Electronic Components Example - Revision history

Chris Kahn at 08:04, 15 August 2012

2012-08-15T08:04:15Z

← Older revision		Revision as of 08:04, 15 August 2012
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	<noinclude>{{Banner_ALTA_Examples}}</noinclude>		<noinclude>{{Banner_ALTA_Examples}}</noinclude>

	An electronic component was redesigned and then tested to failure at three different temperatures. Six units were tested at each temperature level. At the ~~406K~~ stress level, however, a unit was removed from the test due to a test equipment failure which led to a failure of the component. A warranty time of one year is to be given, with an expected return of 10% of the population. The following table shows the times-to-failure and test temperatures.		An electronic component was redesigned and then tested to failure at three different temperatures. Six units were tested at each temperature level. At the 406 K stress level, however, a unit was removed from the test due to a test equipment failure which led to a failure of the component. A warranty time of one year is to be given, with an expected return of 10% of the population. The following table shows the times-to-failure and test temperatures.


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	The operating temperature is ~~356K~~. Using the Arrhenius-Weibull model, determine the following:		The operating temperature is 356 K. Using the Arrhenius-Weibull model, determine the following:

	1) Should the first failure at ~~406K~~ be included in the analysis?		1) Should the first failure at 406 K be included in the analysis?

	2) Determine the warranty time for a 90% reliability.		2) Determine the warranty time for a 90% reliability.
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	1) Since the failure occurred at the very beginning of the test and for an unrelated reason, it can be omitted from the analysis. If it is included it should be treated as a suspension and not as a failure.		1) Since the failure occurred at the very beginning of the test and for an unrelated reason, it can be omitted from the analysis. If it is included it should be treated as a suspension and not as a failure.

	2) Disregard the first failure at ~~406K~~ and analyze the data using the ALTA standard folio. The estimated parameters are:		2) Disregard the first failure at 406 K and analyze the data using the ALTA standard folio. The estimated parameters are:


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	A more accurate way to determine the warranty time would be to use ALTA's Quick Calculation Pad (QCP)~~. In the QCP~~, ~~select to calculate '''Reliable Life''' and enter '''356''' for the stress and '''0.9''' for~~ the ~~required reliability. The~~ reliable life ~~is estimated~~ to be 11,977.792719 hr, as shown next:		A more accurate way to determine the warranty time would be to use ALTA's Quick Calculation Pad (QCP), which estimates the reliable life to be 11,977.792719 hours, as shown next:


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	3) From the use level probability plot, the warranty time for a 90% reliability was estimated to be approximately 12,000 hr. This is above the 1 year (8,760 hr) requirement. However, this is an estimate at the 50% confidence level. In other words, 50% of the time life will be greater than 12,000 hr and 50% of the time life will be less. A known confidence level is therefore crucial before any decisions are made.		3) From the use level probability plot, the warranty time for a 90% reliability was estimated to be approximately 12,000 hours. This is above the 1 year (8,760 hours) requirement. However, this is an estimate at the 50% confidence level. In other words, 50% of the time life will be greater than 12,000 hours and 50% of the time life will be less. A known confidence level is therefore crucial before any decisions are made.

	Plot the confidence bounds on both probability and Arrhenius plots. The following use level probability plot, shows the 90% lower confidence level (LCL). Note that in ALTA, percentile bounds are Type 1 confidence bounds.		Plot the confidence bounds on both probability and Arrhenius plots. The following use level probability plot, shows the 90% lower confidence level (LCL). Note that in ALTA, percentile bounds are Type 1 confidence bounds.
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	To use the QCP to calculate the lower confidence bound~~, click the '''Bounds''' button and select '''Lower-One Sided''' from the drop-down list~~. The result shows a lower bound of 4,436.506367 hr.		You can use the QCP to calculate calculate the lower confidence bound. The result shows a lower bound of 4,436.506367 hours.


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	4) The warranty time for this component is estimated to be 4,436.5 hr at a 90% lower confidence bound. This is much less than the 1 year warranty time required (almost 6 months). Thus the desired warranty is not met. In this case, the following four options are available:		4) The warranty time for this component is estimated to be 4,436.5 hours at a 90% lower confidence bound. This is much less than the 1 year warranty time required (almost 6 months). Thus the desired warranty is not met. In this case, the following four options are available:

	:a) Redesign.		:a) Redesign.
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	:d) Test additional units at stress levels closer to the use level.		:d) Test additional units at stress levels closer to the use level.

	5) Including the unrelated failure of 0.3 hr at 406 K (by treating it as a suspension) in the analysis obtains the following results:		5) Including the unrelated failure of 0.3 hours at 406 K (by treating it as a suspension) in the analysis obtains the following results:


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	6) Repeat the analysis treating the unrelated failure at 500 hr as a suspension. The results are:		6) Repeat the analysis treating the unrelated failure at 500 hours as a suspension. The results are:


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	As you can see, it would be a mistake to neglect the unrelated failure in this case. By neglecting this failure, we would actually underestimate the warranty time. The important observation in this example is that every piece of life information is crucial. In other words, unrelated failures also provide information about the life of the product. An unrelated failure occurring at 500 hr indicates that the product has survived for that period of time under the particular stress level; thus, neglecting it would be a mistake. On the other hand, it would also be a mistake to treat this data point as a failure, since the failure was caused by the faulty test equipment.		As you can see, it would be a mistake to neglect the unrelated failure in this case. By neglecting this failure, we would actually underestimate the warranty time. The important observation in this example is that every piece of life information is crucial. In other words, unrelated failures also provide information about the life of the product. An unrelated failure occurring at 500 hours indicates that the product has survived for that period of time under the particular stress level; thus, neglecting it would be a mistake. On the other hand, it would also be a mistake to treat this data point as a failure, since the failure was caused by the faulty test equipment.

Kate Racaza at 04:49, 15 August 2012

2012-08-15T04:49:08Z

← Older revision		Revision as of 04:49, 15 August 2012
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	An electronic component was redesigned and then tested to failure at three different temperatures. Six units were tested at each temperature level. At the 406K stress level, however, a unit was removed from the test due to a test equipment failure which led to a failure of the component. A warranty time of one year is to be given, with an expected return of 10% of the population. The following table shows the times-to-failure and test temperatures.		An electronic component was redesigned and then tested to failure at three different temperatures. Six units were tested at each temperature level. At the 406K stress level, however, a unit was removed from the test due to a test equipment failure which led to a failure of the component. A warranty time of one year is to be given, with an expected return of 10% of the population. The following table shows the times-to-failure and test temperatures.


	[[Image:11_8ex.gif\|center\|200px\|]]		[[Image:11_8ex.gif\|center\|200px\|]]


	The operating temperature is 356K. Using the Arrhenius-Weibull model, determine the following:		The operating temperature is 356K. Using the Arrhenius-Weibull model, determine the following:
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	6) If the unrelated failure occurred at 500 hr, should it be included in the analysis?		6) If the unrelated failure occurred at 500 hr, should it be included in the analysis?



	'''Solution'''		'''Solution'''
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	2) Disregard the first failure at 406K and analyze the data using the ALTA standard folio. The estimated parameters are:		2) Disregard the first failure at 406K and analyze the data using the ALTA standard folio. The estimated parameters are:


	::<math>\begin{align}		::<math>\begin{align}
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	\end{align}</math>		\end{align}</math>


	The following plot shows the use level probability plot of the analysis. The warranty time for a reliability of 90% (or an unreliability of 10%) can be estimated from this plot, as shown next.		The following plot shows the use level probability plot of the analysis. The warranty time for a reliability of 90% (or an unreliability of 10%) can be estimated from this plot, as shown next.


	[[Image:issue.gif\|center\|600px\| Probability Plot at Use Stress Level.]]		[[Image:issue.gif\|center\|600px\| Probability Plot at Use Stress Level.]]


	This estimate can also be obtained from the Arrhenius plot (Life vs. Stress plot). The 10th percentile (time for a reliability of 90%) is plotted versus stress. This type of plot is useful because it allows you to determine a time for a given reliability for different stress levels.		This estimate can also be obtained from the Arrhenius plot (Life vs. Stress plot). The 10th percentile (time for a reliability of 90%) is plotted versus stress. This type of plot is useful because it allows you to determine a time for a given reliability for different stress levels.


	[[Image:example_1_life_vs_stress.gif\|center\|600px\|10% Unreliability vs Stress plot.]]		[[Image:example_1_life_vs_stress.gif\|center\|600px\|10% Unreliability vs Stress plot.]]


	A more accurate way to determine the warranty time would be to use ALTA's Quick Calculation Pad (QCP). In the QCP, select to calculate '''Reliable Life''' and enter '''356''' for the stress and '''0.9''' for the required reliability. The reliable life is estimated to be 11,977.792719 hr, as shown next:		A more accurate way to determine the warranty time would be to use ALTA's Quick Calculation Pad (QCP). In the QCP, select to calculate '''Reliable Life''' and enter '''356''' for the stress and '''0.9''' for the required reliability. The reliable life is estimated to be 11,977.792719 hr, as shown next:


	[[Image:ex1_qcp.gif\|center\|450px\|]]		[[Image:ex1_qcp.gif\|center\|450px\|]]


	3) From the use level probability plot, the warranty time for a 90% reliability was estimated to be approximately 12,000 hr. This is above the 1 year (8,760 hr) requirement. However, this is an estimate at the 50% confidence level. In other words, 50% of the time life will be greater than 12,000 hr and 50% of the time life will be less. A known confidence level is therefore crucial before any decisions are made.		3) From the use level probability plot, the warranty time for a 90% reliability was estimated to be approximately 12,000 hr. This is above the 1 year (8,760 hr) requirement. However, this is an estimate at the 50% confidence level. In other words, 50% of the time life will be greater than 12,000 hr and 50% of the time life will be less. A known confidence level is therefore crucial before any decisions are made.

	Plot the confidence bounds on both probability and Arrhenius plots. The following use level probability plot, shows the 90% lower confidence level (LCL). Note that in ALTA, percentile bounds are Type 1 confidence bounds.		Plot the confidence bounds on both probability and Arrhenius plots. The following use level probability plot, shows the 90% lower confidence level (LCL). Note that in ALTA, percentile bounds are Type 1 confidence bounds.


	[[Image:example_1_use_prob_plot_with_cb.gif\|center\|600px\|Use Level Probability Plot with the Type I 90% Lower Bound.]]		[[Image:example_1_use_prob_plot_with_cb.gif\|center\|600px\|Use Level Probability Plot with the Type I 90% Lower Bound.]]


	From the plot, we obtain an estimate of 4,437 hr warranty time at a 90% lower confidence level. This means that 90% of the time, life will be greater than this value. In other words, a life of 4,437 hr is a bounding value for the warranty. The Arrhenius plot with the 90% lower confidence level is shown next.		From the plot, we obtain an estimate of 4,437 hr warranty time at a 90% lower confidence level. This means that 90% of the time, life will be greater than this value. In other words, a life of 4,437 hr is a bounding value for the warranty. The Arrhenius plot with the 90% lower confidence level is shown next.


	[[Image:example_1_life_vs_stress_with_cb.gif\|center\|600px\|Life vs Stress plot with the 90% Lower Confidence Level.]]		[[Image:example_1_life_vs_stress_with_cb.gif\|center\|600px\|Life vs Stress plot with the 90% Lower Confidence Level.]]


	To use the QCP to calculate the lower confidence bound, click the '''Bounds''' button and select '''Lower-One Sided''' from the drop-down list. The result shows a lower bound of 4,436.506367 hr.		To use the QCP to calculate the lower confidence bound, click the '''Bounds''' button and select '''Lower-One Sided''' from the drop-down list. The result shows a lower bound of 4,436.506367 hr.


	[[Image:ex1_qcp2.gif\|center\|450px\|]]		[[Image:ex1_qcp2.gif\|center\|450px\|]]


	4) The warranty time for this component is estimated to be 4,436.5 hr at a 90% lower confidence bound. This is much less than the 1 year warranty time required (almost 6 months). Thus the desired warranty is not met. In this case, the following four options are available:		4) The warranty time for this component is estimated to be 4,436.5 hr at a 90% lower confidence bound. This is much less than the 1 year warranty time required (almost 6 months). Thus the desired warranty is not met. In this case, the following four options are available:
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	5) Including the unrelated failure of 0.3 hr at 406 K (by treating it as a suspension) in the analysis obtains the following results:		5) Including the unrelated failure of 0.3 hr at 406 K (by treating it as a suspension) in the analysis obtains the following results:


	::<math>\begin{align}		::<math>\begin{align}

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	\end{align}</math>		\end{align}</math>


	These results are essentially identical to the results obtained when the unrelated failure was excluded. A small difference can be seen only if more significant digits are considered. The warranty time with the 90% lower 1-sided confidence bound is estimated to be:		These results are essentially identical to the results obtained when the unrelated failure was excluded. A small difference can be seen only if more significant digits are considered. The warranty time with the 90% lower 1-sided confidence bound is estimated to be:


	::<math>\begin{align}		::<math>\begin{align}
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	\end{align}</math>		\end{align}</math>


	Again, the difference is negligible. This is due to the very early time at which this unrelated failure occurred.		Again, the difference is negligible. This is due to the very early time at which this unrelated failure occurred.


	6) Repeat the analysis treating the unrelated failure at 500 hr as a suspension. The results are:		6) Repeat the analysis treating the unrelated failure at 500 hr as a suspension. The results are:


	::<math>\begin{align}		::<math>\begin{align}
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	\end{align}</math>		\end{align}</math>


	In this case, the results are very different. The warranty time with the 90% lower 1-sided confidence bound is estimated to be:		In this case, the results are very different. The warranty time with the 90% lower 1-sided confidence bound is estimated to be:


	::<math>\begin{align}		::<math>\begin{align}
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	{{T}_{L}}=\ & 5303.672050\text{ hr}		{{T}_{L}}=\ & 5303.672050\text{ hr}
	\end{align}</math>		\end{align}</math>


	As you can see, it would be a mistake to neglect the unrelated failure in this case. By neglecting this failure, we would actually underestimate the warranty time. The important observation in this example is that every piece of life information is crucial. In other words, unrelated failures also provide information about the life of the product. An unrelated failure occurring at 500 hr indicates that the product has survived for that period of time under the particular stress level; thus, neglecting it would be a mistake. On the other hand, it would also be a mistake to treat this data point as a failure, since the failure was caused by the faulty test equipment.		As you can see, it would be a mistake to neglect the unrelated failure in this case. By neglecting this failure, we would actually underestimate the warranty time. The important observation in this example is that every piece of life information is crucial. In other words, unrelated failures also provide information about the life of the product. An unrelated failure occurring at 500 hr indicates that the product has survived for that period of time under the particular stress level; thus, neglecting it would be a mistake. On the other hand, it would also be a mistake to treat this data point as a failure, since the failure was caused by the faulty test equipment.

Richard House at 07:38, 7 August 2012

2012-08-07T07:38:30Z

Show changes

Richard House at 07:55, 3 August 2012

2012-08-03T07:55:52Z

← Older revision		Revision as of 07:55, 3 August 2012
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	<br>		<br>
	[[Image:issue.gif\|center\|~~450px~~\| Probability Plot at Use Stress Level.]]		[[Image:issue.gif\|center\|600px\| Probability Plot at Use Stress Level.]]

	<br>		<br>
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	<br>		<br>
	[[Image:example_1_life_vs_stress.gif\|center\|~~450px~~\|10% Unreliability vs Stress plot.]]		[[Image:example_1_life_vs_stress.gif\|center\|600px\|10% Unreliability vs Stress plot.]]

	<br>		<br>
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	<br>		<br>
	[[Image:example_1_use_prob_plot_with_cb.gif\|center\|~~450px~~\|Use Level Probability Plot with the Type I 90% Lower Bound.]]		[[Image:example_1_use_prob_plot_with_cb.gif\|center\|600px\|Use Level Probability Plot with the Type I 90% Lower Bound.]]

	<br>		<br>
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	<br>		<br>
	[[Image:example_1_life_vs_stress_with_cb.gif\|center\|~~450px~~\|Life vs Stress plot with the 90% Lower Confidence Level.]]		[[Image:example_1_life_vs_stress_with_cb.gif\|center\|600px\|Life vs Stress plot with the 90% Lower Confidence Level.]]

Kate Racaza at 08:48, 1 August 2012

2012-08-01T08:48:44Z

← Older revision		Revision as of 08:48, 1 August 2012
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	<br>		<br>
	From the plot, we obtain an estimate of 4,437 hr warranty time at a 90% lower confidence level. This means that 90% of the time, life will be greater than this value. In other words, a life of 4,437 hr is a bounding value for the warranty.		From the plot, we obtain an estimate of 4,437 hr warranty time at a 90% lower confidence level. This means that 90% of the time, life will be greater than this value. In other words, a life of 4,437 hr is a bounding value for the warranty. The Arrhenius plot with the 90% lower confidence level is shown next.

	~~<br>~~
	The Arrhenius plot with the 90% lower confidence level is shown next.

	<br>		<br>
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	5) Including the unrelated failure of 0.3 hr at 406 K (by treating it as a suspension ~~at that time~~), the following results ~~are obtained~~:		5) Including the unrelated failure of 0.3 hr at 406 K (by treating it as a suspension) in the analysis obtains the following results:


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	These results are essentially identical to the ~~ones with~~ the unrelated failure excluded. A small difference can be seen only if more significant digits are considered. The warranty time with the 90% lower 1-sided confidence bound is estimated to be:		These results are essentially identical to the results obtained when the unrelated failure was excluded. A small difference can be seen only if more significant digits are considered. The warranty time with the 90% lower 1-sided confidence bound is estimated to be:

Kate Racaza: updated example

2012-08-01T08:38:17Z

updated example

← Older revision		Revision as of 08:38, 1 August 2012
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	{~~\| class="FCK__ShowTableBorders" border="0" cellspacing="0" cellpadding="0" align="center"; style="width:100%;"~~		<noinclude>{{Banner_ALTA_Examples}}</noinclude>
	\|-
	~~\| valign="middle" align="left" bgcolor=EEEDF7\|[[Image: ALTA-Examples-banner.png\|400px\|center]]~~		An electronic component was redesigned and then tested to failure at three different temperatures. Six units were tested at each temperature level. At the 406K stress level, however, a unit was removed from the test due to a test equipment failure which led to a failure of the component. A warranty time of one year is to be given, with an expected return of 10% of the population. The following table shows the times-to-failure and test temperatures.
	\|}
	<br>
	An electronic component was redesigned and ~~was~~ tested to failure at three different temperatures. Six units were tested at each ~~stress~~ level. At the 406K stress level however, a unit was removed from the test due to a test equipment failure which led to a failure of the component. A warranty time of one year is to be given, with an expected return of 10% of the population. The times-to-failure and test temperatures ~~are given next:~~

	<br>		<br>
	<br>		<br>
	[[Image:11_8ex.gif~~\|thumb~~\|center\|~~300px~~\|]]		[[Image:11_8ex.gif\|center\|200px\|]]
	<br>		<br>

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	~~====~~Solution~~====~~		'''Solution'''


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	2) ~~The~~ first failure at 406K ~~was neglected~~ and the data ~~were analyzed~~ using ALTA. The ~~following~~ parameters ~~were obtained~~:		2) Disregard the first failure at 406K and analyze the data using the ALTA standard folio. The estimated parameters are:


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	The use level probability plot ~~(at 356K) can then be obtained~~. The warranty time for a reliability of 90% (or an unreliability of 10%) can be estimated from this plot as shown next.		The following plot shows the use level probability plot of the analysis. The warranty time for a reliability of 90% (or an unreliability of 10%) can be estimated from this plot, as shown next.

	<br>		<br>
	[[Image:issue.gif~~\|thumb~~\|center\|~~300px~~\| ~~The probability plot~~ at ~~use stress level~~.]]		[[Image:issue.gif\|center\|450px\| Probability Plot at Use Stress Level.]]

	<br>		<br>
	This estimate can also be obtained from the Arrhenius plot (a Life vs. Stress plot). The 10th percentile (time for a reliability of 90%) is plotted versus stress. This type of plot is useful because a time for a given reliability ~~can be determined~~ for different stress levels.		This estimate can also be obtained from the Arrhenius plot (Life vs. Stress plot). The 10th percentile (time for a reliability of 90%) is plotted versus stress. This type of plot is useful because it allows you to determine a time for a given reliability for different stress levels.

	<br>		<br>
	[[Image:example_1_life_vs_stress.gif~~\|thumb~~\|center\|~~300px~~\|10% ~~unreliability~~ vs ~~stress~~.]]		[[Image:example_1_life_vs_stress.gif\|center\|450px\|10% Unreliability vs Stress plot.]]

	<br>		<br>
	A more accurate way to determine the warranty time would be to use ALTA's Quick Calculation Pad (QCP). ~~By selecting~~ the Reliable Life ~~option from in the QCP~~ and ~~entering~~ 356 for the ~~temperature~~ and 0.9 for the required reliability~~, a~~ reliable life of 11,977.792719 hr ~~can be determined~~, as shown next:		A more accurate way to determine the warranty time would be to use ALTA's Quick Calculation Pad (QCP). In the QCP, select to calculate '''Reliable Life''' and enter '''356''' for the stress and '''0.9''' for the required reliability. The reliable life is estimated to be 11,977.792719 hr, as shown next:

	<br>		<br>
	[[Image:ex1_qcp.gif~~\|thumb~~\|center\|~~300px~~\|]]		[[Image:ex1_qcp.gif\|center\|450px\|]]

	<br>		<br>
	3) ~~The~~ warranty time for a 90% reliability was estimated to be approximately 12,000 hr. This is above the 1 year (8,760 hr) requirement. However, this is an estimate at the 50% confidence level. In other words, 50% of the time life will be greater than 12,000 hr and 50% of the time life will be less. A known confidence level is therefore crucial before any decisions are made. ~~Using ALTA,~~ confidence bounds ~~can be plotted~~ on both probability and Arrhenius plots. ~~In the~~ following use level probability plot, the 90% lower confidence level (LCL) ~~is plotted~~. Note that percentile bounds are Type 1 confidence bounds ~~in ALTA~~.		3) From the use level probability plot, the warranty time for a 90% reliability was estimated to be approximately 12,000 hr. This is above the 1 year (8,760 hr) requirement. However, this is an estimate at the 50% confidence level. In other words, 50% of the time life will be greater than 12,000 hr and 50% of the time life will be less. A known confidence level is therefore crucial before any decisions are made.

			Plot the confidence bounds on both probability and Arrhenius plots. The following use level probability plot, shows the 90% lower confidence level (LCL). Note that in ALTA, percentile bounds are Type 1 confidence bounds.

	<br>		<br>
	[[Image:example_1_use_prob_plot_with_cb.gif~~\|thumb~~\|center\|~~300px~~\|~~The use level probability plot~~ with the Type I 90% ~~lower bound~~.]]		[[Image:example_1_use_prob_plot_with_cb.gif\|center\|450px\|Use Level Probability Plot with the Type I 90% Lower Bound.]]

	<br>		<br>
	~~An estimated~~ 4,437 hr warranty time at a 90% lower confidence level ~~was obtained from the use level probability plot~~. This means that 90% of the time, life will be greater than this value. In other words, a life of 4,437 hr is a bounding value for the warranty.		From the plot, we obtain an estimate of 4,437 hr warranty time at a 90% lower confidence level. This means that 90% of the time, life will be greater than this value. In other words, a life of 4,437 hr is a bounding value for the warranty.

	<br>		<br>
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	<br>		<br>
	[[Image:example_1_life_vs_stress_with_cb.gif~~\|thumb~~\|center\|~~300px~~\|Life vs Stress plot with the 90% ~~lower confidence level~~.]]		[[Image:example_1_life_vs_stress_with_cb.gif\|center\|450px\|Life vs Stress plot with the 90% Lower Confidence Level.]]


	~~Using~~ the QCP ~~and specifying a 90%~~ lower confidence ~~level~~, a ~~warranty time~~ of ~~4436~~.5 hr ~~is estimated, as shown next~~.		To use the QCP to calculate the lower confidence bound, click the '''Bounds''' button and select '''Lower-One Sided''' from the drop-down list. The result shows a lower bound of 4,436.506367 hr.
	<br>		<br>
	<br>		<br>
	[[Image:ex1_qcp2.gif~~\|thumb~~\|center\|~~300px~~\|]]		[[Image:ex1_qcp2.gif\|center\|450px\|]]

	<br>		<br>
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	These results are essentially identical to the ones with the unrelated failure excluded. A small difference can be seen only if more significant digits are considered. The warranty time with the 90% lower 1-sided confidence bound ~~was~~ estimated to be:		These results are essentially identical to the ones with the unrelated failure excluded. A small difference can be seen only if more significant digits are considered. The warranty time with the 90% lower 1-sided confidence bound is estimated to be:


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	6) ~~The~~ analysis ~~is repeated~~ treating the unrelated failure at 500 hr as a suspension~~, with the following~~ results:		6) Repeat the analysis treating the unrelated failure at 500 hr as a suspension. The results are:


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	It can ~~be seen that in this case~~, it would be a mistake to neglect the unrelated failure. By neglecting this failure, we would actually underestimate the warranty time. The important observation in this example is that every piece of life information is crucial. In other words, unrelated failures also provide information about the life of the product. An unrelated failure occurring at 500 hr indicates that the product has survived for that period of time under the particular stress level, ~~thus~~ neglecting it would be a mistake. On the other hand it would also be a mistake to treat this data point as a failure, since the failure was caused by a test equipment ~~failure~~.		As you can see, it would be a mistake to neglect the unrelated failure in this case. By neglecting this failure, we would actually underestimate the warranty time. The important observation in this example is that every piece of life information is crucial. In other words, unrelated failures also provide information about the life of the product. An unrelated failure occurring at 500 hr indicates that the product has survived for that period of time under the particular stress level; thus, neglecting it would be a mistake. On the other hand, it would also be a mistake to treat this data point as a failure, since the failure was caused by the faulty test equipment.

Nikki Helms at 21:09, 21 March 2012

2012-03-21T21:09:05Z

← Older revision		Revision as of 21:09, 21 March 2012
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	\| valign="middle" align="left" bgcolor=EEEDF7\|[[Image: ALTA-Examples-banner.png\|400px\|center]]		\| valign="middle" align="left" bgcolor=EEEDF7\|[[Image: ALTA-Examples-banner.png\|400px\|center]]
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	An electronic component was redesigned and was tested to failure at three different temperatures. Six units were tested at each stress level. At the 406K stress level however, a unit was removed from the test due to a test equipment failure which led to a failure of the component. A warranty time of one year is to be given, with an expected return of 10% of the population. The times-to-failure and test temperatures are given next:		An electronic component was redesigned and was tested to failure at three different temperatures. Six units were tested at each stress level. At the 406K stress level however, a unit was removed from the test due to a test equipment failure which led to a failure of the component. A warranty time of one year is to be given, with an expected return of 10% of the population. The times-to-failure and test temperatures are given next:

Nikki Helms at 20:15, 21 March 2012

2012-03-21T20:15:06Z

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	An electronic component was redesigned and was tested to failure at three different temperatures. Six units were tested at each stress level. At the 406K stress level however, a unit was removed from the test due to a test equipment failure which led to a failure of the component. A warranty time of one year is to be given, with an expected return of 10% of the population. The times-to-failure and test temperatures are given next:		An electronic component was redesigned and was tested to failure at three different temperatures. Six units were tested at each stress level. At the 406K stress level however, a unit was removed from the test due to a test equipment failure which led to a failure of the component. A warranty time of one year is to be given, with an expected return of 10% of the population. The times-to-failure and test temperatures are given next:

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2012-03-21T20:14:45Z

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An electronic component was redesigned and was tested to failure at three different temperatures. Six units were tested at each stress level. At the 406K stress level however, a unit was removed from the test due to a test equipment failure which led to a failure of the component. A warranty time of one year is to be given, with an expected return of 10% of the population. The times-to-failure and test temperatures are given next:

 
 
[[Image:11_8ex.gif|thumb|center|300px|]]
 

The operating temperature is 356K. Using the Arrhenius-Weibull model, determine the following:

1) Should the first failure at 406K be included in the analysis?

2) Determine the warranty time for a 90% reliability.

3) Determine the 90% lower confidence limit on the warranty time.

4) Is the warranty requirement met? If not, what steps should be taken?

5) Repeat the analysis with the unrelated failure included. Is there any difference?

6) If the unrelated failure occurred at 500 hr, should it be included in the analysis?

====Solution====

1) Since the failure occurred at the very beginning of the test and for an unrelated reason, it can be omitted from the analysis. If it is included it should be treated as a suspension and not as a failure.

2) The first failure at 406K was neglected and the data were analyzed using ALTA. The following parameters were obtained:

::<math>\begin{align}

\beta =\ & 2.965820 \\

B=\ & 10679.567542 \\

C=\ & 2.396615\cdot {{10}^{-9}}

\end{align}</math>

The use level probability plot (at 356K) can then be obtained. The warranty time for a reliability of 90% (or an unreliability of 10%) can be estimated from this plot as shown next.

 
[[Image:issue.gif|thumb|center|300px| The probability plot at use stress level.]]

 
This estimate can also be obtained from the Arrhenius plot (a Life vs. Stress plot). The 10th percentile (time for a reliability of 90%) is plotted versus stress. This type of plot is useful because a time for a given reliability can be determined for different stress levels.

 
[[Image:example_1_life_vs_stress.gif|thumb|center|300px|10% unreliability vs stress.]]

 
A more accurate way to determine the warranty time would be to use ALTA's Quick Calculation Pad (QCP). By selecting the Reliable Life option from in the QCP and entering 356 for the temperature and 0.9 for the required reliability, a reliable life of 11,977.792719 hr can be determined, as shown next:

 
[[Image:ex1_qcp.gif|thumb|center|300px|]]

 
3) The warranty time for a 90% reliability was estimated to be approximately 12,000 hr. This is above the 1 year (8,760 hr) requirement. However, this is an estimate at the 50% confidence level. In other words, 50% of the time life will be greater than 12,000 hr and 50% of the time life will be less. A known confidence level is therefore crucial before any decisions are made. Using ALTA, confidence bounds can be plotted on both probability and Arrhenius plots. In the following use level probability plot, the 90% lower confidence level (LCL) is plotted. Note that percentile bounds are Type 1 confidence bounds in ALTA.

 
[[Image:example_1_use_prob_plot_with_cb.gif|thumb|center|300px|The use level probability plot with the Type I 90% lower bound.]]

 
An estimated 4,437 hr warranty time at a 90% lower confidence level was obtained from the use level probability plot. This means that 90% of the time, life will be greater than this value. In other words, a life of 4,437 hr is a bounding value for the warranty.

 
The Arrhenius plot with the 90% lower confidence level is shown next.

 
[[Image:example_1_life_vs_stress_with_cb.gif|thumb|center|300px|Life vs Stress plot with the 90% lower confidence level.]]

Using the QCP and specifying a 90% lower confidence level, a warranty time of 4436.5 hr is estimated, as shown next.
 
 
[[Image:ex1_qcp2.gif|thumb|center|300px|]]

 
4) The warranty time for this component is estimated to be 4,436.5 hr at a 90% lower confidence bound. This is much less than the 1 year warranty time required (almost 6 months). Thus the desired warranty is not met. In this case, the following four options are available:

:a) Redesign.

:b) Reduce the confidence level.

:c) Change the warranty policy.

:d) Test additional units at stress levels closer to the use level.

5) Including the unrelated failure of 0.3 hr at 406 K (by treating it as a suspension at that time), the following results are obtained:

::<math>\begin{align}

\beta =\ & 2.965804 \\

B=\ & 10679.566625 \\

C=\ & 2.396619\cdot {{10}^{-9}}

\end{align}</math>

These results are essentially identical to the ones with the unrelated failure excluded. A small difference can be seen only if more significant digits are considered. The warranty time with the 90% lower 1-sided confidence bound was estimated to be:

::<math>\begin{align}

T=\ & 11977.729145\text{ hr} \\

{{T}_{L}}=\ & 4436.462084\text{ hr}

\end{align}</math>

Again, the difference is negligible. This is due to the very early time at which this unrelated failure occurred.

6) The analysis is repeated treating the unrelated failure at 500 hr as a suspension, with the following results:

::<math>\begin{align}

\beta =\ & 3.022714 \\

B=\ & 10959.523204 \\

C=\ & 1.23808\cdot {{10}^{-9}}

\end{align}</math>

In this case, the results are very different. The warranty time with the 90% lower 1-sided confidence bound is estimated to be:

::<math>\begin{align}
T=\ & 13780.208409\text{ hr} \\
{{T}_{L}}=\ & 5303.672050\text{ hr}
\end{align}</math>

It can be seen that in this case, it would be a mistake to neglect the unrelated failure. By neglecting this failure, we would actually underestimate the warranty time. The important observation in this example is that every piece of life information is crucial. In other words, unrelated failures also provide information about the life of the product. An unrelated failure occurring at 500 hr indicates that the product has survived for that period of time under the particular stress level, thus neglecting it would be a mistake. On the other hand it would also be a mistake to treat this data point as a failure, since the failure was caused by a test equipment failure.