Handbook of Reliability, Availability, Maintainability and Safety in Engineering Design - Part 43 pptx

4.2 Theoretical Overview of Availability and Maintainability in Engineering Design 403 Equiv. Availability (EA) = Operational Time Time Period × Process Output MDC = ∑ [(T o ) ·n(MDC)] T ·MDC = [480×(1)] + [120×(0.5)] 720×(1) = 0.75 or 75% where: Total time period = 720h Operational time =(480+120)=600 h MDC = maximum dependable capacity MDC = 1×(constant representing capacity,C) Process output =[0.75/(600/720)][(1) ×C] Process output = 0.9C Process output = 90% of MDC. b) Equivalent Maintainability Measures of Downtime and Outage It is necessary to consider mean downtime (MDT) compared to the mean time to repair (MTTR). There is frequently confusion between the two and it is important to understand the difference. Downtime,oroutage, is the period during which equipment is in the failed state. Downtime may commence before repair, as indicated in Fig. 4.11 (Smith 1981). This may be due to a significant time lapse from the onset of the downtime period up till when the actual repair, or corrective action, comm e nces. Repair time may often involve checks or alignments that may extend beyond the downtime period. From the diagram, it can be seen that the combination of down- time plus repair time includes aspects such as realisation time, access time, diag- nosis time, spare parts procurement, replacement time, check time and alignment time. MDT is thus the mean of all the time periods that includ e realisation, access, diagnosis, spares acquisition and replacement or repair. A comparison of downtime and repair time is given in Fig. 4.11. According to the American Military Standard (MIL-STD-721B), a failure is de- fined as “the inability of an item to function within its specified limits of perfor- mance”. Furthermore, the definition o f function was given as “the work that an item is designed to perform”, and functional failure was defined as “the inability of an item to carry-out the work that it is designed to perform within specified limits of performance”. From these definitions, it is evident that there are two degrees of severity of func- tional failure: • A complete loss of function, where the item cannot carry out any of the work that it was d esigned to perform. 404 4 Availability and Maintainability in Engineering Design Fig. 4.11 A comparison of downtime and repair time ( Smith 1981) • A partial loss of function, where the item is unable to function within specified limits of performance. In addition, equipment condition wasdefinedas“the state of an item on which its function depends” and, as described before, the state of an item on whichits function depends can be both an operational as well as a physical condition. An important principle in determining the integrity of engineering design can thus be discerned relating to the expected condition and the required condition as- sessment (such as BIT) of the designed item: An item’s operational condition is related to the state of its operational function or working performance, and its physical condition is related to the state of its physical function or design properties. Equipment in a failed state is thus equipment that has an operational or physical condition that is in such a state that it is unable to carry out the work that it is designed to perform within specified limits of performance. Thus, two levels o f severity of a failed state are implied: • Where the item cannot carry out any of the work that it was designed to p erform, i.e. a total loss of function. • Where the item is unable to function within specified limits of performance, i.e. a partial loss of function. Downtime, or outage, which has been described as the period during which equip- ment is in the failed state, has by implication two levels of severity, whereby the term downtime is indicative of the period during which equipment cannot carry out any of the work that it was designed to perform, and the term outage is indicative of 4.2 Theoretical Overview of Availability and Maintainability in Engineering Design 405 the period during which equipment is unable either to carry out any of the work that it was designed to perform or to function within specified limits of performance. Downtime can be defined as “the period during which an equipment’s opera- tional or physical condition is in such a state that it is unable to carry-out the work that it is designed to p erform”. Outage can be defined as “the period during which an equipment’s operational or physical condition is in such a state that it is unable to carry-out the work that it is designed to perform within specified limits of performance”. It is clear that the term outage encompasses both a total loss of function and a partial loss of function, whereas the term downtime constitutes a total loss of function. Thus, the concept of full outage is indicative of a total loss of function, and the concept of partial outage is indicative of a partial loss of function, whereas downtime is indicative of a total loss of function only. The concepts of full outage and partial outage are significant in determining the equivalent mean time to outage and the equivalent mean time to restore. The equivalent mean time to outage (EM) Equivalent mean time to outage can be defined as “the comparison of the equipment’s operational time, to the number of full and partial outages over a specific period” Equivalent Mean Time to Outage (EM) = Operational Time Full and Partial Outages . (4.133) The measure of equivalent mean time to outage can be illustrated using the previ- ous example. As indicated, the power generator is estimated to be in operation for 480h at maximum dependable capacity, MDC. Thereafter, its output is estimated to derate, with a production efficiency reduction of 50% for 120 h, after which it will be in full outage for 120 h. What is the expected equivalent mean time to outage of the generator over a 30-day cycle? Full power at 100% Xp Half power at 50% Xp MDC MDC/2 120 hours 120 hours480 hours Time period = 720 hours Measure of equivalent mean time to outage of a power generator Full outage EM = ∑ (T o ) N = 480+120 2 = 300 h . (4.134) 406 4 Availability and Maintainability in Engineering Design The significance of the concepts of full outage and partial outage, being indica- tive of a total and a partial loss of function of individual systems, is that it enables the determination of the equivalent mean time to outage of complex integrations of systems, and of the effect that this complexity would have on the availability of engineered installations as a whole. The equivalent mean time to restore (ER) It has previously been shown that the restoration of a failed item to an operational effective condition is normally when repair action,orcorrective action in maintenance is performed in accordance with prescribed standard procedures. The item’s operational effective condition in this context is also considered to be the item’s repairable condition. Mean time to repair (MTTR) in relation to equivalent mean time to restore (ER) The repairable condition of equipment is determined by the mean time to repair (M TTR), which is a measure of its ma intainability MTTR = Mean Time To Repair (4.135) = ∑ ( λ R) ∑ ( λ ) where: λ = failure rate of components R = repair time of components (h). In contrast to the mean time to repair (MTTR), which includes the rate of failure at component level, the concept of equivalent mean time to restore (ER) takes into consideration the equivalent lost time in outages at system level, measured against the number of full and partial outages. This is best understoodby defining equivalent lost time. Equivalent operational time was previously defined as “that operational time during which a system achieves process output which is equivalent to its maximum dependable capacity”. In contrast, equivalent lost time is defined as “that outage time during which a system loses process output, compared to the process output which is equivalent to the maximum dependable capacity that could have been attained if no outages had occurred”. Furthermore, it was previously shown that the maximum dependable capacity (MDC) is reachedwhen the system is operating at maximum efficiency or,expressed as a percentage, when the system is operating at 100% utilisation for a given oper- ational time,i.e.process output at 100% utilisation is equivalent to the system’s maximum dependable capacity Equivalent Lost Time = Lost Output×Operational Time Production Output at MDC (4.136) ELT = ∑ [n(MDC) ·T o ] MDC 4.2 Theoretical Overview of Availability and Maintainability in Engineering Design 407 where: n = fraction of process output. Equivalent mean time to restore (ER) can be defined as “the ratio of equivalent lo st time in outages, to the number of full and partial outages over a specific period”. If the definition of equivalent lost time is included, then equivalent mean time to restore can further be defined as “the ratio of that outage time during which a system loses process output compared to the process output which is equivalent to the maximum dependable capacity that could have been attained if no outages had occurred, to the number of full and partial outages over a specific period”. Thus Equivalent Mean Time to Restore = Equivalent Lost Time No. of Full and Partial Outages ER = ELT N (4.137) ER = ∑ [n(MDC) ·T o ] MDC·N (4.138) where: n = fraction of process output N = number of full and partial outages T o = outage time equal to lost operational time. Themeasureofequivalent mean time to restore can b e illustrated using the previous example. As indicated, the power generator is estimated to be in operation for 480 h at maximum dependable capacity. Thereafter, its output is estimated to diminish (derate), with a production efficiency reduction of 50% for 120h, after which the plant will be in full outage for 120 h. What is the expected equivalent mean time to restore of the generating plant over the 30-day cycle? Full power at 100% Xp Half power at 50% Xp MDC MDC/2 120 hours 120 hours480 hours Time period = 720 hours Measure of equivalent mean time to restore of a power generator Full outage 408 4 Availability and Maintainability in Engineering Design ER = ∑ [n(MDC)·T o ] MDC·N = [0.5(MDC) ×120]+[1(MDC)×120] MDC×2 = 90 h . c) Outage Measurement with the Ratio of ER Over EM Outage measurement includes the concepts of full outage and partial outage in de- termining the ratio of the equivalent mean time to restore (ER) and the equivalent mean time to outage (EM). The significance of the ratio of equivalent mean time to outage (EM) over the equivalent mean time to restore (ER) is that it gives the measure of system unavailability, U. In considering unavailability (U), the ratio of ER over EM is evaluated at system level where ER = ∑ [n(MDC) ·T o ] MDC·N (4.139) EM = ∑ (T o ) N ER EM = ∑ [n(MDC) ·T o ] MDC·N · N ∑ (T o ) ER EM = ∑ [n(MDC) ·T o ] MDC· ∑ (T o ) . Expected availability (A), or the general measure of availability of a system as a ra- tio, was formulated as a comparison of the system’s usable time or operational time, to a total given period or cycle time A = ( ∑ T o ) T . (4.140) If the ratio of ER over EM is multiplied by the availability of a particular system (A system) over a period T, the result is the sum of full and partial outages over the period T, or system unavailability,U (A)system· ER EM = ∑ [n(MDC) ·T o ] MDC· ∑ (T o ) · ( ∑ T o ) T (4.141) = ∑ [n(MDC) ·T o ] MDC·T = Unavailability (U)system. Thus, equivalent availability (EA) is equa l to the ratio o f the equivalent mean time to restore (ER) and the equivalent mean time to outage (EM), multiplied by the expected availability (A) over the period T. 4.2 Theoretical Overview of Availability and Maintainability in Engineering Design 409 Thus, the formula for equivalent availability (EA) can be given as: EA = ∑ [n(MDC) ·T o ] MDC·T ER EM ·A = ∑ [n(MDC) ·T o ] MDC· ∑ (T o ) · ( ∑ T o ) T ER EM ·A = ∑ [n(MDC) ·T o ] MDC·T = EA So far, the equivalent mean time to outage (EM) and the equivalent mean time to restore (ER) have been considered from the point of view of outages at system level. However, the concepts of full outage being indicative of a total loss of system function,andpartial outage being indicative of a partial loss of system function,and their significance in determining EM and ER make it possible to consider outages of individual systems within a complex integration of many systems, as well as the effect that an outage of an individual system would h ave on the availability of the systems as a whole. In other words, the effect of reducing EM and ER in a single system within a complex integration of systems can be determined from an evaluation of the changes in the equivalent a vailability of the systems (engineered installation) as a whole. The effect of single system improvement on installation equivalent availability The extent of the complexity of integration of individual systems in an engineered installation relative to the installation’s hierarchical levels can be determined fr om the relationship of equivalent availability (EA) and unavailability (U) for the indi- vidual systems, and installation as a whole EA system = ER EM ·A system = ER EM · ( ∑ T o ) T = U system (4.142a) EA install. = ER EM ·A install. = ER EM · ( ∑ T o ) T = U install. (4.142b) In this case, the r atio ER/EM would be the ratio of the equivalent mean time to restore (ER) over the equivalent mean time to outage (EM) of the individual systems that are included in the installation. If the installation (or process plant) had only one inherent system in its hierarchicalstructure, then the relationship given above would be adequate. Thus, the effect of improvement in this system’s ER/EM ratio on the equivalent availa bility of the installation that consisted of only the one inherent system in its hierarchical structure can be evaluated. Based on outage data of the system over a period T,thebaseline ER/EM ratio of the system can b e determined. Similarly, improvement in the system’s outage would give a new or future value for the system’s ER/EM ratio, represented as: ER EM baseline and ER EM future . 410 4 Availability and Maintainability in Engineering Design The change in the equivalent availability (A) of the engineered installation, which consists of only the one inherent system in its hierarchical structure, can be formu- lated as ΔEA install. =  ER EM b a seline −ER EM future  · T o install. T . (4.143) If the engineered installation consists of several integrated systems, then the ratio ER/EM would need to be modified to the following ΔEA install. = q ∑ j= 1  ER j EM j ·A install.  (4.144) ΔEA install. = q ∑ j= 1  ER j EM j · T o install. T  where: q = num ber of systems in the installation ER j = equivalent mean time to restore of system j EM j = equivalent mean time to outage of system j T o = operational time of the installation T = evaluation period. The effect of multiple system improvement on installation equivalent avail- ability The change in the equivalent availability (A) of the engineered installation, which consists of multiple systems in its hierarchical structure, can now be formu- lated as ΔEA install. =  q ∑ j= 1 ER j EM j baseline − r ∑ k=1 ER k EM k future  · T o install. T (4.145) where: q = num ber of systems in the engineered installation ER j baseline = equivalent mean time to restore of system j EM j baseline = equivalent mean time to outage of system j r = num ber of improved systems in the installation ER k future = equivalent mean time to restore of system k EM k future = equivalent mean time to outage of system k T o = operational time of the engineered installation T = evaluation period. This change in the equivalent availability (A) of the engineered installation, as a re- sult of an improvement in the performance of multiple systems in the installation’s hierarchical structure, offers an analytic approach in determining which systems are critical in complex integrations of process systems. This is done by determin- ing the optimal change in the equivalent availability of the engineered installation 4.2 Theoretical Overview of Availability and Maintainability in Engineering Design 411 through an iterative process of marginally improving the performance of each sys- tem, through improvements in the equivalent mean time to restore of system k,and the equivalent mean time to outage of system k. The method is, however, compu- tationally cumbersome without the use of algorithmic techniques such as genetic algorithms and/or neural networks. Another, perhaps simpler approach to determining the effects of change in the equivalent availability of the engineered installation, and determining which sys- tems are critical in complex integrations of process systems, is through the method- ology of systems engineering analysis. This approach is considered in detail in Sect. 4.3.3. As an example, consider a sim ple power-generating plant that is a multiple inte- grated system consisting of three major systems, namely #1 turbine, #2 turbine and a boiler, as illustrated in Fig. 4.1 2 below. Statistical probabilities can easily be calculated to determine whether the plant would be up (producing power) or down (outage). In reality, the plant could operate at intermediate levels of rated capacity, or output, depending on the nature of the Fig. 4.12 Example of a simple power-generating plant 412 4 Availability and Maintainability in Engineering Design Table 4.1 Double turbine/boiler generating plant state matrix State Boiler #1 #2 Capacity 1 Up Up Up 100% 2 Up Up Down 50% 3 Up Down Up 50% 4DownUpUp 0% 5 Down Up Down 0% 6 Down Down Up 0% 7 Down Down Down 0% 8 Up Down Down 0% outages of each of the three systems. This notion of plant state is indicated in Ta- ble 4.1, in which the outages are regarded as full outages, and no partial outages are considered. Referring back to Eq. (4.20), maximum process capacity was measured in terms of the average outpu t rate and the average utilisation rate expressed as a percentage Maximum Capacity (C max ) = Average Output Rate Average Utilisation/100 (4.146) Average Output Rate =(C max ) ·Average Utilisation . Asystem’smaximum dependable capacity (MDC) was defined in Eq. (4.129) as being equivalent to process output at 100% utilisation. Thus MDC = Output (100% utilisation) (4.147) The plant’s average output rate can now be determined where individual system outages are regarded to be full outages, and no partial outages are taken into con- sideration. The plant is in state 1 if all the sub-systems are operating and output is based on 100% utilisation (i.e. MDC). Seven other states are defined in Table 4.1, which is called a state matrix. However, to calculate the expected or average process output rate of the plant (expressed as a percentage of maximum output at maximum design capacity), the percentage capacity for each state (at 100% utilisation) is multiplied b y the avail- abilities of each integrated system. Thus: Average plant output rate with full outages only = Σ (capacity of plant state at 100% utilisation of systems that are operational × availability of each integrated system). As an example: what would be the expected or average output of the plant if the estimated boiler availability is 0.95 and the estimated turbine generator availabilities are 0.9 each? . done by determin- ing the optimal change in the equivalent availability of the engineered installation 4.2 Theoretical Overview of Availability and Maintainability in Engineering Design 411 through. as: ER EM baseline and ER EM future . 410 4 Availability and Maintainability in Engineering Design The change in the equivalent availability (A) of the engineered installation, which consists of only. system function,andpartial outage being indicative of a partial loss of system function ,and their significance in determining EM and ER make it possible to consider outages of individual systems within a