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Design for ReliabilityBASED ON CHAPTER 12, BLANCHARD, B.S. & FABRYCKY, W.J. (2011) SYSTEMS ENGINEERING AND ANALYSIS, PEARSON.

IntroductionOne of the most significant objectives in fulfilling the requirements for system operational feasibility is achieved through design for reliability.Reliability is important and needs to be considered at at all levels, as evidenced by the Challenger disaster and its aftermath:https://www.youtube.com/watch?v=j4JOjcDFtBEhttps://www.youtube.com/watch?v=8qAi_9quzUY

Definitions

Reliability is the probability that a system/entity will perform in a satisfactory manner for a given time period when used under specified operating conditions.Probability: The number of times that one can expect an event to occur in a total number of trials.Satisfactory Performance: Performance that meets the system operational requirements.Specified Operating Conditions: These are the conditions under which a system or product is expected to function.

Measures of ReliabilityA widely used measure of reliability is the failure rate, often defined as

Note that this (unlike our definition of reliability) is NOT a probabilityFailure Rate: Example 110 components were tested for 600 hours. Component 1 failed after 75 hrs, component 2 failed after 125 hours, component 3 failed after 130 hours, component 4 failed after 325 hours, and component 5 failed after 525 hours. There were 5 five failures, over a total operating time of 1180 + 5*600 = 4180 hours. So, λ=5/4180=0.001196

Failure Rate: Example 2

In this example, the operating cycle for system is 169 hrs. Six failures occur. So, the failure rate, λ=6/142=0.04225Reliability DeterminationKnowing the failure rate of a component is useful.However, what is more useful in system design is the reliability of a component, that is the likelihood that it will fail within a given time period. Furthermore, we would like to also determine the reliability of combinations of components.

To determine the likelihood (probability) that a component will fail within a given time period requires knowledge of how the time to failure is distributed over time (the probability distribution function (pdf) and not just the failure rate.Given such a pdf for a component, determination of a reliability function for the component is straightforward – it is given by the cumalitive distribution function (cdf):

Reliability function

(http://www.engineeredsoftware.com/nasa/reliabil.htm)Mathematically, the reliability function is the integral of the pdf from x to infinity:

If the number of failures per unit time (average the failure rate) is constant (i.e. failures are described by a Poisson process), then the distribution of the time between failures is exponential and

The mean life, θ, is the arithmetic average of the lifetimes of all items considered, which for the exponential function is the mean time between failure (MTBF).

Reliability functionThus,

where λ is the instantaneous failure rate and M the mean time between failures (MTBF)

Mean life and failure are related as:

Figure 12.1. shows the exponential reliability function. For a given normalised time, one can read off (calculate) the reliability.

Constant Failure RateThe preceding analysis assumes that the failure rate is constant and that an exponential distribution can therefore be used. How realistic is this assumption?

Component RelationshipsComponents can be composed as Series NetworksIn a series network, all components must operate in a satisfactory manner if the system is to function properly. For serially connected subsystems a,b,c, the reliability of the system isR =RaRbRcParallel NetworksA pure parallel network is one where several of the same components are in parallel and where all the components must fail to cause total system failure. If subsystems a,b,c are identical (and in parallel) thenR= 1-(1-R)n, with n=3Combined Series-Parallel NetworksApply the rules above.Reliability ModellingReliability in the System Life CycleReliability Requirements AllocationDesign GuidelinesPrefer standardised components and materialsTest and evaluate all components and materials prior to design acceptanceIf appropriate, consider the use of redundancyReliability Methods: FMECAFailure Mode, Effects and Criticality Analysis is a methodology used to identify and investigate potential product or process weaknesses in a systemFMECA can be applied to either functional or physical entities, ie potential failures in process or potential failures in product.With FMECA, start with a potential weakness (cause) and determine the effects of that weakness. The steps in the methodology are summarised in Figure 12.17:

Reliability Methods: FTAFault Tree Analysis iFTA) is the reverse of FMEA in that we start with a particular effect and determine the conditions that lead to the occurrence of that effect (cause)Fishbone diagrams are often employed to guide causal analysis, as in Figure 12.19Such a diagram is then transformed into fault trees (one per failure mode)Figure 12.19 Ishikawa cause-and-effect “fishbone” diagram.

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