You have been instructed to quantify and improve the failure rates associated wi

Question

You have been instructed to quantify and improve the failure rates associated with components made in a car assembly plant that’s just coming online (still working out a lot of bugs). Below are the incident rates of faults (flaw or problem, but still functions) and failures for selected systems and subsystems that are known to have the highest rates at the plant. You can assume the failures occur independent of each other (e.g., A wiring failures does not cause an alternator failure).

(Please solve ploblams L - P and show something, and show R studio code)

2. Car Fault Assignment (Software) You have been instructed to quantify and improve the failure rates associated with components made in a car assembly plant that's just coming online (still working out a lot of bugs). Below are the incident rates of faults (flaw or problem but still functions) and failures for selected systems and subsystems that are known to have the highest rates at the plant. You can assume the failures occur independent of each other (e.g., A ring failures does not cause an alternator failure P(fault) P(fault and failure) Subsystem System Braking brake pad5 17500 1/100000 1/2000 1/1000 calipers 17100 1/20000 brake line 1/1500 1/1500 master cylinder Drive train Engine head gasket 1/2000 1/400000 1/2500 1/800000 engine block Transmission 1/1500 1/7000 each gear 1/500 1/3000 Rear Differential 1/550 1/3000 Front Differential Electrical 60 1/600 Wiring 1/100 1/150 alternator Note: To input these values into an R dataframe you can use the following syntax frame (subsystem c brake pads calipers "brake line Car master. cylinder "head cover engine block rear diff front. d iff gea. Wiring

Explanation / Answer

The R Codes are as follows:

car.df=data.frame(subsystem=c("brake.pads","calipers","brake.line","master.cylinder"
,"head.cover","engine.block","gear","rear.diff","front.diff","wiring",
"alternator"),p.fault=c(1/500,1/1000,1/100,1/1500,1/2000,1/2500,1/1500,
1/1500,1/550,1/60,1/100),p.failure=c(1/100000,1/2000,1/20000,1/1500,1/400000,
1/800000,1/7000,1/3000,1/3000,1/600,1/150))

#----------Answer L-----------
Z =1- car.df$p.fault
hi1= matrix(Z)

prob_of_no_fault=prod(hi1)

Answer_L = 1-prob_of_no_fault

#----------Answer M-----------
X =1- car.df$p.failure
hi2= matrix(X)

prob_of_no_failure=prod(hi2)

Answer_M = 1-prob_of_no_failure

#----------Answer N-----------
ANSWER_N = data.frame(car.df$subsystem,car.df$p.failure)

#----------Answer 0-----------
num = 100000000
car.df$failures = 0
for (subsystem.index in 1:length(car.df$subsystem)){car.df$expexted.failures[subsystem.index]<-rbinom(1,num,car.df$p.failure[subsystem.index])}

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