(a) An electronic assembly consists of two subsystems. A and B. Each assembly is given one...

 

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(a) An electronic assembly consists of two subsystems. A and B. Each assembly is given one preliminary checkout test. Records on 100 preliminary checkout tests show that subsystem A failed 10 times (i.e. alone or with subsystem B). Subsystem B alone failed 15 times. Both subsystems A and B failed together five times. i) What is the probability of A failing, given that B has failed. (2 marks) ii) What is the probability that A alone fails. (2 marks) (b) Prove that the scale parameter of a Weibull distribution is defined as the time when 63.2% of the sample or population has failed. (2 marks) (c) In a short-deterministic replacement model, what is the optimal replacement interval, if operating cost c(t) is a linear function of time, i.e. c(t)=a+bt? (Details of the proof must be provided). (4 marks) (a) An electronic assembly consists of two subsystems. A and B. Each assembly is given one preliminary checkout test. Records on 100 preliminary checkout tests show that subsystem A failed 10 times (i.e. alone or with subsystem B). Subsystem B alone failed 15 times. Both subsystems A and B failed together five times. i) What is the probability of A failing, given that B has failed. (2 marks) ii) What is the probability that A alone fails. (2 marks) (b) Prove that the scale parameter of a Weibull distribution is defined as the time when 63.2% of the sample or population has failed. (2 marks) (c) In a short-deterministic replacement model, what is the optimal replacement interval, if operating cost c(t) is a linear function of time, i.e. c(t)=a+bt? (Details of the proof must be provided). (4 marks)

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