Question

2 The following data represent field failures of the automatic transmission of a particular car type. Number of failures Interval in months 0< t <5 5< t <9 9< t < 13 13 < t <17 17 < t < 21 21 < t < 25 25 < t < 29 29 < t <33 34 < t <37 37 < t < 41 Assuming that the population size is 46 cars, Find the reliability and the hazard rate function at each interval, and then plot them.

Answer 1

Interval in months	Number of failures	f(t)	F(t)	Reliability function	Hazard function
0<t<5	0	0.000	0.000	1.000	0
5<t<9	3	0.079	0.079	0.921	0.085714286
9<t<13	3	0.079	0.158	0.842	0.09375
13<t<17	2	0.053	0.211	0.789	0.066666667
17<t<21	7	0.184	0.395	0.605	0.304347826
21<t<25	9	0.237	0.632	0.368	0.642857143
25<t<29	11	0.289	0.921	0.079	3.666666667
29<t<33	1	0.026	0.947	0.053	0.5
34<t<37	0	0.000	0.947	0.053	0
37<t<41	2	0.053	1.000	0.000	not applicable
Total	38	1.000

Chart Title 4.000 3.500 3.000 2.500 2.000 1.500 1.000 0.500 0.000 1 2 5 8 9 3 4 Reliability function 6 7 Hazard function