RGA Overview - Revision history

Kate Racaza: /* Why Reliability Growth? */

2015-12-11T17:21:35Z

Why Reliability Growth?

← Older revision		Revision as of 17:21, 11 December 2015
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	In summary, the initial MTBF is the value actually achieved by the basic reliability tasks. The growth potential is the MTBF that can be attained if the test is conducted long enough with the current management strategy. See the figure below.		In summary, the initial MTBF is the value actually achieved by the basic reliability tasks. The growth potential is the MTBF that can be attained if the test is conducted long enough with the current management strategy. See the figure below.

	[[Image:rga2.1.png\|center\|450px]		[[Image:rga2.1.png\|center\|450px]]

	==Elements of a Reliability Growth Program==		==Elements of a Reliability Growth Program==

David J. Groebel at 23:18, 2 June 2014

2014-06-02T23:18:54Z

Chris Kahn: /* Why Reliability Growth? */

2014-05-15T20:03:42Z

Why Reliability Growth?

← Older revision		Revision as of 20:03, 15 May 2014
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	\|104\|\|Failure Reporting, Analysis and Corrective Action System (FRACAS)\|\|204\|\|Failure Modes, Effects and Criticality Analysis (FMECA)\|\|304\|\|Production Reliability Acceptance Test (PRAT) Program		\|104\|\|Failure Reporting, Analysis and Corrective Action System (FRACAS)\|\|204\|\|Failure Modes, Effects and Criticality Analysis (FMECA)\|\|304\|\|Production Reliability Acceptance Test (PRAT) Program
	\|-		\|-
	\|105\|\|Failure Review Board(FRB)\|\|205\|\|Sneak Circuit Analysis (SCA) \|\| \|\|		\|105\|\|Failure Review Board (FRB)\|\|205\|\|Sneak Circuit Analysis (SCA) \|\| \|\|
	\|-		\|-
	\| \|\| \|\|206\|\|Electronic Parts/Circuit Tolerance Analysis \|\| \|\|		\| \|\| \|\|206\|\|Electronic Parts/Circuit Tolerance Analysis \|\| \|\|

Chris Kahn: /* Why Reliability Growth? */

2014-05-15T20:03:27Z

Why Reliability Growth?

← Older revision		Revision as of 20:03, 15 May 2014
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	\|101 \|\|Reliability Program Plan\|\|201\|\|Reliability modeling\|\|301\|\|Environmental Stress Screening (ESS)		\|101 \|\|Reliability Program Plan\|\|201\|\|Reliability modeling\|\|301\|\|Environmental Stress Screening (ESS)
	\|-		\|-
	\|102\|\|Monitor/Control of Subcontractors and Suppliers\|\|202\|\|Reliability Allocations\|\|302\|\|Reliability Development/Growth Test(RDGT) Program		\|102\|\|Monitor/Control of Subcontractors and Suppliers\|\|202\|\|Reliability Allocations\|\|302\|\|Reliability Development/Growth Test (RDGT) Program
	\|-		\|-
	\|103\|\|Program Reviews\|\|203\|\|Reliability Predictions\|\|303\|\|Reliability Qualification Test (RGT) Program		\|103\|\|Program Reviews\|\|203\|\|Reliability Predictions\|\|303\|\|Reliability Qualification Test (RGT) Program
	\|-		\|-
	\|104\|\|Failure Reporting, Analysis and Corrective Action System (FRACAS)\|\|204\|\|Failure Modes, Effects and Criticality Analysis(FMECA)\|\|304\|\|Production Reliability Acceptance Test (PRAT) Program		\|104\|\|Failure Reporting, Analysis and Corrective Action System (FRACAS)\|\|204\|\|Failure Modes, Effects and Criticality Analysis (FMECA)\|\|304\|\|Production Reliability Acceptance Test (PRAT) Program
	\|-		\|-
	\|105\|\|Failure Review Board(FRB)\|\|205\|\|Sneak Circuit Analysis(SCA) \|\| \|\|		\|105\|\|Failure Review Board(FRB)\|\|205\|\|Sneak Circuit Analysis (SCA) \|\| \|\|
	\|-		\|-
	\| \|\| \|\|206\|\|Electronic Parts/Circuit Tolerance Analysis \|\| \|\|		\| \|\| \|\|206\|\|Electronic Parts/Circuit Tolerance Analysis \|\| \|\|

Chris Kahn: /* Introduction */

2014-01-22T23:33:20Z

Introduction

← Older revision		Revision as of 23:33, 22 January 2014
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	*The time-to-failure of a product after a redesign is dependent on how good or bad the redesign action was.		*The time-to-failure of a product after a redesign is dependent on how good or bad the redesign action was.
	*The time-to-failure of the product after the redesign may follow a distribution that is different than the times-to-failure distribution before the redesign.		*The time-to-failure of the product after the redesign may follow a distribution that is different than the times-to-failure distribution before the redesign.
	There is a dependency between the failures that occur on a repairable system. Events that occur first will affect future failures. Given this dependency, applying a Weibull distribution, for example, is not valid since life data analysis assumes that the events are IID. Reliability growth and repairable systems analysis provide methodologies for analyzing data/events that are associated with systems ~~which~~ are part of a stochastic process.		There is a dependency between the failures that occur on a repairable system. Events that occur first will affect future failures. Given this dependency, applying a Weibull distribution, for example, is not valid since life data analysis assumes that the events are IID. Reliability growth and repairable systems analysis provide methodologies for analyzing data/events that are associated with systems that are part of a stochastic process.

	==What is Reliability Growth?==		==What is Reliability Growth?==

Chris Kahn: /* Introduction */

2014-01-22T23:30:43Z

Introduction

← Older revision		Revision as of 23:30, 22 January 2014
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	{{template:RGA BOOK\|1\|Overview}}		{{template:RGA BOOK\|1\|Overview}}
	==Introduction==		==Introduction==
	When conducting distribution analysis (and in life data analysis), the events that are observed are assumed to be statistically independent and identically distributed (IID). ~~In other words, a~~ sequence or collection of random variables is IID if:		When conducting distribution analysis (and life data analysis), the events that are observed are assumed to be statistically independent and identically distributed (IID). A sequence or collection of random variables is IID if:
	*Each has the same probability distribution as any of the others.		*Each has the same probability distribution as any of the others.
	*All are mutually independent, which implies that knowing whether or not one occurred makes it neither more nor less probable that the other occurred.		*All are mutually independent, which implies that knowing whether or not one occurred makes it neither more nor less probable that the other occurred.

Chris Kahn: /* Introduction */

2014-01-22T23:28:03Z

Introduction

← Older revision		Revision as of 23:28, 22 January 2014
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	When conducting distribution analysis (and in life data analysis), the events that are observed are assumed to be statistically independent and identically distributed (IID). In other words, a sequence or collection of random variables is IID if:		When conducting distribution analysis (and in life data analysis), the events that are observed are assumed to be statistically independent and identically distributed (IID). In other words, a sequence or collection of random variables is IID if:
	*Each has the same probability distribution as any of the others.		*Each has the same probability distribution as any of the others.
	*All are mutually independent which implies that knowing whether or not one occurred makes it neither more nor less probable that the other occurred.		*All are mutually independent, which implies that knowing whether or not one occurred makes it neither more nor less probable that the other occurred.
	In life data analysis, the unit/component placed on test is assumed to be as-good-as-new. However, this is not the case when dealing with repairable systems ~~which~~ have more than one life. They are able to have multiple lives as they fail, are repaired and put back into service. The age just after the repair is basically the same as it was just before the failure. This is called as-bad-as-old. For reliability growth and repairable systems analysis, the events that are observed are part of a stochastic process. A stochastic process is defined as a sequence of inter-dependent random events. Therefore, the events are dependent and are not identically distributed.		In life data analysis, the unit/component placed on test is assumed to be ''as-good-as-new''. However, this is not the case when dealing with repairable systems that have more than one life. They are able to have multiple lives as they fail, are repaired and then put back into service. The age just after the repair is basically the same as it was just before the failure. This is called ''as-bad-as-old''. For reliability growth and repairable systems analysis, the events that are observed are part of a ''stochastic process''. A stochastic process is defined as a sequence of inter-dependent random events. Therefore, the events are dependent and are not identically distributed.
	*The time-to-failure of a product after a redesign is dependent on how good or bad the redesign action was.		*The time-to-failure of a product after a redesign is dependent on how good or bad the redesign action was.
	*The time-to-failure of the product after the redesign may follow a distribution that is different than the times-to-failure distribution before the redesign.		*The time-to-failure of the product after the redesign may follow a distribution that is different than the times-to-failure distribution before the redesign.
	There is a dependency between the failures that occur on a repairable system. Events that occur first will affect future failures. Given this dependency, applying a Weibull distribution, for example, is not valid since life data analysis assumes that the events are IID. Reliability growth and repairable systems analysis provide methodologies for analyzing data/events that are associated with systems which are part of a stochastic process.		There is a dependency between the failures that occur on a repairable system. Events that occur first will affect future failures. Given this dependency, applying a Weibull distribution, for example, is not valid since life data analysis assumes that the events are IID. Reliability growth and repairable systems analysis provide methodologies for analyzing data/events that are associated with systems which are part of a stochastic process.

	==What is Reliability Growth?==		==What is Reliability Growth?==
	In general, the first prototypes produced during the development of a new complex system will contain design, manufacturing and/or engineering deficiencies. Because of these deficiencies, the initial reliability of the prototypes may be below the system's reliability goal or requirement. In order to identify and correct these deficiencies, the prototypes are often subjected to a rigorous testing program. During testing, problem areas are identified and appropriate corrective actions (or redesigns) are taken. Reliability growth is defined as the positive improvement in a reliability metric (or parameter) of a product (component, subsystem or system) over a period of time due to changes in the product's design and/or the manufacturing process. A reliability growth program is a well-structured process of finding reliability problems by testing, incorporating corrective actions and monitoring the increase of the product's reliability throughout the test phases. The term "growth" is used since it is assumed that the reliability of the product will increase over time as design changes and fixes are implemented. However, in practice, no growth or negative growth may occur.		In general, the first prototypes produced during the development of a new complex system will contain design, manufacturing and/or engineering deficiencies. Because of these deficiencies, the initial reliability of the prototypes may be below the system's reliability goal or requirement. In order to identify and correct these deficiencies, the prototypes are often subjected to a rigorous testing program. During testing, problem areas are identified and appropriate corrective actions (or redesigns) are taken. Reliability growth is defined as the positive improvement in a reliability metric (or parameter) of a product (component, subsystem or system) over a period of time due to changes in the product's design and/or the manufacturing process. A reliability growth program is a well-structured process of finding reliability problems by testing, incorporating corrective actions and monitoring the increase of the product's reliability throughout the test phases. The term "growth" is used since it is assumed that the reliability of the product will increase over time as design changes and fixes are implemented. However, in practice, no growth or negative growth may occur.

Chris Kahn: /* Time Terminated vs. Failure Terminated */

2014-01-22T23:23:37Z

Time Terminated vs. Failure Terminated

← Older revision		Revision as of 23:23, 22 January 2014
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	===Time Terminated vs. Failure Terminated===		===Time Terminated vs. Failure Terminated===
	When a reliability growth test is conducted, it must be determined how much operation time the system will accumulate during the test. ~~In other words~~, at which ~~point will~~ the test reach its end. There are two possible options under which a reliability growth test may be terminated (or truncated); time terminated or failure terminated.		When a reliability growth test is conducted, it must be determined how much operation time the system will accumulate during the test (i.e., the point at which the test will reach its end). There are two possible options under which a reliability growth test may be terminated (or truncated): time terminated or failure terminated.

	*A time terminated test ~~represents to a test that was~~ stopped after a certain amount of test time.		*A time terminated test is stopped after a certain amount of test time.
	*A failure terminated test ~~represents a test that was~~ stopped at a time which corresponds to a failure.		*A failure terminated test is stopped at a time which corresponds to a failure (e.g., the time of the tenth failure).

	It is determined a priori whether a test is time terminated or failure terminated. The test data does not determine this.		It is determined a priori whether a test is time terminated or failure terminated. The test data does not determine this.

Chris Kahn: /* Instantaneous vs. Cumulative */

2014-01-22T23:16:06Z

Instantaneous vs. Cumulative

← Older revision		Revision as of 23:16, 22 January 2014
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	===Instantaneous vs. Cumulative===		===Instantaneous vs. Cumulative===
	In RGA, metrics such as MTBF and failure intensity can be calculated as instantaneous or cumulative. Cumulative MTBF is the average time-between-failure from the beginning of the test (i.e. t=0) up to time t. The instantaneous MTBF is the average time-between-failure in a given interval, dt. Consider a grouped data set, where 4 failures are found in the interval 0-100 hours and 2 failures are found in the second interval 100-180 hours. The cumulative MTBF at 180 hours of test time is equal to 180/6 = 30 hours. However, the instantaneous MTBF is equal to 80/2 = 40 hours. Another analogy for this relates to the ~~miler~~ per gallon (mpg) that your car ~~is exhibiting~~. In many cars, there are readouts that indicates the current mpg as you are driving. This is the instantaneous value. The average mpg on the current tank of gas is the cumulative value.		In RGA, metrics such as MTBF and failure intensity can be calculated as instantaneous or cumulative. ''Cumulative MTBF'' is the average time-between-failure from the beginning of the test (i.e., t = 0) up to time t. The ''instantaneous MTBF'' is the average time-between-failure in a given interval, dt. Consider a grouped data set, where 4 failures are found in the interval 0-100 hours and 2 failures are found in the second interval 100-180 hours. The cumulative MTBF at 180 hours of test time is equal to 180/6 = 30 hours. However, the instantaneous MTBF is equal to 80/2 = 40 hours. Another analogy for this relates to the miles per gallon (mpg) that your car gets. In many cars, there are readouts that indicates the current mpg as you are driving. This is the instantaneous value. The average mpg on the current tank of gas is the cumulative value.

	Relative to the [[Crow-AMSAA (NHPP)]] model, when ~~Beta~~ is equal to one, the system's MTBF is not changing over time; therefore, the cumulative MTBF equals the instantaneous MTBF. If ~~Beta~~ is greater than one, then the system's MTBF is decreasing over time and the cumulative MTBF is greater than the instantaneous MTBF. If ~~Beta~~ is less than one, then the system's MTBF is increasing over time and the cumulative MTBF is less than the instantaneous MTBF.		Relative to the [[Crow-AMSAA (NHPP)]] model, when beta is equal to one, the system's MTBF is not changing over time; therefore, the cumulative MTBF equals the instantaneous MTBF. If beta is greater than one, then the system's MTBF is decreasing over time and the cumulative MTBF is greater than the instantaneous MTBF. If beta is less than one, then the system's MTBF is increasing over time and the cumulative MTBF is less than the instantaneous MTBF.

	Now the concern is, how do you know whether you should estimate the instantaneous or cumulative value of a metric (e.g., MTBF or failure intensity)? In general, system requirements are usually represented as instantaneous values. After all, you want to know where the system is now terms of its MTBF. The cumulative MTBF can be used to observe trends in the data.		Now the concern is, how do you know whether you should estimate the instantaneous or cumulative value of a metric (e.g., MTBF or failure intensity)? In general, system requirements are usually represented as instantaneous values. After all, you want to know where the system is ''now'' in terms of its MTBF. The cumulative MTBF can be used to observe trends in the data.

	===Time Terminated vs. Failure Terminated===		===Time Terminated vs. Failure Terminated===

Chris Kahn: /* Failure Rate vs. Failure Intensity */

2014-01-22T23:09:11Z

Failure Rate vs. Failure Intensity

← Older revision		Revision as of 23:09, 22 January 2014
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	::<math>u(t)=\lambda \beta t^{\beta -1}\,\!</math>		::<math>u(t)=\lambda \beta t^{\beta -1}\,\!</math>

	This is the power law model. It can be viewed as an extension of the Weibull distribution. The Weibull distribution governs the first system failure and the power law model governs each succeeding system failure. Additional information on the power law model is available at [[Repairable Systems Analysis]].		This is the power law model. It can be viewed as an extension of the Weibull distribution. The Weibull distribution governs the first system failure and the power law model governs each succeeding system failure. Additional information on the power law model is available in [[Repairable Systems Analysis]].

	===Instantaneous vs. Cumulative===		===Instantaneous vs. Cumulative===

← Older revision		Revision as of 23:18, 2 June 2014
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	In summary, the initial MTBF is the value actually achieved by the basic reliability tasks. The growth potential is the MTBF that can be attained if the test is conducted long enough with the current management strategy. See the figure below.		In summary, the initial MTBF is the value actually achieved by the basic reliability tasks. The growth potential is the MTBF that can be attained if the test is conducted long enough with the current management strategy. See the figure below.

	[[Image:rga2.1.png\|center\|~~400px\|Growth potential and management strategy.\|link=]~~]		[[Image:rga2.1.png\|center\|450px]

	==Elements of a Reliability Growth Program==		==Elements of a Reliability Growth Program==
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	*Whether the stated reliability requirements will be achieved		*Whether the stated reliability requirements will be achieved

	*The associated time for meeting such requirements		*The associated time for meeting such requirements

	*The associated costs of meeting such requirements		*The associated costs of meeting such requirements

	*The correlation of reliability changes with reliability activities		*The correlation of reliability changes with reliability activities

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	*Establishing warranties		*Establishing warranties

	*Planning for maintenance resources and logistic activities		*Planning for maintenance resources and logistic activities

	*Life-cycle-cost analysis		*Life-cycle-cost analysis

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	Failure rate and failure intensity are very similar concepts. The term ''failure intensity'' typically refers to a process such as a reliability growth program. The system age when a system is first put into service is time 0. Under the non-homogeneous Poisson process (NHPP), the first failure is governed by a distribution <math>F(x) \,\!</math> with failure rate of <math>r(x) \,\!</math>. Each succeeding failure is governed by the intensity function <math>u(t) \,\!</math> of the process. Let <math>t \,\!</math> be the age of the system and let <math>\Delta t \,\!</math> be a very small value. The probability that a system of age <math>t \,\!</math> fails between <math>t \,\!</math> and <math>t+\Delta t \,\!</math> is given by the intensity function <math>u(t)\Delta t \,\!</math>. Notice that this probability is not conditioned on not having any system failures up to time <math>t \,\!</math>, as is the case for a failure rate. The failure intensity <math>u(t) \,\!</math> for the NHPP has the same functional form as the failure rate governing the first system failure. Therefore, <math>u(t)=r(t) \,\!</math>, where <math>r(t) \,\!</math> is the failure rate for the distribution function of the first system failure. If the first system failure follows the Weibull distribution, the failure rate is:		Failure rate and failure intensity are very similar concepts. The term ''failure intensity'' typically refers to a process such as a reliability growth program. The system age when a system is first put into service is time 0. Under the non-homogeneous Poisson process (NHPP), the first failure is governed by a distribution <math>F(x) \,\!</math> with failure rate of <math>r(x) \,\!</math>. Each succeeding failure is governed by the intensity function <math>u(t) \,\!</math> of the process. Let <math>t \,\!</math> be the age of the system and let <math>\Delta t \,\!</math> be a very small value. The probability that a system of age <math>t \,\!</math> fails between <math>t \,\!</math> and <math>t+\Delta t \,\!</math> is given by the intensity function <math>u(t)\Delta t \,\!</math>. Notice that this probability is not conditioned on not having any system failures up to time <math>t \,\!</math>, as is the case for a failure rate. The failure intensity <math>u(t) \,\!</math> for the NHPP has the same functional form as the failure rate governing the first system failure. Therefore, <math>u(t)=r(t) \,\!</math>, where <math>r(t) \,\!</math> is the failure rate for the distribution function of the first system failure. If the first system failure follows the Weibull distribution, the failure rate is:

	::<math>r(x)=\lambda \beta x^{\beta -1}\,\!</math>		:<math>r(x)=\lambda \beta x^{\beta -1}\,\!</math>

	Under minimal repair, the system intensity function is:		Under minimal repair, the system intensity function is:

	::<math>u(t)=\lambda \beta t^{\beta -1}\,\!</math>		:<math>u(t)=\lambda \beta t^{\beta -1}\,\!</math>

	This is the power law model. It can be viewed as an extension of the Weibull distribution. The Weibull distribution governs the first system failure and the power law model governs each succeeding system failure. Additional information on the power law model is available in [[Repairable Systems Analysis]].		This is the power law model. It can be viewed as an extension of the Weibull distribution. The Weibull distribution governs the first system failure and the power law model governs each succeeding system failure. Additional information on the power law model is available in [[Repairable Systems Analysis]].