Failures can be caused by defects, but also by environmental conditions. A failure is an event in which the software system does not perform a required function or performs a function incorrectly, according to the expected behavior. A defect is a flaw in the software system or a deviation from the requirements or the specifications, that may cause a failure. However, not all failures are caused by defects, as some failures may be caused by environmental conditions, such as hardware malfunctions, network interruptions, power outages, incompatible configurations, etc. Environmental conditions are factors that affect the operation of the software system, but are not part of the software system itself. The other statements are false, because:
A defect does not always produce a failure, while a bug always produces a failure. This statement is false, because a defect may or may not produce a failure, depending on the inputs, the outputs, the states, or the scenarios of the software system, and a bug is just another term for a defect, so it has the same possibility of producing a failure as a defect. For example, a defect in a rarely used feature or a hidden branch of the code may never produce a failure, while a defect in a frequently used feature or a critical path of the code may produce a failure often. A bug is not a different concept from a defect, but rather a synonym or a colloquial term for a defect, so it has the same definition and implications as a defect.
A defect may cause a failure which, when occurring, always causes an error. This statement is false, because an error is not a consequence of a failure, but rather a cause of a defect. An error is a human action or a mistake that produces a defect in the software system, such as a typo, a logic flaw, a requirement misunderstanding, etc. An error is not observable in the software system, but rather in the human mind or the human work products, such as the code, the design, the documentation, etc. A failure is not a cause of an error, but rather a result of a defect, which is a result of an error. For example, an error in the code may cause a defect in the software system, which may cause a failure in the software behavior.
Bugs are defects found during component testing, while failures are defects found at higher test levels. This statement is false, because bugs and failures are not different types of defects, but rather different terms for defects and their manifestations. As mentioned before, bugs are just another word for defects, and failures are the events in which the software system does not perform as expected due to defects. Bugs and failures can be found at any test level, not only at component testing or higher test levels. Test levels are the stages of testing that correspond to the levels of integration of the software system, such as component testing, integration testing, system testing, and acceptance testing. Defects and failures can occur and be detected at any test level, depending on the test objectives, the test basis, the test techniques, and the test environment. References: ISTQB Certified Tester Foundation Level (CTFL) v4.0 sources and documents:
ISTQB® Certified Tester Foundation Level Syllabus v4.0, Chapter 1.1.2, Testing and Quality1
ISTQB® Certified Tester Foundation Level Syllabus v4.0, Chapter 1.2.1, Testing Principles1
ISTQB® Certified Tester Foundation Level Syllabus v4.0, Chapter 1.3.1, Testing in Software Development Lifecycles1
ISTQB® Glossary of Testing Terms v4.0, Failure, Defect, Bug, Environmental Condition, Error, Test Level2