Series Reliability Simulator — Required Components in Series Interactive

Interactive 3D reliability laboratory: a switch, motor and pump in series; set failure rates and mission time and watch survival probabilities multiply.

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About the Series Reliability Simulator

This simulator models a process chain in which a feed switch, a drive motor and a transfer pump must all work for product to flow. You set the mission duration and each component's failure rate, toggle faults by hand, and compare the live service state with the mission survival probability.

What the simulator shows

• A 3D feed switch and contacts, finned drive motor and shaft, transfer pump and delivered process stream. • Sliders for mission duration (100-3000 h) and three failure rates, for the switch, motor and pump, each from 0.05 to 2 per 1000 h, plus three manual fault switches and a motion-marker toggle. • Four live readouts: mission survival, mission failure probability, equivalent failure rate and whether live service is available. • Two presets: One failed motor (service stops although the switch and pump are healthy) and All equipment restored (flow resumes).

Why series systems are fragile

Each component survives the mission with probability Ri = exp(-lambda_i T). Because all three are required, the system survives only if all do, so R_series = R1 R2 R3 and the failure probability is Q = 1 - R_series. Equivalent failure rate is the sum of the individual rates, lambda_eq = sum of lambda_i. The product is always lower than the weakest single component, so adding another required part can only reduce reliability.

Model limits and reading the two kinds of failure

The model is independent, exponential and nonrepairable over a mission. Manual faults demonstrate the Boolean dependency (a failed required part stops service) and do not change the unconditional mission probability shown in the readouts. There is no hydraulic or motor performance model. Use the Experiments tab to load the presets and the model checks to verify the probability calculation.

Frequently asked questions

What does series reliability multiply?

The component survival probabilities. A successful mission needs every required component to survive, so R_series = R1 x R2 x R3.

Can a healthy pump overcome a failed motor?

No. In a series chain each part is required, so one failed component stops service even if the others are fine.

How do failure rates combine in a series system?

For exponential components they add: the equivalent failure rate is the sum of the individual rates, which is the same as multiplying the survival probabilities over time.

What does this simulator not model?

It is an independent exponential nonrepairable mission model. Repair, common-cause failures and the hydraulic or electrical performance of the equipment are not included.

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