#Solving complex 4 equation systems pro#
The probability of system success is calculated to be 97.85%, which agrees, as it should, with the results from the QuART PRO Redundancy Calculator.Thhe Casio FX-9860G SD can solve a polynomial equation Lastly, the probabilities for the successful outcomes are added, as follows: Table 1 lists all the possible combinations. Since each block has a 90% probability of working we can calculate the probability of each potential system state for each outcome combination. We then generate a list of all possible combinations for the five blocks in the circuit. These four “cut-sets” are shown in Figure 6. If we look at the original circuit we notice that there are four block combinations that can cause the system to fail. Here you simply examine the circuit in terms of all the combinations that would result in system failure. Given the stated mission time, we can translate this failure rate to a system reliability number.įigure 5 – QuART PRO Failure Rate CalculatorĪnother approach is to use a technique familiar with Fault Tree practitioners, the “cut-set” method. Had the blocks not been identical, we could have just as easily used the Failure Rate calculator in QuART PRO, as seen in Figure 5, to calculate the failure rate for the two scenarios. The result is then multiplied by the probability that C is in the failed state, 1 – Reliability of C.Ĭombining the two results yields a System reliability of 97.85% We can do the same for Scenario B (the parallel arrangements of AB and DE). Since the product of these two parallel groups reflects the circuit when C is functioning, we then multiply this product by the reliability of Block C.įigure 4 – QuART PRO Redundancy Calculator
Using a failure rate of 10FPMH and 1000 hours, we get a reliability of 99.99% for each. Since each block in parallel circuit AD and BE is identical we can use the Redundancy Calculator tool in QuART PRO, as seen in Figure 4. We begin by calculating the reliability of Scenario A. R s = C * ( ( A + D – AD ) * ( B + E – BE ) ) + ( 1 – C ) * ( AB + DE – ABDE ) R System = R SystemC working * Probability C working + R System C failed * Probability C failedįigures 2 and 3 show the block diagrams of the two scenarios:īased on these two scenarios, the following equation expresses the system reliability: According to Bayes Theorem, the probability that the system is working (reliability) can be summed up from two components first, the reliability of the system when Block C is functioning properly multiplied by the probability that C is working properly, and second, the reliability of the system when C is not functioning properly multiplied by the probability that C is not working properly. The most commonly used method of solving this problem is by way of using a Bayesian approach.
For a 1,000 hour mission, what is the reliability of the circuit? Each of the blocks is identical and each has a failure rate of 10 failures per million hours (FPMH). You are often given the reliability of each block and asked to calculate the reliability of the circuit.įor example let’s say we are given the following five block arrangement pictured in Figure 1.
#Solving complex 4 equation systems series#
The general form of this type of reliability block diagram has two series circuits in a parallel arrangement combined through a center or “keystone” unit. Solving the Complex RBD-Series Parallel System with a Keystone Component
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