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49.8 Mathematical Approximation Alternative
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Frequency
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Mean (mTask)
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Time Minimum Task Cycle Time Nominal Task Cycle Time Budgeted (Maximum) Task Cycle Time Allocated Task Cycle Time
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Queue Time Queue Time Allocated Queue Time Mean (mQueue)
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Allocated Task Cycle Time Allocated Task Cycle Time Capability Performance Time Transport Time Capability Performance Time Transport Time Allocated Capability Performance Time Mean (mCap) Allocated Transport Time Mean (mTransport)
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-3s +3s tQMin. tQMean tQBudget tQMargin.
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Figure 49.9 Task Timeline (MET) Statistical Analysis
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How does this relate to SE If a given capability or task is supposed to be completed within the allocated cycle time and you are designing a system with queues, computational devices, and transmission lines you need to factor in these times as performance budgets and safety margins to ow down to lower levels.
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Applying Statistics to Overall System Performance
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Our discussions to this point focused on the task and multi-tasking level. The ultimate challenge for SEs is: HOW will the overall system perform Figure 49.10 illustrates the effects of statistical variability of the System Element Architecture and its OPERATING ENVIRONMENT.
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49.8 MATHEMATICAL APPROXIMATION ALTERNATIVE
Our conceptual discussions of statistical system performance analysis were intended to highlight key considerations for establishing and allocating performance budgets and margins and analyzing data for system performance tuning. Most people do not have the time to perform the statistical analyses. For some applications, this may be acceptable and you should use the method appropriate for your application. There is an alternative method you might want to consider using, however. Scheduling techniques such as the Program Evaluation and Review Technique (PERT) employ approximations that serve as analogs to a Gaussian (normal) distribution. The formula stated below is used: Expected or mean time = where ta + 4t b + t c 6 (49.1)
49
System Performance Analysis, Budgets, and Safety Margins
OPERATING ENVIRONMENT Element
SYSTEM OF INTEREST (SOI)
-3s +3s
MISSION SYSTEM EQUIPMENT EQUIPMENT Element Element Hardware Hardware Software Software SYSTEM SYSTEM RESPONSES RESPONSES Element Element
MAN-MADE MAN-MADE Systems Systems Element Element
INDUCED INDUCED ENVIRONMENT ENVIRONMENT Element Element
PERSONNEL PERSONNEL Element Element MISSION MISSION RESOURCES RESOURCES Element Element
PROCEDURAL PROCEDURAL DATA Element DATA Element
NATURAL NATURAL ENVIRONMENT ENVIRONMENT Element Element
SUPPORT SYSTEM SUPPORT SYSTEM
-3s +3s
Figure 49.10 Statistical Variations in SYSTEM Level Performance
ta = optimistic time tb = most likely time tc = pessimistic time
Do SEs Actually Perform This Type of Analysis
Our discussion here highlights the theoretical viewpoint of task analysis. A question people often ask is: Do people actually go to this level of detail In general, the answer is yes, especially in manufacturing and scheduling environments. In those environments statistical process control (SPC) is used to minimize process and material variations in the production of parts, and this translates into cost reduction.
Modeling and Simulation
If you develop a model of a system whereby each of the capabilities, operations, processes, and tasks is represented by a series of sequential and concurrent elements or feedback loops, you can apply statistics to the processing time associated with each of those elements. By analyzing how each of the input variables varies over value ranges bounded on the 3s points, you can determine the overall system performance relative to a mean. Guidepost 49.4 Our discussions highlighted some basic task-oriented methods that support a variety of systems engineering activities. These methods can be applied to Mission Event Timelines (METs), system capabilities and performance as a means of determining overall system performance. Through decomposition and allocation of overall requirements, developers can establish the appropriate performance budgets and safety margins for lower level system entities.
49.10 System Performance Optimization
49.9 REAL-TIME CONTROL AND FRAME-BASED SYSTEMS
Some systems operate as real-time, closed loop, feedback systems. Others are multi-tasking whereby they have to serve multiple processing tasks on a priority basis. Let s explore each of these types further.
Real-Time, Closed Loop Feedback Systems
Electronic, mechanical, and electromechanical systems include real-time, closed loop, feedback systems that condition or process input data and produce an output, which is sampled and summed with the input as negative feedback. Rather than feedback impulse functions to the input, lters may be required to dampen the system response. Otherwise, the system might overcompensate and go unstable while attempting to regain control. The challenge for SEs is determining and allocating performance for the optimal feedback responses to ensure system stability.
Frame-Based System Performance
Electronic systems often employ software to accomplish CYCLICAL data processing tasks using combinations of OPEN and CLOSED loop cycles. Systems of these types are referred to as framebased systems. Frame-based systems perform accomplish multi-task processing via time-based blocks of time such as 30 Hertz (Hz) or 60 Hz. Within each block, processing of multiple CONCURRENT tasks is accomplished by allocating a portion of each frame to a speci c task, depending on priorities. For these cases, apply performance analysis to determine the appropriate mix of concurrent task processing times. Author s Note 49.3 One approach to frame-based system task scheduling is rate monotonic analysis (RMA). Research this topic further if frame-based systems apply to your business domain.