Question

A production station has a naturally occurring rate of unexpected breakdowns. The mean time between interruptions is 6 hours. The average repair time is 20 minutes, and the CV for repair time is 1.75. The mean natural processing time is 10 minutes with standard deviation 1 minute.

a. What is the effective processing time and the CV of effective process time?

b. If the arrival rate to the station is 5 jobs per hour, what is the station’s utilization?

c. The line engineer decides to try a planned maintenance interruption on the after line every 50 jobs. The maintenance time is 30 minutes (constant). Now what is the effective processing time and its CV? Assume that the maintenance prevents unexpected breakdowns.

d. Before implementing the planned maintenance program, the line engineer determines that she can reduce variability of the repair time. What would be the CV needed for the repair process to achieve the same CV of effective processing time as the planned maintenance alternative?

CV = coefficient of variance

Answer 1

Solushon Gtven that the Production Haton nateraliy rate of unenpected Break downs ccung The mean -tmes Betwcens nterruphen n6 hours The Cve10ge repairtime ir 20 minifuey The CV fer repair time St1 POan mean natural Processing Tие time to minufes a Efechive process T.mes ESfechve -pras times faclude Fyps, outage etc- mf mean time to failure =6 60-300minufe mT mean time to aepair =20 to-base process timme 10 p base process time = / to-ceefhcient o! val variesilily repair tine-Hs CV Calculton (Fractiony Ame machine Avaitabitly / A f/Caftm) 0-947 Scanned with CamScanner

co-Coe fficient of anabilty /cu base process Hine 4ne bae processin time O.1 1 O415 1동), (m2 t0%)01-4)o Amy m y f te C-Coeftcent of van onatly, effechve prucer hme Efehn variab. Iity) 7 D.649 CS Scanned with CamScanner

fx K22 1 2 mf-mean time to failure 4 360 to-base process time 5 10 s.d of base process time 6 . 7 mr-mean time to repair 20 8 9 CO-(coefficient of variability Jcv of base process time Cr-(coefficient of va riability)cv of repair time s.d of base processing time/base processing time 10 = F6 / F5 11 1.75 12 rasthe rate arrivals in customers (jobs) per unit time 1/ta 5/60 13 14 15 16 mathe number of machines. 1 17 =F4/ ( F4 + F7 ) 18 Availability ,Afraction fo time machine is up) mf/imf+mr) 19 Effective processing time ,te t0/A F5/F18 number of machines/te -F16/F19 20 Efective processing rate, re 21 F10 2+ ( 1 + F 11 A2)F18 ( 1 - F18 ) (F7/FS) SQRT(F22) 22 (Ce2 23 Ce-coefficient of variability/cv, of effective process time (Efective variability) 24 25 26 27 uutilization of station ra/re-ra.te F12/F20 28 29 30

K22 D E 2 3 mf-mean time to failure 360 to-base process time 10 5 s.d of base process time 1 6 mr-mean time to repair 20 7 8 s.d of repair time 9 r0-base capacity 1/to CO-(coefficient of variability )cv of base process time s.d of base processing time/base processing time 0.100 10 Cr-(coefficient of variability)cv of repair time 1.750 11 ra-the rate of arrivals in customers (jobs) per unit time 1/ta 0.083 12 13 ta the average time between arrivals. 1/ra 14 5.D of time between arrivals S.D of time between arrivals/the average time between arrivals 15 ca the CV of inter-arrival times. m-the number of machines. 1.000 16 17 18 Availability,A (fraction fo time machine is up) mf/(mf+mr) 0.947 t0/A 10.556 Effective processing time,te 19 0.095 number of machines/te 20 Efective processing rate, re 21 22 (Ce2 0.415 0.644 23 Ce-coefficient of variability/cv, of effective process time (Efective variability) 24 25 26 0.880 27 uutilization of station ra/re-ra.te 28 n 00

gobs per hour The rate to thi ffation U-Uhlization of flation 11 d.990 Jobs The after line cvey 50 minuty The mainlance Aime 30 minutes 50* 10 time kaken fer 50 minutey 500 Per Tob plane d inferuption taty fter o 5o Tobr time to falure = 500minutes mean mean to vepaiy = 30 minules mY- CS Scanned with CamScanner

Page Layout Insert Formulas Data Review View Developer Home K21 B C D G H 1 4 mf-mean time to failure 500 to-base process time 10 6 s.d of base process time 1 mr-mean time o repair 30 8 s.d/mean time Cr-lcoafficient ofvaria vof base process time arrivals in customers (jobs) per unit time CO-( coefficient o S.d of base processing time/base processing time 0.100 11 1750 12 0 083 1/ta ra=the rate 13 14 15 16 m-the number of machines 1.000 17 0.943 Availability,A (fraction fotime machine is up) mf/(mf+mr) 18 10.600 Effective processing time,te t0/A 19 0.094 Efective processing rate, re number of machines/te 20 21 (Ce2 22 0.661 0.813 23 Ce-coefficient of variability/cv, of effective process time (Efective variability) 24 25 26 0.883 uutilization of station ra/re -ra.te 27 28 29 30 31 32

Semplemeatsung the planned maintaince Uing Ce cv, of effechive process time Cefeckve varial:fily) =688 3 with repair alfe rnative Ce-Cv of edf echive Precest time to change C-Geffient of veriabit ty Cv apair hme we Such that Cvof fchve precess fime becomes 6.883 Scanned with CamScanner

Show Detail Hide Detail Connections Clear Reapply Advanced Properties Refresha Edit Links Consolidate bis 2 Sort Filter Group Ungroup Subtotal From Other Esting ta Celumne Dunlicates Accece Wab ns on Get External Data Connections Sort & Filter Data Tools Outline fc F11 F B C G 1 mf-mean tima to failuro 4 60 Goal Seek to-base process time 10 s.d of base process time 1 5 Set cell: $F$23 mr-mean time o repai 20 7 To yalue: 0.883 8 9 By changing cel: $F$11 CO-lcoefficient of varia bility )cv of base process time s.d of base processing time/base processing time 10 .100 s.d/mean time Cancel OK ra-the rate of arrivals in customers fioba)per unit time 1/ta 13 14 15 m-the number of machines 1.000 16 17 Availability A(fraction fo time machine is upl mf/mfmr) 18 0.947 t0/A Effective processing time,te 10.55 19 0.095 Efective processing rate, re number of machines/te 20 (Ce 2 0.415 22. o 644 23 Ce-coefficient of veriability/cv, of effective process time (Efective variability) 24 25

L Hide Detail Reapply Refresh roperties All Existing Connections Sort Group Ungroup Subtotal From From Access Web From From Other Sources Filter Remove Columns Duplicates Validation Text to Data Consolidate What-If Edit Links Advanced Analysis Tex Get External Data Connections Sort & Filter Data Tools Outline K10 C G 1 mf-mean time to failure 360 4 Goal Seek Status se process time 5 10 Goal Seeking with Cel F23 found a solution. Step 20 7 mr-mean time to repair 8 Pause Target value: 0.883 Current value: 0.883 .d of base processing time/base processing time CO-(coefficient of variability lev of base process time s.d/maan time Cr(coatficiant of variability)cv of rapair tima .100 10 2,592 11 Cancel OK rathe rate of arrivals in customers (jobs)per unit time 1/ta o 083 12 13 14 1.000 m-the number of machines 17 0,947 Availability.A Ifraction fo time machine is up) mt/mf+mr) 18 10.556 Effective processing time,te 10/A 19 Efective processing rate, re number of machines/ter o.095 20 21 lo 780 (Ce 2 22 lo 883 23 Ce-coafficient of va riability/cv, of effective process time (Efective variability) 24 25