4.2 Theoretical Overview of Availability and Maintainability in Engineering Design 323 where: Y t = the net cash flow at the end of period t. In applying NPV, the net cash flows are usually available as input data, which are assumed to occur instantaneously at the ends of the periods t. Also usually known is an estimate of the discounting rate, i, to be used. Under these conditions, finding the NPV is straightforward. The result is a point estimate of a single value at a partic- ular interest rate i. While the point estimate of NPV is informative, in that one can determine if it is positive, negative, zer o or indeter minate, the behaviour of the cri- terion as a function is more informative. For the case of unconstrained assumptions concerning project acceptance, the general rule is to accept the project if the NPV is positive. This is true when the present value of the cash inflows exceeds the present value of the cash outflows (Bussey 1978). The NPV decreases with increasing discount rate. This is true of any project for which the cash flow increases on average throughout the project. Secondly, if the cash flow is negative in the first part of the project, as is true of any project requiring an initial capital investment, th ere exists some discount rate for which the NPV becomes zero. This is known as the internal rate of return (IRR).The IRR constitutes the most useful single characterisation of the financial viability of a project. It represents the break-even discount rate that will just allow repaym ent of the initial investment. If the actual discount rate (i.e. interest rate plus any other related financial charges) is less than the IRR, a profit will result. However, if the discount rate is higher than the IRR,theNPV will be negative, and the project will result in a loss, prompting the need for redesign o f critical systems of the proposed engineered installation, or outright rejection o f an engineering project’s particular technology, or even of the project itself. In the alternative approach of using future value, rather than present value, the estimated life-cycle costs over the project lifetime are reflected for each significant period in the project’s life-cycle stages, calculated from the required cap ital and the interest rate for that period. Subtracting these estimated life-cycle cost of capital from each period’s expected net cash flows yields the future net value. As expected, it also goes to zero as the discount rate reaches the IRR, which is independent of the method of calculation. Net profit, or future net value, results from subtracting the cost of capital from the net cash flow. The internal rate of return criterion The net present value, described in the pre- vious sub-section, depends upon the knowledge of an external interest rate for its application (i.e. external to the project, such as the cost of capital). The internal rate of return (IRR) method is closely related to NPV in that it also is a discounted cash flow method, but it seeks to avoid the arbitrary choice of an interest rate. In- stead, it attempts to find some interest rate, initially unknown, which is internal to the project. The procedure is to find an interest rate that will make the present value of the cash flow of a project zero—that is, some interest rate that will cause the present value of cash inflows to equal the present value of cash outflows. IRR is defined as the interest rate i that will cause the net present value P to become zero. Thus, IRR 324 4 Availability and Maintainability in Engineering Design is the value i such that P(i)= N ∑ t=0 Y t (1+ i) −t = 0 . (4.14) The IRR must be found by trial and error or by a computer search algorithm tech- nique, since it is an unknown root (or roots) of a polynomial in i. Thus, if we start with known values of each cash flow, we can possibly find one or more values that will make the above equation tru e. These values, if they exist as real numbers, are known as the project’s internal rate of return,ortheeconomic yield of the project (in contrast to the economic loss consid ered previously). The selection criterion is to accept the design project if the IRR is greater than the ma rginal investment rate; otherwise, the p roject is rejected or, as in the case of a negative NPV, the result is the redesign of critical systems or the rejection of the project’s specific technology, rather than of the pro ject itself. Internal rate of return (IRR) has long been advocated as a project acceptance cri- terion because, in this criterion, the interest rate is the unknown value that relates project returns to capital investment outlays. In the sense that it is the functional value to be established by the expected cash outlays and inflows of the project itself, it has been called the internal rate of return. However, in many cases, the economic meaning of IRR as a selection criterion of a design project or proposed engineered installation is not fully understood.For example, the IRR is not only the interest rate that causes the net present value of the cash flow of a project to be zero, but it is also the interest rate that causes exact recovery of investment over the life of the project, plus a return on the un-recovered investment balances during the life of the project. A common misinterpretation of IRR is that it is an interest rate expressing a rate o f return on the initial investment. This is not so. If the IRR is applied periodically to the initial investment only, then the cash flows fail to recover the initial investment plus interest at the end of the project life. The fundamental economic meaning o f IRR is the rate of interest earned on the time-varying, un-recovered balances of in- vestment, such that the final investment balance is zero at the end of the project’s life. Since the IRR does not measure the return on initial investment, it has meaning only when the level of investment is considered along with all the other cash flows of the project, relative to the project’s total life-cycle costs. These are estimated total costs incurred in the design, development, production, operation, maintenance, sup- port and final disposition of the proposed engineered installation over its anticipated useful life (Aslaksen et al. 1992). Internal rate of return as a figure-of-merit Under the assumptions of certainty, it is sometimes possible to use internal rate of return as a figure-of-merit for de- termining whether a particular design project should be undertaken. It could thus be viewed as an economic trade-off measure to assess the conditions under which the IRR may be used as a selection criterion, and when it may not. One of the main problems encountered in using IRR as such a criterion is the concept of multiple and indeterminate rates of return. When attempting to obtain the internal rate of return with certain forms of cash flow, it is possible to find either that a unique so- lution does not exist for the IRR, and more than one interest rate will satisfy the 4.2 Theoretical Overview of Availability and Maintainability in Engineering Design 325 formula, or that no solution can be found at all. When more than one solution exists mathematically, the cash flow is said to yield multiple rates of return and, when no solution exists, it is said to have an indeterminate rate of return. e) Trade-Off Measurement for Life-Cycle Costs LCC needs to be calculated early in the engineering design stage, to influence final design outcomes of the proposed engineered installation. Making major changes in LCC after engineering design projects reach the production stage is often not possible. LCC helps d etermine optimal maintenance and repair shutdown cycles of inadequately assessed engineering installations subject to frequent repair at great expense. Sufficient financing is seldom available to design the project correctly but, somehow, there is always money available to make major modifications to poorly configured engineering design installations (Barringer 1998). Consequently, trade- off measurement methods for LCC early in the life cycle become essential. The cost effectiveness (CE) equation is one method for LCC trade-off calculations involv- ing operational and failure probabilities. It offers a figur e-of-merit, and measures the chances of achieving the intended final design results against predefined life- cycle costs. The effectiveness equation has been described in several different f or- mats (Aslaksen et al. 1992; Kececioglu 1995; Pecht 1995; Blanchard et al. 1995). Each element is a probability. The issue, however, is finding a system effective- ness value that gives lowest long-term cost of ownership with trade-off considera- tions. Cost effectiveness and life-cycle costs Cost effectiveness (CE), as viewed from a systems engineeringperspective,can be defined as the ratio of system effectiveness (SE) to its life-cycle cost (LCC; Aslaksen et al. 1992), which is expressed in the following relationship CE = SE LCC . (4.15) In this context, SE is expressed in dollars; so, CE will be a dimensionless parameter. It is apparent that the evaluation of CE cou ld be separated into the evaluation of SE and the evaluation of LCC. The definition therefore leads to a conceptually simple, universal criterion governing all engineering decisions—the decision is good if it results in an increase in cost effectiveness. This criterion is appropriate for engi- neering decisions—however, it may not always be entirely suitable for investment decisions, and there is a significant d ifference between cost effectiveness and IRR as a figure-of-merit. System effectiveness System effectiveness (SE) can be defined as a measure of how well a system will perform the functions that it was designed for, or how well it will meet the requirements of the system specification. It is often expressed as the prob- ability that the system can successfully meet an operational d emand within a g iven operating time under specified conditions. This definition implies a number of im- portant aspects: 326 4 Availability and Maintainability in Engineering Design • Operating time may be critical, and SE is often a function of time. • Maintenance is not excluded; and the specified conditions will in most cases include both scheduled and unscheduled shutdowns. • Operational demand implies that there aretwo separate classes ofsystem failures: – The system can be in an inoperable condition when needed. – The system can fail to perform sufficiently during the required operating pe- riod. • The inclusion of both operational demand and specified conditions shows that possible failure (i.e. failure to meet operationaldemand)and the conditions under which the system is intended to be utilised (i.e. operationa l stresses) are related. It thus follows that, while SE is obviously influenced by system design, it is equally influenced by the way the system will be used and maintained b y the logistic system that supports its operation. The definition expressed in terms of a probability is par- ticularly useful for systems that are required to operate for a prescribed, relatively short period (i.e. systems fulfilling an intermittent task, as is the case for periodic operational requirements). For most other systems, however, the period of opera- tion is the lifetime of the system, and this is usually very long, compared with the timescales for other events affecting the system, such as shutdowns, etc. As a result, the system settles into a steady state that is characterised by an aver- age performance or, more specifically, by an average deviation from design specifi- cation performance. However, as the performance of a system is usually a complex multi-dimensional variable, measuring it in terms of a probability is not very appro- priate. The proper approach is to determine the decrease in the value of the system as a function of the decrease in performance. The definition of SE can thus be for- mulated as th e value of the system over its design lifetime (Aslaksen et al. 1992). Factors affecting the value o f a system: Every system has some value—otherwise, its development would not even be contemplated. Furthermore, this value must in some way depend on how well the system performs; if it did not perform at all, its value would be zero. The problem arises in tryin g to move from a qualitative state- ment, such as ‘improved availability’, to a quantitative statement such as ‘incr ease in availability from 0.85 to 0.90 is worth $3.285 million’. It is then found that the value of a system, particularly its dependence o n various performance parameters, is often a highly subjective matter. Nevertheless, it is a problem that must be solved because, without assigning some value to system performance, there is no basis for taking rational engineering decisions with respect to its cost effectiveness. Design effectivenessand life-cycle costs Design effectiveness (DE) for LCC trade- off calculations involves probabilities of design integrity criter ia (i.e. reliability, availability, maintainability and safety) offering a figure-of-merit that measures the chances of achieving the intended final design results against integrity constraints (Blanchard et al. 1995). Such an effectiveness equation is of the following format Design effectiveness (DE) = System effectiveness (SE) Life-cycle costs (LCC) . (4.16) 4.2 Theoretical Overview of Availability and Maintainability in Engineering Design 327 LCC in this case is a measure of resource usage that cannot include all possible cost elements but must include critical cost items. System effectiveness System effectiveness in this case is a measure of integrity (although it rarely includes all integrity elements, as many are often too difficult to quantify). Based on probability, it varies from 0 to 1. Thus: System effectiveness = Design integrity×Capability . Design integrity is reliability/availability/maintainability/safety, and capability is product of efficiency multiplied b y utilisation. System effectiveness quantifies important elements of design integrity and life- cycle costs to find areas for improvement to increase overall effectiveness and to reduce economic loss. For example, if availability is 98% and capability is 65%, the opportunity for im- proving capability is usually much gr eater than for improving availability. System effectivenessin this contextis helpful for understandingbenchmarksand future pos- sible status for LCC trade-off information. Figure 4.6 gives a graphical presentation of effectiveness and life-cycle costs. Although the preference is to select engineer- ing designs, or projects that have low life-cycle costs and high effectiveness, this may often not be accomplished in reality (Barringer 1998). Capability deals with productive output compared to inherent productive out- put. This index measures the systems capability to pe rform the intended function on a system basis, and can be expressed as the product of efficiency multiplied by utilisation. Efficiency measures the expected productive work output versus the work input. Utilisation is the ratio of expected time spent on productive effort to the total operational time. For example, suppose efficiency is estimated at 80% and utilisation is 82.19% because the operation is conducted 300 days per year out of 365 days: the capab ility is 0.8×0.8219= 65.75%.Capability measures how well the Parameter Effectiveness LCC New Plant Last Plant Last Plant Best Plant Last Plant New Plant Best Plant A 0.95 0.3 0.7 0.7 0.14 80 0.95 0.4 0.7 0.8 0.22 100 0.98 0.6 0.7 0.6 0.25 95 BC Availability Reliability Maintainability Capability Effectiveness LCC Trade-off Area Worst Best A C ? ? B Fig. 4.6 Design effectiveness and life-cycle costs (Barringer 1998) 328 4 Availability and Maintainability in Engineering Design production activity is performed compared to the datum (Barringer 1998). A more comprehensive and, in fact, mathematically cor rect definitio n of process capability is considered in Sect. 4.2.1.2. Availability and maintainability compared to IRR as figure-of-merit for LCC Putting aside the elements of reliability and safety in the design integrity equation in this chapter, the sign ificance of availability and maintainability in design effec- tiveness and life-cycle costs is specifically considered. Availability deals w ith the duration of uptime for system s and e quipment. Availability characteristics are usu- ally determined by the expected operational conditions, which then impact upon operational procedures and the expected durations of productive time. Availability measures how productive time is used. Thus, as availability increases, because the systems and equipment are functional and operational for a longer period of time, so also does the potential for an increase in the IRR. Maintainability deals with the duration of downtime for maintenance outages, or how long it takes to complete maintenance actions compared to a standard. Main- tainability characteristics are usually de termined by engineering design, which then impacts upon maintenance procedures and the expected durations of shutdowns. A key maintainability figure-of-merit is the mean time to repair (MTTR) c ompared to a limit for th e maximum repair time. Qualitatively, it refers to the ease with which systems and eq uipment are restored to a functioning state. Quantitatively, it is a probability measure based on the total downtime for maintenance. Maintain- ability measures the probability of timely repairs. Thus, as maintain abilityincreases, because systems and equipment are down for a shorter period of time, so also does the potential for increase in the IRR. 4.2.1.2 Availability Modelling Based on System Performance System performance, in the context of designing for availability, can be perceived as the combination of a system’s process capability with regard to the process char- acteristics of capacity, input, throughput, output and quality, a system’s functional effectiveness with regard to the functional characteristics of efficiency and utilisa- tion, as well as consideration of a system’s operational condition with regard to operational measures such as temperatures, pressures, flows, etc. All these charac- teristics may serve as useful indicators in designing for availability without having to formulate the specific operational variables of each individual system,andto consider instead a system’s capability, effectiveness and condition. In order for designers to be confident about using novel manufacturingprocesses, and still achieve the necessary availability constraints during the design of engi- neered installations, a more intimate dialogue between engineering design and man- ufacturing is necessary. Ideally, all aspects of the manufacturing process should be accessible and understood. For example, designers should be able to run process simulations, at either a superficial or detailed level, on partial or whole designs. D e- sign engineers should be able to obtain ‘manufacturability’ and ‘constructability’ 4.2 Theoretical Overview of Availability and Maintainability in Engineering Design 329 rules and guidelines that can be loaded directly into the relative engin eering de- signs’ computer aided design (CAD) environments. Furthermore, design engineers should be able to load processing constraints (e.g. materials or feature dimensions) into their CAD systems and have these checked and enforced before submitting de- signs to manufacturers. In this way, designers can become familiar with the design’s specific manufacturing and construction requirements. In some cases, an overview description of the process capabilities may suffice. In other cases, when it is es- sential to minimise manufacturing costs, or to meet stringent demands on design specifications or material properties, the d esigner must have detailed information on the specific design’smanufacturing characteristics and constraints. An important aspect of being able to submit designs with confidence that the end result will meet design specifications is the adoption of conservative design rules that specify design features that are manufacturable (Mead 1994). A variety of CAD tools can be used that provide a standard mechanism by which designers can obtain process capability models from disparate processes, and load these into their CAD environments. Specifically, the mechanism should enable de- signers to acquire capability models that can be used to compute a system’s process capability, functional effectiveness, operational condition and manufacturability of evolving designs with accuracies necessary to meet the design requirements. (In this context, ‘manufacturability ’ includes both the ease of fabrication and the ease of assembly/construction, as considered by Taguchi’s methodology for implementing rob ust design; Taguchi 1993.) Robust design (RD) is an important methodology for improving the design’s manufacturability and for increasing process system stability. Since its introduction to the US industry in 1980, Taguchi’s approach to quality engineering and robust design has received much attention from designers, manufacturers, statisticians, and quality professionals. Essentially, the central idea in robust design is that variations in a process sys- tem’s performance can inevitably result in poor quality and monetary losses during the system’s life cycle. The sources of these variations can directly be classified into the two categories of controllable and uncontrollableparameters. In a typical design application, factors such as geometric dimensions (sizing) of equipment can easily be controlled by designers. Uncontrollable factors, such as environmental variables, component deterioration or manufacturing imperfections, are also sources of vari- ations having effects that cannot be eliminated, and must especially be considered in designing for availability. Therefore, RD’s main function is to reduce a design’s potential variation by reducing the sensitivity of the design to the sources of vari- ation, rather than by controlling these sources. In oth er words, RD reduces poten- tial system response variations by designing appropriate capability model settings for controllable parameters, in order to dampen the effects of hard-to-control vari- ables. Taguchi’s methodology for implementing robust design is essentially a four- step procedure that includes not only formulating the design problem but planning, analysing and verifying the design results as well (Taguchi et al. 1989). A communication mechanism should also allow unsolicited information, such as updates on process capabilities, to be transmitted from manufacturing facilities 330 4 Availability and Maintainability in Engineering Design to designers. To enable such a dialogue between designers and manufacturers, the following issues must be addressed: • How is process capability or func tional effectiveness represented? • How are capability models located and acquired by the designer? • How are capability models mapped into the design space? • How is information contained in these models applied throughout engineering design? These issues require some further form of methodology for information exchange, not only between engineering design teams but also between designers and manu- facturers. Such a methodology should include an object-oriented architecture that expedites the task of combining CAD environments with process manufacturing and/or construction planning, a mechanism for knowledge representation that en- ables the exchange of design integrity information, and a communication protocol between designers and manufacturers. Such a methodology addresses the possible and practical application of artificial intelligence (AI) modelling techniques, with the inclusion of knowledge-based ex- pert systems within a blackboard model, in the development of intelligent computer automated methodology for determining the integrity of engineering design. The blackboard model provides for automated continual design reviews of engineering design, including communication protocols and an object-oriented language that al- lows segregate design groups to remotely exchange collaborative information via the internet (McGuire et al. 1993; Olsen et al. 1995; Pancerella et al. 1995). On this basis, different engineering design expertise groups, and manufacturing companies specialising in specific engineering systems can concurrently participate in collaborative design from around the world, whereby input of design parameters and criteria into a blackboard model provides for automated continual design re- views of the overall engineering design. Such a blackboard model, together with its knowledge-based expert systems, must be suitable both in programming language efficiency and in communication protocols for internet application. a) Process Capability In the context of industrial processes, the definition of process is “a series of op- erations performed to produce a result or product”, and capability is defined as “effective action”. Process capability can thus be defined as “the effective action of a series of operations to produce a result or product”. A process capability model is a m athematical model that compares the behaviour of a process characteristic to engineering specifications. A process capability index is a numerical summary of th e model, also called a capability or performance in- dex or ratio, where capability index is used as the generic term. A capability index relates design specification limits to a particular process characteristic. The index indicates that the process is capable of producing results that, in all likelihood, will meet or exceed the design’s requirements. A capability index is convenient because 4.2 Theoretical Overview of Availability and Maintainability in Engineering Design 331 it reduces complex information about the process to a single number. Capability in- dices have several applications, though the use of the indices is driven mostly by monitoring requirements specified by design criteria. Many design engineers require manufacturers to record capability indices for all the design’s process characteristics on a heuristic basis. The indices are used to in- dicate how well the process may perform. For stable or predictable processes, it is assumed that these indices will also indicate expected future performance. Suppli- ers or manufacturers may use capability indices for specific system characteristics to establish priorities for improvements after installation. Sim ilarly, the effects of process change can be assessed by comparing capability indices that are calculated before and after the change. However, despite the widespread use of capability in- dices in industry, and some good review articles (Gunter 1989a, b, c, d), there is much confusion and misunderstanding regarding their interpretation and appropri- ate use, particularly as a tool for comparing process characteristic to engineering specifications in designing for availability. Process capability in quantified terms is the ratio of the deviation of a process characteristic from the specification limit, divided by a measure of a process char- acteristic’s variability. Process capability can be r epresented in mathematical terms as (Steiner et al. 1995): Process Cap ability = min USL− μ 3 σ μ −LSL 3 σ (4.17) where: USL and LSL are the upper and lower specification limits respectively, μ and σ are the mean and standard deviation respectively for measures of the process characteristic of interest. Calculating the process capability requires knowledge of the process characteristic’s mean and standard deviation, μ and σ . These values are usually estimated from trial or test data collected from a pilot process. The two most widely used capability indices, P pk and C pk , are defined as Capability P pk = min USL− ¯a 3 σ ¯a−LSL 3 σ (4.18a) where: USL and LSL are the upper and lower specification limits respectively, ¯a the overall average, is used to estimate the process m ean μ and σ , σ is the stand ard deviation of the process characteristic of interest. Capability C pk = min USL− ¯a 3 σ Rd ¯a−LSL 3 σ Rd (4.18b) where: ¯a the overall average, is used to estimate the process mean μ and σ , σ Rd is the estimate o f the process standard deviation σ , 332 4 Availability and Maintainability in Engineering Design d is an adjustment factor that is needed to estimate the process standard deviation from the average trial or test data sample range R. The sample standard deviation is given by the formula σ = n ∑ j= 1 m ∑ i=1 (X ij − ¯a) 2 /(nm−1) (4.19) where: m is the total number of subgroups, and n is the subgroup sample size. Since d is also used in the derivation of control limits for X and R control charts, it is also tabulated in standard references on statistical process control, such as in the QS-9000 SPC manual (Montgomery 1991). Large values of P pk and C pk for several specific process characteristics should correspondto a processthat is capable of operating within the design specification limits. The commonly used index P p and the related index C p in process design are similar to P pk and C pk .However,P p and C p ignore the current estimate of the process characteristic mean, and relate the specification range directly to the process characteristic variation. In effect, P p and C p can be considered convenient conceptual design measures that suggest how capable the process should be if the process characteristic’s mean is centred midway between the specification limits. The indices P p and C p are not recommended for process evaluation purposes dur- ing the detail design phase, since the information they provide to supplement P pk and C pk is independent of data. Histograms of trial or test data collected from a pilot process, usually established during the detail design phase of the engineeringdesign process, are preferable because they also provide other useful process information. However, various important issues relating to the calculation and interpretation of capability indicesrequire closer attention. The designcapability of a process is even- tually estimated from pilot trial or test data that represent a sample of the envisaged total production. Clearly, the capability indices P pk and C pk are greatly influenced by the way in which the process data are collected, what is normally called the process view. A process view is defined by the time frame and sampling method (sampling fre- quency, sample size, etc.) u sed to obtain the pilot process data. Using an appropriate process view is crucial, since different views can lead to very different conclusions. For example, in one view the process may appear stable, while in another the pro- cess could appear unstable. To define the process view, the first choice involves the time frame over which the pilot process data will be collected. Often, the time frame is stipulated as a typical cycle-time in terval. For example, the capab ility of each se- lected process characteristic may be measured as a function of the operating time in relation to the process cycle-time. In other situations, the time frame is restricted to a shorter interval, such as the period needed for the pilot process to produce a specific number of productionunits. . trade- off calculations involves probabilities of design integrity criter ia (i.e. reliability, availability, maintainability and safety) offering a figure -of- merit that measures the chances of. LCC trade-off calculations involv- ing operational and failure probabilities. It offers a figur e -of- merit, and measures the chances of achieving the intended final design results against predefined. 1992). Internal rate of return as a figure -of- merit Under the assumptions of certainty, it is sometimes possible to use internal rate of return as a figure -of- merit for de- termining whether a particular