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4 Reliability Growth Models
Pages 47-62

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From page 47...
... We then look at the hardware growth models commonly used, their applications, and the implications for DoD use. Reliability growth models for software are covered in Chapter 9.
From page 48...
... Part a of the figure depicts real growth: growth occurs in incremental step increases, with larger gains occurring in the earlier tests -- because failure modes with higher failure rates (or failure probabilities) are more likely to occur and contribute more to reliability growth when fixed than their counterparts with smaller failure rates (or probabilities of failure)
From page 49...
... RELIABILITY GROWTH MODELS 49 A A Phase I Phase II True Reliability Time B B Observed and Modeled Reliability Phase I Phase II Time (cumulative hours) FIGURE 4-1  Illustrations of reliability growth using the TAAF (test, analyze, and fix)
From page 50...
... . Reliability growth models generally assume that the sole change between successive developmental testing events is the system reliability design enhancements introduced between the events.
From page 51...
... COMMON DoD MODELS Two reliability growth models are used in a majority of current DoD applications: one is a system-level nonhomogeneous Poisson process model with a particular specification of a time-varying intensity function λ(T) ; the other is a competing risk model in which the TAAF program finds and eliminates or reduces failure modes, the remaining risk is reduced, and reliability grows.
From page 52...
... . Indeed, the power law model is commonly referred to as the AMSAA model, the Crow model, or the AMSAA-Crow model.8 This continuous reliability growth formulation has been extended to accommodate one-shot reliability data by treating "failure probability" in a manner that parallels that of "failure intensity" in the context of a nonhomogeneous Poisson process, and the "learning curve property" structure is imposed to establish an assumed pattern of reliability growth.
From page 53...
... Although the number of distinct failure modes is unknown, tractable results have been obtained by considering the limit as this count is allowed to approach infinity. The power law and failure mode-removal models can be viewed as convenient frameworks that facilitate the application of statistical methods to the analysis of reliability test data and the evaluation of reliability testing programs.
From page 54...
... DoD APPLICATIONS Reliability growth models can be used to plan the scope of develop­ mental tests, specifically, how much testing time should be devoted to provide a reasonable opportunity for the system design to mature sufficiently in developmental testing (U.S. Department of Defense, 2011b, Ch.
From page 55...
... all FIGURE 4-2  PM-2 reliability growth planning curve. NOTES: DT = developmental testing; IOTE = initial test operation evaluation; OT = operational testing; MTBF = mean time between failures.
From page 56...
... The final developmental testing reliability goal (in Figure 4-2, 90 hours mean time between failures) is higher than the assumed operational reliability of the initial operational test and evaluation (81 hours mean time between operational mission failures or a 10 percent reduction)
From page 57...
... Third, since the construction of a planning curve rests on numerous assumptions, some of which may turn out to be incompatible with the subsequent testing experience, sensitivity and robustness of the modeling need to be understood and modifications made when warranted. Once a developmental program begins system-level testing, reliability growth methodologies are available for estimating model parameters, constructing curves that portray how demonstrated reliabilities have evolved 16  In the extreme, given a general sense of the developmental testing time available for a particular system and the customary nature of development tests ordinarily undertaken for such classes of systems, one could imagine divining a simple eye-ball fit through a potentially suitable smooth curve that traces from RI to some established mark above RG.
From page 58...
... There are a number of reasons that reliability results recorded over the course of developmental testing may not match target values or thresholds prescribed in advance by the associated reliability growth planning curve. Not all of these differences should translate to alarms that system reliability is problematic or deficient, nor should one assume that close conformity of developmental testing results to a reliability planning curve by itself ensures the adequacy of system operational reliability (e.g., the developmental tests may be unrepresentative of more stressful operational circumstances)
From page 59...
... Another disturbing situation is that after a few test events reliability estimates stagnate well below targeted values, while the counts of new failure modes continue to increase. A visually detectable major departure from the planning curve by itself could provide a triggering mechanism for instituting an in-depth program review.
From page 60...
... The panel could not determine whether this approach is currently commonplace. Second, during development, reliability growth models are used to combine reliability assessments over test events to track the current level of reliability attained.
From page 61...
... Here, the questions concerning the validity of reliability growth models are of the greatest concern because extrapolation is a more severe test than interpolation. Consequently, the panel does not support the use of these models for such predictions, absent a comprehensive validation.


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