Introduction to Accelerated Life Testing - Revision history

Lisa Hacker at 18:48, 15 September 2023

2023-09-15T18:48:08Z

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	For products which do not operate continuously under normal conditions, if the test units are operated continuously, failures are encountered earlier than if the units were tested at normal usage. For example, a microwave oven operates for small periods of time every day. One can accelerate a test on microwave ovens by operating them more frequently until failure. The same could be said of washers. If we assume an average washer use of 6 hours a week, one could conceivably reduce the testing time 28-fold by testing these washers continuously.		For products which do not operate continuously under normal conditions, if the test units are operated continuously, failures are encountered earlier than if the units were tested at normal usage. For example, a microwave oven operates for small periods of time every day. One can accelerate a test on microwave ovens by operating them more frequently until failure. The same could be said of washers. If we assume an average washer use of 6 hours a week, one could conceivably reduce the testing time 28-fold by testing these washers continuously.

	Data obtained through usage acceleration can be analyzed with the same methods used to analyze regular times-to-failure data. These typical life data analysis techniques are thoroughly described in ~~[[Life Data Analysis Reference Book\|~~ReliaSoft's ~~Life Data Analysis Reference]]~~.		Data obtained through usage acceleration can be analyzed with the same methods used to analyze regular times-to-failure data. These typical life data analysis techniques are thoroughly described in ReliaSoft's life data analysis reference.

	The limitation of usage rate acceleration arises when products, such as computer servers and peripherals, maintain a very high or even continuous usage. In such cases, usage acceleration, even though desirable, is not a feasible alternative. In these cases the practitioner must stimulate the product to fail, usually through the application of stress(es). This method of accelerated life testing is called overstress acceleration and is described next.		The limitation of usage rate acceleration arises when products, such as computer servers and peripherals, maintain a very high or even continuous usage. In such cases, usage acceleration, even though desirable, is not a feasible alternative. In these cases the practitioner must stimulate the product to fail, usually through the application of stress(es). This method of accelerated life testing is called overstress acceleration and is described next.

Nicolette Young: /* Looking at a Single Constant Stress Accelerated Life Test */

2015-12-16T22:05:33Z

Looking at a Single Constant Stress Accelerated Life Test

← Older revision		Revision as of 22:05, 16 December 2015
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	To understand the process involved with extrapolating from overstress test data to use level conditions, let's look closely at a simple accelerated life test. For simplicity we will assume that the product was tested under a single stress at a single constant stress level. We will further assume that times-to-failure data have been obtained at this stress level. The times-to-failure at this stress level can then be easily analyzed using an underlying life distribution. A ''pdf'' of the times-to-failure of the product can be obtained at that single stress level using traditional approaches. This ''pdf'', the overstress ''pdf'', can likewise be used to make predictions and estimates of life measures of interest at that particular stress level. The objective in an accelerated life test, however, is not to obtain predictions and estimates at the particular elevated stress level at which the units were tested, but to obtain these measures at another stress level, the use stress level.		To understand the process involved with extrapolating from overstress test data to use level conditions, let's look closely at a simple accelerated life test. For simplicity we will assume that the product was tested under a single stress at a single constant stress level. We will further assume that times-to-failure data have been obtained at this stress level. The times-to-failure at this stress level can then be easily analyzed using an underlying life distribution. A ''pdf'' of the times-to-failure of the product can be obtained at that single stress level using traditional approaches. This ''pdf'', the overstress ''pdf'', can likewise be used to make predictions and estimates of life measures of interest at that particular stress level. The objective in an accelerated life test, however, is not to obtain predictions and estimates at the particular elevated stress level at which the units were tested, but to obtain these measures at another stress level, the use stress level.

	[[Image:Use stress vs high stress.png\|center\|~~550px~~\|link=]]		[[Image:Use stress vs high stress.png\|center\|600px\|link=]]

	To accomplish this objective, we must devise a method to traverse the path from the overstress ''pdf'' to extrapolate a use level ''pdf''. The next figure illustrates a typical behavior of the ''pdf'' at the high stress (or overstress level) and the ''pdf'' at the use stress level.		To accomplish this objective, we must devise a method to traverse the path from the overstress ''pdf'' to extrapolate a use level ''pdf''. The next figure illustrates a typical behavior of the ''pdf'' at the high stress (or overstress level) and the ''pdf'' at the use stress level.

Nicolette Young: /* Looking at a Single Constant Stress Accelerated Life Test */

2015-12-16T22:05:04Z

Looking at a Single Constant Stress Accelerated Life Test

← Older revision		Revision as of 22:05, 16 December 2015
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	To understand the process involved with extrapolating from overstress test data to use level conditions, let's look closely at a simple accelerated life test. For simplicity we will assume that the product was tested under a single stress at a single constant stress level. We will further assume that times-to-failure data have been obtained at this stress level. The times-to-failure at this stress level can then be easily analyzed using an underlying life distribution. A ''pdf'' of the times-to-failure of the product can be obtained at that single stress level using traditional approaches. This ''pdf'', the overstress ''pdf'', can likewise be used to make predictions and estimates of life measures of interest at that particular stress level. The objective in an accelerated life test, however, is not to obtain predictions and estimates at the particular elevated stress level at which the units were tested, but to obtain these measures at another stress level, the use stress level.		To understand the process involved with extrapolating from overstress test data to use level conditions, let's look closely at a simple accelerated life test. For simplicity we will assume that the product was tested under a single stress at a single constant stress level. We will further assume that times-to-failure data have been obtained at this stress level. The times-to-failure at this stress level can then be easily analyzed using an underlying life distribution. A ''pdf'' of the times-to-failure of the product can be obtained at that single stress level using traditional approaches. This ''pdf'', the overstress ''pdf'', can likewise be used to make predictions and estimates of life measures of interest at that particular stress level. The objective in an accelerated life test, however, is not to obtain predictions and estimates at the particular elevated stress level at which the units were tested, but to obtain these measures at another stress level, the use stress level.

	[[Image:Use stress vs high stress.png\|center\|~~650px~~\|link=]]		[[Image:Use stress vs high stress.png\|center\|550px\|link=]]

	To accomplish this objective, we must devise a method to traverse the path from the overstress ''pdf'' to extrapolate a use level ''pdf''. The next figure illustrates a typical behavior of the ''pdf'' at the high stress (or overstress level) and the ''pdf'' at the use stress level.		To accomplish this objective, we must devise a method to traverse the path from the overstress ''pdf'' to extrapolate a use level ''pdf''. The next figure illustrates a typical behavior of the ''pdf'' at the high stress (or overstress level) and the ''pdf'' at the use stress level.

Nicolette Young: /* Stress is Time-Dependent */

2015-12-16T21:59:29Z

Stress is Time-Dependent

← Older revision		Revision as of 21:59, 16 December 2015
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	The step-stress model, as discussed in [[Appendix_E:_References\|[31]]], and the related ramp-stress model are typical cases of time-dependent stress tests. In these cases, the stress load remains constant for a period of time and then is stepped/ramped into a different stress level, where it remains constant for another time interval until it is stepped/ramped again. There are numerous variations of this concept.		The step-stress model, as discussed in [[Appendix_E:_References\|[31]]], and the related ramp-stress model are typical cases of time-dependent stress tests. In these cases, the stress load remains constant for a period of time and then is stepped/ramped into a different stress level, where it remains constant for another time interval until it is stepped/ramped again. There are numerous variations of this concept.

	[[Image:Step stress model.png\|center\|~~250px~~\|Graphical representation of the step-stress model.\|link=]]		[[Image:Step stress model.png\|center\|300px\|Graphical representation of the step-stress model.\|link=]]

	[[Image:Ramp stress model.png\|center\|~~250px~~\|Graphical representation of the ramp-stress model.\|link=]]		[[Image:Ramp stress model.png\|center\|300px\|Graphical representation of the ramp-stress model.\|link=]]

	The same idea can be extended to include a stress as a continuous function of time.		The same idea can be extended to include a stress as a continuous function of time.

	[[Image:Constantly increasing stress.png\|center\|~~250px~~\|Graphical representation of a constantly increasing (or progressive) stress model.\|link=]]		[[Image:Constantly increasing stress.png\|center\|300px\|Graphical representation of a constantly increasing (or progressive) stress model.\|link=]]


	[[Image:Time dependent stress.png\|center\|~~250px~~\|Graphical representation of a completely time-dependent stress model.\|link=]]		[[Image:Time dependent stress.png\|center\|300px\|Graphical representation of a completely time-dependent stress model.\|link=]]

	== Summary of Accelerated Life Testing Analysis ==		== Summary of Accelerated Life Testing Analysis ==

	In summary, accelerated life testing analysis can be conducted on data collected from carefully designed quantitative accelerated life tests. Well-designed accelerated life tests will apply stress(es) at levels that exceed the stress level the product will encounter under normal use conditions in order to accelerate the failure modes that would occur under use conditions. An underlying life distribution (like the exponential, Weibull and lognormal lifetime distributions) can be chosen to fit the life data collected at each stress level to derive overstress ''pdf''s for each stress level. A life-stress relationship (Arrhenius, Eyring, etc.) can then be chosen to quantify the path from the overstress ''pdf''s in order to extrapolate a use level ''pdf''. From the extrapolated use level ''pdf'', a variety of functions can be derived, including reliability, failure rate, mean life, warranty time etc.		In summary, accelerated life testing analysis can be conducted on data collected from carefully designed quantitative accelerated life tests. Well-designed accelerated life tests will apply stress(es) at levels that exceed the stress level the product will encounter under normal use conditions in order to accelerate the failure modes that would occur under use conditions. An underlying life distribution (like the exponential, Weibull and lognormal lifetime distributions) can be chosen to fit the life data collected at each stress level to derive overstress ''pdf''s for each stress level. A life-stress relationship (Arrhenius, Eyring, etc.) can then be chosen to quantify the path from the overstress ''pdf''s in order to extrapolate a use level ''pdf''. From the extrapolated use level ''pdf'', a variety of functions can be derived, including reliability, failure rate, mean life, warranty time etc.

Nicolette Young: /* Stress is Time-Independent (Constant Stress) */

2015-12-16T21:59:09Z

Stress is Time-Independent (Constant Stress)

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	When the stress is time-independent, the stress applied to a sample of units does not vary. In other words, if temperature is the thermal stress, each unit is tested under the same accelerated temperature, (e.g., 100° C), and data are recorded. This is the type of stress load that has been discussed so far.		When the stress is time-independent, the stress applied to a sample of units does not vary. In other words, if temperature is the thermal stress, each unit is tested under the same accelerated temperature, (e.g., 100° C), and data are recorded. This is the type of stress load that has been discussed so far.

	[[Image:Time-vs-time.png\|center\|~~250px~~\|Graphical representation of time vs. stress in a time-independent stress loading.\|link=]]		[[Image:Time-vs-time.png\|center\|300px\|Graphical representation of time vs. stress in a time-independent stress loading.\|link=]]

	This type of stress loading has many advantages over time-dependent stress loadings. Specifically:		This type of stress loading has many advantages over time-dependent stress loadings. Specifically:

Nicolette Young: /* Looking at a Single Constant Stress Accelerated Life Test */

2015-12-16T21:57:14Z

Looking at a Single Constant Stress Accelerated Life Test

← Older revision		Revision as of 21:57, 16 December 2015
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	To accomplish this objective, we must devise a method to traverse the path from the overstress ''pdf'' to extrapolate a use level ''pdf''. The next figure illustrates a typical behavior of the ''pdf'' at the high stress (or overstress level) and the ''pdf'' at the use stress level.		To accomplish this objective, we must devise a method to traverse the path from the overstress ''pdf'' to extrapolate a use level ''pdf''. The next figure illustrates a typical behavior of the ''pdf'' at the high stress (or overstress level) and the ''pdf'' at the use stress level.

	[[Image:Use v high stress.png\|center\|~~250px~~\|pdf at different stress levels\|link=]]		[[Image:Use v high stress.png\|center\|450px\|pdf at different stress levels\|link=]]

	To further simplify the scenario, let's assume that the ''pdf'' for the product at any stress level can be described by a single point. The next figure illustrates such a simplification where we need to determine a way to project (or map) this single point from the high stress to the use stress.		To further simplify the scenario, let's assume that the ''pdf'' for the product at any stress level can be described by a single point. The next figure illustrates such a simplification where we need to determine a way to project (or map) this single point from the high stress to the use stress.

Nicolette Young: /* Looking at a Single Constant Stress Accelerated Life Test */

2015-12-16T21:56:50Z

Looking at a Single Constant Stress Accelerated Life Test

← Older revision		Revision as of 21:56, 16 December 2015
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	To accomplish this objective, we must devise a method to traverse the path from the overstress ''pdf'' to extrapolate a use level ''pdf''. The next figure illustrates a typical behavior of the ''pdf'' at the high stress (or overstress level) and the ''pdf'' at the use stress level.		To accomplish this objective, we must devise a method to traverse the path from the overstress ''pdf'' to extrapolate a use level ''pdf''. The next figure illustrates a typical behavior of the ''pdf'' at the high stress (or overstress level) and the ''pdf'' at the use stress level.

	[[Image:Use v high stress.png\|center\|~~350px~~\|pdf at different stress levels\|link=]]		[[Image:Use v high stress.png\|center\|250px\|pdf at different stress levels\|link=]]

	To further simplify the scenario, let's assume that the ''pdf'' for the product at any stress level can be described by a single point. The next figure illustrates such a simplification where we need to determine a way to project (or map) this single point from the high stress to the use stress.		To further simplify the scenario, let's assume that the ''pdf'' for the product at any stress level can be described by a single point. The next figure illustrates such a simplification where we need to determine a way to project (or map) this single point from the high stress to the use stress.

Nicolette Young: /* Looking at a Single Constant Stress Accelerated Life Test */

2015-12-16T21:55:50Z

Looking at a Single Constant Stress Accelerated Life Test

← Older revision		Revision as of 21:55, 16 December 2015
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	To understand the process involved with extrapolating from overstress test data to use level conditions, let's look closely at a simple accelerated life test. For simplicity we will assume that the product was tested under a single stress at a single constant stress level. We will further assume that times-to-failure data have been obtained at this stress level. The times-to-failure at this stress level can then be easily analyzed using an underlying life distribution. A ''pdf'' of the times-to-failure of the product can be obtained at that single stress level using traditional approaches. This ''pdf'', the overstress ''pdf'', can likewise be used to make predictions and estimates of life measures of interest at that particular stress level. The objective in an accelerated life test, however, is not to obtain predictions and estimates at the particular elevated stress level at which the units were tested, but to obtain these measures at another stress level, the use stress level.		To understand the process involved with extrapolating from overstress test data to use level conditions, let's look closely at a simple accelerated life test. For simplicity we will assume that the product was tested under a single stress at a single constant stress level. We will further assume that times-to-failure data have been obtained at this stress level. The times-to-failure at this stress level can then be easily analyzed using an underlying life distribution. A ''pdf'' of the times-to-failure of the product can be obtained at that single stress level using traditional approaches. This ''pdf'', the overstress ''pdf'', can likewise be used to make predictions and estimates of life measures of interest at that particular stress level. The objective in an accelerated life test, however, is not to obtain predictions and estimates at the particular elevated stress level at which the units were tested, but to obtain these measures at another stress level, the use stress level.

	[[Image:Use stress vs high stress.png\|center\|~~550px~~\|link=]]		[[Image:Use stress vs high stress.png\|center\|650px\|link=]]

	To accomplish this objective, we must devise a method to traverse the path from the overstress ''pdf'' to extrapolate a use level ''pdf''. The next figure illustrates a typical behavior of the ''pdf'' at the high stress (or overstress level) and the ''pdf'' at the use stress level.		To accomplish this objective, we must devise a method to traverse the path from the overstress ''pdf'' to extrapolate a use level ''pdf''. The next figure illustrates a typical behavior of the ''pdf'' at the high stress (or overstress level) and the ''pdf'' at the use stress level.

Nicolette Young: /* Looking at a Single Constant Stress Accelerated Life Test */

2015-12-16T21:43:52Z

Looking at a Single Constant Stress Accelerated Life Test

← Older revision		Revision as of 21:43, 16 December 2015
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	Obviously, there are infinite ways to map a particular point from the high stress level to the use stress level. We will assume that there is some model (or a function) that maps our point from the high stress level to the use stress level. This model or function can be described mathematically and can be as simple as the equation for a line. The next figure demonstrates some simple models or relationships.		Obviously, there are infinite ways to map a particular point from the high stress level to the use stress level. We will assume that there is some model (or a function) that maps our point from the high stress level to the use stress level. This model or function can be described mathematically and can be as simple as the equation for a line. The next figure demonstrates some simple models or relationships.

	[[Image:Linear Exponential Relationship.png\|center\|~~600px~~\|link=]]		[[Image:Linear Exponential Relationship.png\|center\|800px\|link=]]

	Even when a model is assumed (e.g., linear, exponential, etc.), the mapping possibilities are still infinite since they depend on the parameters of the chosen model or relationship. For example, a simple linear model would generate different mappings for each slope value because we can draw an infinite number of lines through a point. If we tested specimens of our product at two different stress levels, we could begin to fit the model to the data. Clearly, the more points we have, the better off we are in correctly mapping this particular point or fitting the model to our data.		Even when a model is assumed (e.g., linear, exponential, etc.), the mapping possibilities are still infinite since they depend on the parameters of the chosen model or relationship. For example, a simple linear model would generate different mappings for each slope value because we can draw an infinite number of lines through a point. If we tested specimens of our product at two different stress levels, we could begin to fit the model to the data. Clearly, the more points we have, the better off we are in correctly mapping this particular point or fitting the model to our data.

Nicolette Young: /* Life Distributions and Life-Stress Models */

2015-12-16T21:43:23Z

Life Distributions and Life-Stress Models

← Older revision		Revision as of 21:43, 16 December 2015
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	The analysis of accelerated life test data consists of (1) an underlying life distribution that describes the product at different stress levels and (2) a life-stress relationship (or model) that quantifies the manner in which the life distribution changes across different stress levels. These elements of analysis are graphically shown next:		The analysis of accelerated life test data consists of (1) an underlying life distribution that describes the product at different stress levels and (2) a life-stress relationship (or model) that quantifies the manner in which the life distribution changes across different stress levels. These elements of analysis are graphically shown next:

	[[Image:Life Distribution.png\|center\|~~600px~~\|link=]]		[[Image:Life Distribution.png\|center\|800px\|link=]]

	The combination of both an underlying life distribution and a life-stress model can be best seen in the next figure where a ''pdf'' is plotted against both time and stress.		The combination of both an underlying life distribution and a life-stress model can be best seen in the next figure where a ''pdf'' is plotted against both time and stress.