Question

Problem 1. A manufacturer has a machine that, when operational at the beginning of a day, has a probability of 0.13 of breaking down sometime during the day. When this happens, the repair is done the next day and completed at the end of that day (a) Formulate the evolution of the status of the machine as a Markov chain by identifying three possible states at the end of each day and then constructing the (one-step) transition matrix (b) Find the expected first passage time Mi from state 1 to state j, for all i and j. Use these results to identify the expected number of full days that the machine will remain operational before the next breakdown after a repair is completed. (c) Now suppose that the machine already has gone 15 full days without a breakdowin since the last repair was completed. How does the expected number of full days here- after that the machine will remain operational before the next breakdown compare with the corresponding result from part (b) when the repair had just been completed? Explain

I know the final answer but I need to know all steps please show work for good rate

Answer 1

A mauulactave has a machine -that h opratiornal at the bening has a. Pobabi1ธุ์ 2 0-13 breaking dan Sometime duving the (a) fom -thae data prolabili bxakirg don, n 4- 0-13 ohese, S: so, 1, 2 whane the slate ot s-o :-machine uus Yot broken duainattuda S-1 machine has baoken duxthg the da, emi daij

0) 0.13 o 0.81 013 o we ne st pRMa ime u e Know -that 00 01 1- Po omanssfion 1-0.8:t 0.13 . 692 80

we have it is qiven O0 02 20 ● P , 0-13 mat orm besult = I+ 810-13 1+1.04 =2.04 1 to 1 11 12. -from 02 12. 02 : 113 口,15 02ニキ·53

t 0 1+ 126 to 12 人12-1 ו 구.ut2- 22 M2l 22 20

20 = 1+0-13 + 0-13(10) O-13 i20 一0-13-as = 1-13 20느 1.13 0.8チ 20 1.2988 50 20 씌 1.298 1+1.298 = 2.298 H0动(9.53)+0.130) : : 122ーチ6811

-phu"ฯ0we, the าย.lts, gd we 'as , to = 2.2988, In=8.96, 1 0 - t.HE, ^2)- -9%, ^, - j.6 ire alveady has gone Is -full day* uoithoutbrkdoon, Sine the epa Ans rachine Completed using maskowan Pro Pe9 rea ay's withot badoon 15 +8 23 01=8 9