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Industrial Engineering Maintainability & Availability 1 Industrial Engineering Maintainability Definition Maintainability Maintainability Functions Maintainability implies a built in characteristics of the equipment design which imparts to the cell an inherent ability to be maintained so as to keep the equipment productively operating by employing a minimum number of maintenance man-hour, skill levels, and maintenance costs. Examples 2 Industrial Engineering Maintainability Maintainability Various measures are used in maintainability analysis: Mean Time To Repair (MTTR) Mean Preventive Maintenance Time ( MPMT) Maintainability Functions Mean Maintenance Downtime (MMD) Examples In addition to these measures, maintainability functions are used to predict the probability that a repair, starting at time t =0, will be completed in a time t. 3 Maintainability Industrial Engineering Maintainability It measures the elapsed time required to perform a given maintenance activity. MTTR is expressed by: MTTR = ( ∑ λi CMTi ) / ∑ λi Maintainability Functions Examples Where: k = number of units or parts λi = failure rate of unit/part i , for i= 1, 2, 3, .....k CMTi = Corrective Maintenance or repair Time required to repair unit or part i, for i= 1, 2, 3, ....., k Usually, times to repair follow exponential, lognormal, and normal probability distributions 4 Maintainability Industrial Engineering The mean preventive maintenance time is defined by: Maintainability MPMT = (∑ FPMi x ETPMTi) / ∑ FPMi Where: MPMT Maintainability Functions m = total number of preventive maintenance tasks FPMi Examples = Mean Preventive Maintenance Time = Frequency of Preventive Maintenance task i, for i = 1, 2, 3, ....., m ETPMTi = Elapsed Time for Mreventive Maintenance Task i, for i= 1, 2, 3, ....., m Note that if the frequencies FPMi are given in maintenance task per hour, then ETPMTi should also be given in hours. 5 Industrial Engineering Maintainability Maintainability Functions Maintainability Mean maintenance downtime (MMD) is described as the total time required either to restore system to a given performance level or to keep it at that level of performance. It is composed of corrective maintenance, preventive maintenance, administrative delay, and logistic delay times. The administrative delay time is the system or item downtime due to administrative constraints. Examples Logistic delay time is the time spent waiting for a required resource such as spare part, a specific test, or a facility 6 Maintainability Industrial Engineering Maintainability MMD = MAMT + LDT + ADT Where: Maintainability Functions ADT = Administrative Delay Time LDT = Logistic Delay Time MAMT = Mean Active Maintenance Time or mean Examples time needed to perform preventive and corrective maintenance associated tasks. 7 Maintainability Functions Industrial Engineering Maintainability Maintainability functions predict the probability that a repair, starting at time t = 0, will be completed in a time t. The maintainability function for any distribution is defined by: M(t) = ∫ ƒr (t) dt Maintainability Functions Where: t = time M(t) = maintainability function (probability that a repair action will be finished at time t) Examples ƒr(t) = probability density function of the repair time 8 Industrial Engineering Maintainability Functions Exponential p.d.f: Maintainability Maintainability Functions Exponential p.d.f is widely used in maintainability work to represent repair times. It is expressed by: ƒr(t) = (1/MTTR) exp (-t/MTTR) The maintainability function in this case is: Examples M(t) = ∫ (1/ MTTR) exp (- t/ MTTR) dt = 1- exp (- t/ MTTR) 9 Maintainability Functions Industrial Engineering Weibull p.d.f: Maintainability Weibull p.d.f can also be used to represent times to repair. It is defined by: ƒr(t) = (β/θ) t exp (- (t / θ)) Maintainability Functions where: β = shape parameter θ = scale parameter The maintainability function in this case is: M(t) Examples = ∫ (β/ θ ) t exp (- (t / θ) ) d = 1- exp (- (t / θ) ) When β= 1 and θ= MTTR , the M(t) reduces to the M(t) in the case of exponential distribution 10 Maintainability Functions Industrial Engineering Normal p.d.f: Maintainability Normal p.d.f can also be used to represent times to repair. It is defined by: ƒr(t) = 1/σ √ 2 π exp (- 1/2(t – θ/ σ)²) Maintainability Functions where: σ= θ= standard deviation of the variable maintenance time t around the mean value θ mean of maintenance times Examples The maintainability function in this case is: M(t) = 1/σ √ 2 π ∫ exp (- 1/2(t – θ/ σ)²) dt 11 Maintainability Functions Industrial Engineering The mean of the maintenance times is: Maintainability θ = ∑ ti / k where: Maintainability Functions k = total number of maintenance tasks performed ti = ith maintenance time, for i= 1, 2, 3, ...... K Examples The standard deviation is : σ = [ ∑ (ti – θ)²/ (k – 1)]½ 12 Industrial Engineering Availability Maintainability Availability is the probability that a facility scheduled for service will be operating at any point in time. Maintainability Functions System availability predicts the actual running or uptime in terms of ratio of actual operating time to the scheduled operating time: Availability Availability = Actual operating time / Standard Operating Time 13 Industrial Engineering Availability Maintainability Maintainability Functions Availability = MTBF or MTTF / (MTBF or MTTF + MFOT or MTTR) Availability 14 Industrial Engineering Maintainability Maintainability Functions Availability Availability This means an increase in maintainability (results in small MTTR) or reliability (results in a high MTBF or MTTF) or both increases the availability of the system. Therefore, sound design provides both high reliability and maintainability. 15 Industrial Engineering Maintainability Maintainability Functions Examples Example A mechanical machine has three important subsystems. The first subsystem has failure rate of 0.003 failures per hour and repair time of 1 hour. The second and the third subsystems have failure rates of 0.005 and 0.004 failures per hour and repair times of 4 hours and 3 hours respectively. The times to repair of this machine are exponentially distributed. Find: 1. The probability that a repair on this machine will be performed in 5 hours. 2. The MTTR of this machine 3. The MMD of this machine, if the authorization of the maintenance work order takes 12 min and the time to get the required materials and spare parts from the store is 20 min 16