{"id":"reliability-function","model_id":"Reliability or survival function","name":"Reliability (survival) function R(t)","summary":"The reliability or survival function R(t) gives the probability that a unit survives beyond a given time t. Because a unit either fails or survives, R(t) = 1 − F(t), where F(t) is the probability of failure by time t. For a system of independent components, the system reliability is the product of the reliability functions of all the components, since every component must survive for the system to survive.","study_notes":["Survival is the complementary event to failure; one of the two mutually exclusive alternatives must occur.","F(t) = 1 − R(t), so the failure distribution and the reliability function carry the same information.","The reliability of a system of independent components is the product of the reliability functions of all the components.","The product rule holds because every component must survive in order for the system to survive.","The document states that building the system reliability up from individual components is treated in detail under the \"Bottom-Up\" method."],"safety_notes":[],"sources":[{"url":"https://www.itl.nist.gov/div898/handbook/apr/section1/apr122.htm","title":"8.1.2.2. Reliability or survival function","accessed":"2026-10-25"}],"verification":{"status":"source_checked","checked_at":"2026-10-25","values":7,"method":"llm_source_check"},"updated_at":"2026-10-25","type":"operational","spec":{"kind":"metric","formula":{"expression":"R(t) = 1 - F(t)","variables":[{"symbol":"R(t)","name":"Reliability (survival) function: probability a unit survives beyond time t","unit":"probability","min":0,"max":1},{"symbol":"F(t)","name":"Failure probability by time t","unit":"probability","min":0,"max":1}],"output_unit":"probability"},"related":[]},"url":"https://machineschema.com/operational/reliability-function","license":"https://creativecommons.org/licenses/by/4.0/"}