial model assumes that the suspensions occur in the middle of the interval, which has the effect of reducing the number of available units in the interval by half of the suspensions in that interval or:

::<math>n_{i}^{\prime }={{n}_{i}}-\frac{{{s}_{i}}}{2}</math>

With this adjustment, the calculations are carried out just as they were for the simple actuarial model in Eqn. (simpact) or:

::<math>\widehat{R}({{t}_{i}})=\underset{j=1}{\overset{i}{\mathop \prod }}\,\left( 1-\frac{{{r}_{j}}}{n_{j}^{\prime }} \right),\text{ }i=1,...,m</math>

====Example 11====
Find reliability estimates for the data in Example 10 using the standard actuarial method.
=====Solution to Example 11=====
The solution to this example is similar to that of Example 10, with the exception of the inclusion of the <math>n_{i}^{\prime }</math> term, which is used in Eqn. (standact). Applying this equation to the data, we can generate the following table:

<center><math>\begin{matrix}
Start & End & Number of & Number of & Adjusted & {} & {} \\
Time & Time & Failures, {{r}_{i}} & Suspensions, {{s}_{i}} & Units, n_{i}^{\prime } & 1-\tfrac{{{r}_{j}}}{n_{j}^{\prime }} & \mathop{}_{}^{}1-\tfrac{{{r}_{j}}}{n_{j}^{\prime }} \\
0 & 50 & 2 & 4 & 53 & 0.962 & 0.962 \\
50 & 100 & 0 & 5 & 46.5 & 1.000 & 0.962 \\
100 & 150 & 2 & 2 & 43 & 0.953 & 0.918 \\
150 & 200 & 3 & 5 & 37.5 & 0.920 & 0.844 \\
200 & 250 & 2 & 1 & 31.5 & 0.937 & 0.791 \\
250 & 300 & 1 & 2 & 28 & 0.964 & 0.762 \\
300 & 350 & 2 & 1 & 25.5 & 0.922 & 0.702 \\
350 & 400 & 3 & 3 & 21.5 & 0.860 & 0.604 \\
400 & 450 & 3 & 4 & 15 & 0.800 & 0.484 \\
450 & 500 & 1 & 2 & 9 & 0.889 & 0.430 \\
500 & 550 & 2 & 1 & 6.5 & 0.692 & 0.298 \\
550 & 600 & 1 & 0 & 4 & 0.750 & 0.223 \\
600 & 650 & 2 & 1 & 2.5 & 0.200 & 0.045 \\
\end{matrix}</math></center>

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