Introduction to Life Data Analysis - Revision history

Nicolette Young: /* Reliability Engineering */

2015-12-16T17:09:17Z

Reliability Engineering

← Older revision		Revision as of 17:09, 16 December 2015
Line 50:		Line 50:
	Since the beginning of history, humanity has attempted to predict the future. Watching the flight of birds, the movement of the leaves on the trees and other methods were some of the practices used. Fortunately, today's engineers do not have to depend on Pythia or a crystal ball in order to predict the future of their products. Through the use of life data analysis, reliability engineers use product life data to determine the probability and capability of parts, components, and systems to perform their required functions for desired periods of time without failure, in specified environments.		Since the beginning of history, humanity has attempted to predict the future. Watching the flight of birds, the movement of the leaves on the trees and other methods were some of the practices used. Fortunately, today's engineers do not have to depend on Pythia or a crystal ball in order to predict the future of their products. Through the use of life data analysis, reliability engineers use product life data to determine the probability and capability of parts, components, and systems to perform their required functions for desired periods of time without failure, in specified environments.
	<br>		<br>
	[[Image:reliabilityengineeringfinal.png\|center\|~~500px~~\|link=]]		[[Image:reliabilityengineeringfinal.png\|center\|600px\|link=]]
	<br>		<br>
	<br>		<br>

Nicolette Young: /* Estimation */

2015-12-16T17:08:59Z

Estimation

← Older revision		Revision as of 17:08, 16 December 2015
Line 61:		Line 61:
	<br>		<br>
	<br>		<br>
	[[Image:estimation.png\|center\|~~400px~~\|]]		[[Image:estimation.png\|center\|300px\|]]
	<br>		<br>

Nicolette Young: /* The Reliability Bathtub Curve */

2015-12-16T17:08:36Z

The Reliability Bathtub Curve

← Older revision		Revision as of 17:08, 16 December 2015
Line 103:		Line 103:
	Most products (as well as humans) exhibit failure characteristics as shown in the bathtub curve of the following figure. (Do note, however, that this figure is somewhat idealized.)		Most products (as well as humans) exhibit failure characteristics as shown in the bathtub curve of the following figure. (Do note, however, that this figure is somewhat idealized.)

	[[Image:bathtub.png\|center\|~~500px~~]]		[[Image:bathtub.png\|center\|550px]]

	This curve is plotted with the product life on the x-axis and with the failure rate on the y-axis. The life can be in minutes, hours, years, cycles, actuations or any other quantifiable unit of time or use. The failure rate is given as failures among surviving units per time unit. As can be seen from this plot, many products will begin their lives with a higher failure rate (which can be due to manufacturing defects, poor workmanship, poor quality control of incoming parts, etc.) and exhibit a decreasing failure rate. The failure rate then usually stabilizes to an approximately constant rate in the useful life region, where the failures observed are chance failures. As the products experience more use and wear, the failure rate begins to rise as the population begins to experience failures related to wear-out. In the case of human mortality, the mortality rate (failure rate), is higher during the first year or so of life, then drops to a low constant level during our teens and early adult life and then rises as we progress in years.		This curve is plotted with the product life on the x-axis and with the failure rate on the y-axis. The life can be in minutes, hours, years, cycles, actuations or any other quantifiable unit of time or use. The failure rate is given as failures among surviving units per time unit. As can be seen from this plot, many products will begin their lives with a higher failure rate (which can be due to manufacturing defects, poor workmanship, poor quality control of incoming parts, etc.) and exhibit a decreasing failure rate. The failure rate then usually stabilizes to an approximately constant rate in the useful life region, where the failures observed are chance failures. As the products experience more use and wear, the failure rate begins to rise as the population begins to experience failures related to wear-out. In the case of human mortality, the mortality rate (failure rate), is higher during the first year or so of life, then drops to a low constant level during our teens and early adult life and then rises as we progress in years.

Nicolette Young: /* Minimizing the Manufacturer's Cost */

2015-12-16T17:08:21Z

Minimizing the Manufacturer's Cost

← Older revision		Revision as of 17:08, 16 December 2015
Line 113:		Line 113:
	The following shows the product reliability on the x-axis and the producer's cost on the y-axis.		The following shows the product reliability on the x-axis and the producer's cost on the y-axis.

	[[Image:costvreliability.png\|center\|~~400px~~]]		[[Image:costvreliability.png\|center\|500px]]

	If the producer increases the reliability of his product, he will increase the cost of the design and/or production of the product. However, a low production and design cost does not imply a low overall product cost. The overall product cost should not be calculated as merely the cost of the product when it leaves the shipping dock, but as the total cost of the product through its lifetime. This includes warranty and replacement costs for defective products, costs incurred by loss of customers due to defective products, loss of subsequent sales, etc. By increasing product reliability, one may increase the initial product costs, but decrease the support costs. An optimum minimal total product cost can be determined and implemented by calculating the optimum reliability for such a product. The figure depicts such a scenario. The total product cost is the sum of the production and design costs as well as the other post-shipment costs. It can be seen that at an optimum reliability level, the total product cost is at a minimum. The "optimum reliability level" is the one that coincides with the minimum total cost over the entire lifetime of the product.		If the producer increases the reliability of his product, he will increase the cost of the design and/or production of the product. However, a low production and design cost does not imply a low overall product cost. The overall product cost should not be calculated as merely the cost of the product when it leaves the shipping dock, but as the total cost of the product through its lifetime. This includes warranty and replacement costs for defective products, costs incurred by loss of customers due to defective products, loss of subsequent sales, etc. By increasing product reliability, one may increase the initial product costs, but decrease the support costs. An optimum minimal total product cost can be determined and implemented by calculating the optimum reliability for such a product. The figure depicts such a scenario. The total product cost is the sum of the production and design costs as well as the other post-shipment costs. It can be seen that at an optimum reliability level, the total product cost is at a minimum. The "optimum reliability level" is the one that coincides with the minimum total cost over the entire lifetime of the product.

Nicolette Young: /* Disciplines Covered by Reliability Engineering */

2015-12-16T17:08:06Z

Disciplines Covered by Reliability Engineering

← Older revision		Revision as of 17:08, 16 December 2015
Line 88:		Line 88:


	[[Image:disciplines.png\|~~400px~~\|center]]		[[Image:disciplines.png\|250px\|center]]

Nicolette Young: /* Disciplines Covered by Reliability Engineering */

2015-12-16T17:07:46Z

Disciplines Covered by Reliability Engineering

← Older revision		Revision as of 17:07, 16 December 2015
Line 88:		Line 88:


	[[Image:disciplines.png\|~~125px~~\|center]]		[[Image:disciplines.png\|400px\|center]]

Nicolette Young: /* Reliability Engineering */

2015-12-16T17:07:25Z

Reliability Engineering

← Older revision		Revision as of 17:07, 16 December 2015
Line 50:		Line 50:
	Since the beginning of history, humanity has attempted to predict the future. Watching the flight of birds, the movement of the leaves on the trees and other methods were some of the practices used. Fortunately, today's engineers do not have to depend on Pythia or a crystal ball in order to predict the future of their products. Through the use of life data analysis, reliability engineers use product life data to determine the probability and capability of parts, components, and systems to perform their required functions for desired periods of time without failure, in specified environments.		Since the beginning of history, humanity has attempted to predict the future. Watching the flight of birds, the movement of the leaves on the trees and other methods were some of the practices used. Fortunately, today's engineers do not have to depend on Pythia or a crystal ball in order to predict the future of their products. Through the use of life data analysis, reliability engineers use product life data to determine the probability and capability of parts, components, and systems to perform their required functions for desired periods of time without failure, in specified environments.
	<br>		<br>
	[[Image:reliabilityengineeringfinal.png\|center\|~~400px~~\|link=]]		[[Image:reliabilityengineeringfinal.png\|center\|500px\|link=]]
	<br>		<br>
	<br>		<br>
Line 61:		Line 61:
	<br>		<br>
	<br>		<br>
	[[Image:estimation.png\|center\|~~500px~~\|]]		[[Image:estimation.png\|center\|400px\|]]
	<br>		<br>

Nicolette Young: /* Reliability Engineering */

2015-12-16T17:07:01Z

Reliability Engineering

← Older revision		Revision as of 17:07, 16 December 2015
Line 61:		Line 61:
	<br>		<br>
	<br>		<br>
	[[Image:estimation.png\|center\|~~400px~~\|]]		[[Image:estimation.png\|center\|500px\|]]
	<br>		<br>

Line 103:		Line 103:
	Most products (as well as humans) exhibit failure characteristics as shown in the bathtub curve of the following figure. (Do note, however, that this figure is somewhat idealized.)		Most products (as well as humans) exhibit failure characteristics as shown in the bathtub curve of the following figure. (Do note, however, that this figure is somewhat idealized.)

	[[Image:bathtub.png\|center\|~~400px~~]]		[[Image:bathtub.png\|center\|500px]]

	This curve is plotted with the product life on the x-axis and with the failure rate on the y-axis. The life can be in minutes, hours, years, cycles, actuations or any other quantifiable unit of time or use. The failure rate is given as failures among surviving units per time unit. As can be seen from this plot, many products will begin their lives with a higher failure rate (which can be due to manufacturing defects, poor workmanship, poor quality control of incoming parts, etc.) and exhibit a decreasing failure rate. The failure rate then usually stabilizes to an approximately constant rate in the useful life region, where the failures observed are chance failures. As the products experience more use and wear, the failure rate begins to rise as the population begins to experience failures related to wear-out. In the case of human mortality, the mortality rate (failure rate), is higher during the first year or so of life, then drops to a low constant level during our teens and early adult life and then rises as we progress in years.		This curve is plotted with the product life on the x-axis and with the failure rate on the y-axis. The life can be in minutes, hours, years, cycles, actuations or any other quantifiable unit of time or use. The failure rate is given as failures among surviving units per time unit. As can be seen from this plot, many products will begin their lives with a higher failure rate (which can be due to manufacturing defects, poor workmanship, poor quality control of incoming parts, etc.) and exhibit a decreasing failure rate. The failure rate then usually stabilizes to an approximately constant rate in the useful life region, where the failures observed are chance failures. As the products experience more use and wear, the failure rate begins to rise as the population begins to experience failures related to wear-out. In the case of human mortality, the mortality rate (failure rate), is higher during the first year or so of life, then drops to a low constant level during our teens and early adult life and then rises as we progress in years.

Nicolette Young: /* Reliability Engineering */

2015-12-16T17:06:30Z

Reliability Engineering

← Older revision		Revision as of 17:06, 16 December 2015
Line 50:		Line 50:
	Since the beginning of history, humanity has attempted to predict the future. Watching the flight of birds, the movement of the leaves on the trees and other methods were some of the practices used. Fortunately, today's engineers do not have to depend on Pythia or a crystal ball in order to predict the future of their products. Through the use of life data analysis, reliability engineers use product life data to determine the probability and capability of parts, components, and systems to perform their required functions for desired periods of time without failure, in specified environments.		Since the beginning of history, humanity has attempted to predict the future. Watching the flight of birds, the movement of the leaves on the trees and other methods were some of the practices used. Fortunately, today's engineers do not have to depend on Pythia or a crystal ball in order to predict the future of their products. Through the use of life data analysis, reliability engineers use product life data to determine the probability and capability of parts, components, and systems to perform their required functions for desired periods of time without failure, in specified environments.
	<br>		<br>
	[[Image:reliabilityengineeringfinal.png\|center\|~~300px~~\|link=]]		[[Image:reliabilityengineeringfinal.png\|center\|400px\|link=]]
	<br>		<br>
	<br>		<br>
Line 61:		Line 61:
	<br>		<br>
	<br>		<br>
	[[Image:estimation.png\|center\|~~200px~~\|]]		[[Image:estimation.png\|center\|400px\|]]
	<br>		<br>

Line 73:		Line 73:
	Reliability engineering assessment is based on the results of testing from in-house (or contracted) labs and data pertaining to the performance results of the product in the field. The data produced by these sources are utilized to accurately measure and improve the reliability of the products being produced. This is particularly important as market concerns drive a constant push for cost reduction. However, one must be able to keep a perspective on the big picture instead of merely looking for the quick fix. It is often the temptation to cut corners and save initial costs by using cheaper parts or cutting testing programs. Unfortunately, cheaper parts are usually less reliable and inadequate testing programs can allow products with undiscovered flaws to get out into the field. A quick savings in the short term by the use of cheaper components or small test sample sizes will usually result in higher long-term costs in the form of warranty costs or loss of customer confidence. The proper balance must be struck between reliability, customer satisfaction, time to market, sales and features. The figure below illustrates this concept. The polygon on the left represents a properly balanced project. The polygon on the right represents a project in which reliability and customer satisfaction have been sacrificed for the sake of sales and time to market.		Reliability engineering assessment is based on the results of testing from in-house (or contracted) labs and data pertaining to the performance results of the product in the field. The data produced by these sources are utilized to accurately measure and improve the reliability of the products being produced. This is particularly important as market concerns drive a constant push for cost reduction. However, one must be able to keep a perspective on the big picture instead of merely looking for the quick fix. It is often the temptation to cut corners and save initial costs by using cheaper parts or cutting testing programs. Unfortunately, cheaper parts are usually less reliable and inadequate testing programs can allow products with undiscovered flaws to get out into the field. A quick savings in the short term by the use of cheaper components or small test sample sizes will usually result in higher long-term costs in the form of warranty costs or loss of customer confidence. The proper balance must be struck between reliability, customer satisfaction, time to market, sales and features. The figure below illustrates this concept. The polygon on the left represents a properly balanced project. The polygon on the right represents a project in which reliability and customer satisfaction have been sacrificed for the sake of sales and time to market.

	[[Image:balanced_unbalanced.png\|center\|~~275px~~\|Graphical Representation of balanced and unbalanced projects.]]		[[Image:balanced_unbalanced.png\|center\|400px\|Graphical Representation of balanced and unbalanced projects.]]


Line 103:		Line 103:
	Most products (as well as humans) exhibit failure characteristics as shown in the bathtub curve of the following figure. (Do note, however, that this figure is somewhat idealized.)		Most products (as well as humans) exhibit failure characteristics as shown in the bathtub curve of the following figure. (Do note, however, that this figure is somewhat idealized.)

	[[Image:bathtub.png\|center\|~~375px~~]]		[[Image:bathtub.png\|center\|400px]]

	This curve is plotted with the product life on the x-axis and with the failure rate on the y-axis. The life can be in minutes, hours, years, cycles, actuations or any other quantifiable unit of time or use. The failure rate is given as failures among surviving units per time unit. As can be seen from this plot, many products will begin their lives with a higher failure rate (which can be due to manufacturing defects, poor workmanship, poor quality control of incoming parts, etc.) and exhibit a decreasing failure rate. The failure rate then usually stabilizes to an approximately constant rate in the useful life region, where the failures observed are chance failures. As the products experience more use and wear, the failure rate begins to rise as the population begins to experience failures related to wear-out. In the case of human mortality, the mortality rate (failure rate), is higher during the first year or so of life, then drops to a low constant level during our teens and early adult life and then rises as we progress in years.		This curve is plotted with the product life on the x-axis and with the failure rate on the y-axis. The life can be in minutes, hours, years, cycles, actuations or any other quantifiable unit of time or use. The failure rate is given as failures among surviving units per time unit. As can be seen from this plot, many products will begin their lives with a higher failure rate (which can be due to manufacturing defects, poor workmanship, poor quality control of incoming parts, etc.) and exhibit a decreasing failure rate. The failure rate then usually stabilizes to an approximately constant rate in the useful life region, where the failures observed are chance failures. As the products experience more use and wear, the failure rate begins to rise as the population begins to experience failures related to wear-out. In the case of human mortality, the mortality rate (failure rate), is higher during the first year or so of life, then drops to a low constant level during our teens and early adult life and then rises as we progress in years.
Line 113:		Line 113:
	The following shows the product reliability on the x-axis and the producer's cost on the y-axis.		The following shows the product reliability on the x-axis and the producer's cost on the y-axis.

	[[Image:costvreliability.png\|center\|~~350px~~]]		[[Image:costvreliability.png\|center\|400px]]

	If the producer increases the reliability of his product, he will increase the cost of the design and/or production of the product. However, a low production and design cost does not imply a low overall product cost. The overall product cost should not be calculated as merely the cost of the product when it leaves the shipping dock, but as the total cost of the product through its lifetime. This includes warranty and replacement costs for defective products, costs incurred by loss of customers due to defective products, loss of subsequent sales, etc. By increasing product reliability, one may increase the initial product costs, but decrease the support costs. An optimum minimal total product cost can be determined and implemented by calculating the optimum reliability for such a product. The figure depicts such a scenario. The total product cost is the sum of the production and design costs as well as the other post-shipment costs. It can be seen that at an optimum reliability level, the total product cost is at a minimum. The "optimum reliability level" is the one that coincides with the minimum total cost over the entire lifetime of the product.		If the producer increases the reliability of his product, he will increase the cost of the design and/or production of the product. However, a low production and design cost does not imply a low overall product cost. The overall product cost should not be calculated as merely the cost of the product when it leaves the shipping dock, but as the total cost of the product through its lifetime. This includes warranty and replacement costs for defective products, costs incurred by loss of customers due to defective products, loss of subsequent sales, etc. By increasing product reliability, one may increase the initial product costs, but decrease the support costs. An optimum minimal total product cost can be determined and implemented by calculating the optimum reliability for such a product. The figure depicts such a scenario. The total product cost is the sum of the production and design costs as well as the other post-shipment costs. It can be seen that at an optimum reliability level, the total product cost is at a minimum. The "optimum reliability level" is the one that coincides with the minimum total cost over the entire lifetime of the product.

Nicolette Young: /* Parameter Estimation */

2015-12-16T17:05:49Z

Parameter Estimation

← Older revision		Revision as of 17:05, 16 December 2015
Line 21:		Line 21:
	In order to fit a statistical model to a life data set, the analyst estimates the parameters of the life distribution that will make the function most closely fit the data. The parameters control the scale, shape and location of the ''pdf'' function. For example, in the 3-parameter Weibull model (shown above), the scale parameter, <math>\eta\,\!</math>, defines where the bulk of the distribution lies. The shape parameter, <math>\beta\,\!</math>, defines the shape of the distribution and the location parameter, <math>\gamma\,\!</math>, defines the location of the distribution in time.		In order to fit a statistical model to a life data set, the analyst estimates the parameters of the life distribution that will make the function most closely fit the data. The parameters control the scale, shape and location of the ''pdf'' function. For example, in the 3-parameter Weibull model (shown above), the scale parameter, <math>\eta\,\!</math>, defines where the bulk of the distribution lies. The shape parameter, <math>\beta\,\!</math>, defines the shape of the distribution and the location parameter, <math>\gamma\,\!</math>, defines the location of the distribution in time.

	[[Image:effectsofn.png\|center\|~~300px~~\|link= ]]		[[Image:effectsofn.png\|center\|400px\|link= ]]

	Several methods have been devised to estimate the parameters that will fit a lifetime distribution to a particular data set. Some available parameter estimation methods include probability plotting, rank regression on x (RRX), rank regression on y (RRY) and maximum likelihood estimation (MLE). The appropriate analysis method will vary depending on the data set and, in some cases, on the life distribution selected.		Several methods have been devised to estimate the parameters that will fit a lifetime distribution to a particular data set. Some available parameter estimation methods include probability plotting, rank regression on x (RRX), rank regression on y (RRY) and maximum likelihood estimation (MLE). The appropriate analysis method will vary depending on the data set and, in some cases, on the life distribution selected.