Mechanical properties of various alloys and metals used in implants [13, 14].
\r\n\tThe applications are those related to intelligent monitoring activities such as the quality assessment of the environmental matrices through the use of innovative approaches, case studies, best practices with bottom-up approaches, machine learning techniques, systems development (for example algorithms, sensors, etc.) to predict alterations of environmental matrices. The goal is also to be able to protect natural resources by making their use increasingly sustainable.
\r\n\r\n\tContributions related to the development of prototypes and software with an open-source component are very welcome.
\r\n\r\n\tThis book is intended to provide the reader with a comprehensive overview of the current state of the art in the field of Ambient Intelligence. A format rich in figures, tables, diagrams, and graphical abstracts is strongly encouraged.
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From chapter submission and review, to approval and revision, copyediting and design, until final publication, I work closely with authors and editors to ensure a simple and easy publishing process. I maintain constant and effective communication with authors, editors and reviewers, which allows for a level of personal support that enables contributors to fully commit and concentrate on the chapters they are writing, editing, or reviewing. I assist authors in the preparation of their full chapter submissions and track important deadlines and ensure they are met. I help to coordinate internal processes such as linguistic review, and monitor the technical aspects of the process. As an ASM I am also involved in the acquisition of editors. 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Venkateswarlu",coverURL:"https://cdn.intechopen.com/books/images_new/371.jpg",editedByType:"Edited by",editors:[{id:"58592",title:"Dr.",name:"Arun",surname:"Shanker",slug:"arun-shanker",fullName:"Arun Shanker"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"878",title:"Phytochemicals",subtitle:"A Global Perspective of Their Role in Nutrition and Health",isOpenForSubmission:!1,hash:"ec77671f63975ef2d16192897deb6835",slug:"phytochemicals-a-global-perspective-of-their-role-in-nutrition-and-health",bookSignature:"Venketeshwer Rao",coverURL:"https://cdn.intechopen.com/books/images_new/878.jpg",editedByType:"Edited by",editors:[{id:"82663",title:"Dr.",name:"Venketeshwer",surname:"Rao",slug:"venketeshwer-rao",fullName:"Venketeshwer Rao"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"4816",title:"Face Recognition",subtitle:null,isOpenForSubmission:!1,hash:"146063b5359146b7718ea86bad47c8eb",slug:"face_recognition",bookSignature:"Kresimir Delac and Mislav Grgic",coverURL:"https://cdn.intechopen.com/books/images_new/4816.jpg",editedByType:"Edited by",editors:[{id:"528",title:"Dr.",name:"Kresimir",surname:"Delac",slug:"kresimir-delac",fullName:"Kresimir Delac"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"3621",title:"Silver Nanoparticles",subtitle:null,isOpenForSubmission:!1,hash:null,slug:"silver-nanoparticles",bookSignature:"David Pozo Perez",coverURL:"https://cdn.intechopen.com/books/images_new/3621.jpg",editedByType:"Edited by",editors:[{id:"6667",title:"Dr.",name:"David",surname:"Pozo",slug:"david-pozo",fullName:"David Pozo"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}}]},chapter:{item:{type:"chapter",id:"73479",title:"Dental Implants",doi:"10.5772/intechopen.91377",slug:"dental-implants-1",body:'Modern dentistry aims to restore a patient’s oral esthetics, contour, function, and speech. Depending on the patient’s needs, the total treatment may range from treating a single tooth with caries to restoring edentulous arches with severe bone resorption.
Implant dentistry has made predictable success a reality for cases in the more difficult part of this spectrum through research, improvements in diagnostic tools, techniques, implant materials, and designs. Endosteal implants are manufactured materials inserted in edentulous ridges via surgery so they can serve as a foundation for the prosthesis [1]. Most implants that will be discussed in this chapter will be root form implants which mimic the root shape of a tooth.
The desire to restore lost teeth is not a new concept. Dental implant surgery is one of the oldest practices in dentistry second only to tooth extractions. There is archeological evidence that humans have attempted to replace missing teeth with root form implants for thousands of years. Remains from ancient China dating 4000 years ago have carved bamboo pegs, tapped into the bone, to replace lost teeth, and 2000-year-old remains from ancient Egypt have similarly shaped pegs made of precious metals. Some Egyptian mummies were found to have transplanted human teeth, and in other instances, teeth made of ivory [2]. Central American Incas tapped seashells in bone similar to the Chinese [3].
In 1809, Maggiolo introduced root shaped gold implants followed by Harris introducing porcelain teeth supported by lead-coated platinum posts [4, 5]. Gold, magnesium, copper, brass, aluminum, silver, and soft steel plated with nickel and gold was used to fabricate implants by Lambotte in 1900s [6]. Corrosion of most of these metals by body tissues was observed which in return caused electrolytic action. In 1909, Greenfield introduced an implant in the form of a cylindrical lattice-cage which differed substantially from the root form implants [7]. A calibrated cylindrical bur was used for the osteotomy to preserve an inner core of bone within the implant. This was also the first design which separated the endosteal implant from the abutment which was to be connected on the implant weeks later through an internal attachment after healing. In 1940, Bothe described a titanium implant and bone interface as bone fusing [8]. The first two-piece titanium screw-type implant was designed in 1946 by Strock [9]. The direct implant-bone interface desired by Strock was called ankylosis.
Brånemark’s studies in bone marrow healing in 1952 led to dental implant application in dogs in early 1960s, and implant integrations in bone were achieved without adverse reaction in surrounding tissues. Implant applications in humans with Brånemark philosophy were started in 1965, and 10-year results were published in 1977 [10]. Osseointegration, which has become the term used today for implants instead of ankylosis or bone fusing, was defined by Brånemark as a direct contact between the implant surface and living bone that can be observed through a light microscope [11].
Through advances in material sciences, manufacturing processes, research, and clinical studies, the usage of dental implants have become an essential part of contemporary restorative dentistry.
Majority of the dental implants to date have been fabricated from metals and alloys. American Society for Testing and Materials and International Standards Organization have created guidelines for standardizing implant materials [12, 13].
Titanium and its alloys are the most widely used materials for dental implants [14]. This metal group forms retentive oxides in contact with room temperature air or solutions containing oxygen such as tissue fluids. This provides an advantage since this titanium oxide surface minimizes biocorrosion. In the case of an oxide surface becoming scratched or removed during implant placement into bone, the surface reoxidizes in the bone tissue. This regenerative biocorrosion preventing layer is one of the reasons for the wide use of titanium in dental implants [15].
Bothe et al. reported bone growth in contact with titanium surfaces in rabbits [8]. Several researchers studied and expanded the indications for use of titanium in implant devices. The reason reported is titanium’s non-reactive nature and its resilience to corrosion [16, 17]. General properties of alloys and metal used in implant fabrication are detailed in Table 1 [12].
Nominal analysis (w/o) | Modulus of elasticity GN/m2 (psi μ 106) | Ultimate tensile strength MN/m2 (ksi) | Elongation to fracture (%) | |
---|---|---|---|---|
Titanium | 99+Ti | 97 (14) | 240–550 (25–70) | >15 |
Titanium-aluminum-vanadium | 90Ti-6Al-4V | 117 (17) | 869–896 (125–130) | >12 |
Cobalt-chromium-molybdenum (casting) | 66Co-27Cr-7Mo | 235 (34) | 655 (95) | >8 |
Stainless steel (316 L) | 70Fe-18Cr-12Ni | 193 (28) | 480–1000 (70–145) | >30 |
Zirconium | 99+Zr | 97 (14) | 552 (80) | 20 |
Tantalum | 99+Ta | — | 690 (100) | 11 |
Gold | 99+Au | 97 (14) | 207–310 (30–45) | >30 |
Platinum | 99+Pt | 166 (24) | 131 (19) | 40 |
The titanium alloy with the most widespread use is titanium-aluminum-vanadium. This alloy has approximately six times the strength of compact bone, and as a result, thinner structural parts can be incorporated into the implants without risking breakage or cracking. The alloys modulus of elasticity is 5.6 times greater than compact bone. Several studies have investigated and documented the titanium oxide layer on both pure titanium and its alloy which can vary depending on surface properties [18]. The techniques for casting titanium and alloys are limited because of high melting points and high chance of hydrogen, nitrogen, and oxygen absorption. Different purity levels can be achieved through an ultrapure protective gas environment or a high vacuum [18].
This alloy is made up of cobalt, chromium, and molybdenum. Alloys containing cobalt are usually used as they are cast and are sometimes additionally annealed. This allows custom designs otherwise unachievable. The named elements with minor additions of nickel, manganese, and carbon provide strength four times greater than compact bone and chromium provides resistance to corrosion. These concentrations are critical so the fabrication processes must be carefully controlled and followed. Cobalt-based alloys are the least ductile of the ones used in dental implants [12]. Excellent biocompatibility has been observed with implants from cobalt-based alloys when they are manufactured properly.
Stainless steel alloys are one of the oldest materials to be used in the medical field. The alloy is most often used in a wrought and heat treated condition, same as titanium alloys, which gives the material high strength and ductility. Among all alloys used in implant fabrication steel alloys are the ones most susceptible to biocorrosion so the applied oxide surface must be protected. Another concerning aspect of iron-based alloys are galvanic potentials. If a steel-based implant abutment contacted a bridge containing a noble metal, for example, a circuit would be formed. This would not be a cause of concern if these units function without contact [19, 20].
Several other metals been used in implant manufacturing. Notably, among these, gold and platinum have been evaluated but the low strength of these materials limit implant design.
Ceramics are non-metal, non-polymer, inorganic materials. Oxide ceramic dental implants were fabricated to make use of their resistance to biodegradation, strength, color, low conductivity, and elastic properties [21, 22]. Despite their low ductility and brittle nature, ceramics are being used both as coatings on other materials and in bulk form.
Main properties of these materials are listed in Table 2 [12]. High strength oxide ceramics have been used as several implant forms including root form implants [23]. Ceramics have approximately 3–5 times the strength of compact bone. Creating a different implant design for these materials is necessary because of their high strength and high modulus of elasticity. Metallic oxide ceramics generally have a white hue of color which makes them a viable option for implants in the esthetic area in cases where gingival recession leaves implants visible. When compared with other materials, minimal reactivity with oral tissues paired with low electrical and thermal conductivity are notable benefits.
Modulus of elasticity GN/m2 (psi μ 106) | Ultimate bending strength MN/m2 (ksi) | Elongation to fracture (%) | Surface | |
---|---|---|---|---|
Polycrystalline aluminum oxide | 372 (54) | 300–550 (43–80) | 0 | Al2O3 |
Single crystal aluminum oxide (sapphire) | 392 (56) | 640 (93) | 0 | Al2O3 |
Zirconium oxide zirconia (PSZ) | 195–210 (28–30) | 500–650 (72–94) | 0 | ZrO2 |
Titanium oxide (titania) | 280 (41) | 69–103 (10–15) | 0 | TiO2 |
As with titanium implants, bone growth directly adjacent to the implant surface has been observed. Going a step further, areas of bonding have been reported in gingival attachment zones of sapphire dental implants in animal studies [24, 25, 26]. There are also special requirements for sterilization of metallic oxide ceramic implants. Since steam and chemical solutions can lead to micro weaknesses which can lead to fractures or leftover residues; dry heat is the best choice for sterilization of ceramics. Their improved strength and excellent biocompatibility make ceramics a viable choice as an implant material.
First implants manufactured from CPCs aimed to reduce bone resorption after tooth extractions by filling the bone socket with cone-shaped implants [27]. The materials limited strength led researchers to either reinforcing the material internally with metal parts or to coat other materials with CPCs [28]. Out of these techniques, coating metal implants via flame or plasma spraying was more widely used with the intent of making metal implants more biocompatible [29].
The advantages of the application are the materials chemical similarity to living tissues, biocompatibility, and low conductivity which means it can act as a barrier to metallic ion transport between bone and metal implants. Disadvantages are its low strength and the materials possibility to dissolve or alter in time. Main properties of these materials can be found in Table 3 [12]. Generally, bioceramics are characterized by lower hardness, strength, and elasticity modulus than ceramics like zirconia or aluminum oxide. Overall, CPCs are one of the most widely accepted, studied, and used biomaterials developed in the last decades and could find its applications expanding further as future implant surfaces as they evolve themselves through technology and research [30].
Modulus of elasticity GN/m2 (psi μ 106) | Ultimate bending strength MN/m2 (ksi) | Elongation to fracture (%) | Surface | |
---|---|---|---|---|
Hydroxyapatite | 40–120 (6–17) | 40–300 (6–43) | 0 | Ca10(PO4)6(OH)2 |
Tricalcium phosphate | 30–120 (4–17) | 15–120 (2–17) | 0 | Ca3(PO4)2 |
Bioglass or Ceravital | 40–140 (6–20) | 20–350 (3–51) | 0 | CaPO4 |
Carbon | 25–40 (4–6) | 150–250 (22–36) | 0 | C |
Carbon-silicon (LTI) | 25–40 (4–6) | 200–700 (29–101) | 0 | CSi |
Carbon and carbon silicon materials are regarded as ceramics for their non-reactive nature, but they conduct electricity and heat. Its elasticity is close to bone, and it is a biocompatible material. Clinical trials of carbon-based dental implants were carried out. Limitations in material properties, design, and applications led to clinical failures in trials which resulted in withdrawal of carbon-based materials in dental implant designs.
Implant surgery begins with an incision on the edentulous ridge and flap elevation to expose the alveolar bone. At the end of the surgery, the same flap will be sutured and a primary wound healing of masticatory mucosa will follow. If a submerged (placed under oral mucosa level) implant is being used, a recovery surgery will be performed after a period of healing. If a non-submerged (placed on the same level as oral mucosa) implant is being used, no recovery surgery is necessary.
Most implant systems available today allow creation of a recipient intrabony site for implant placement via rotary instruments. A tight fit is crucial for primary stabilization of the implant and for preventing soft tissue from penetrating the gap between the implant and the bone, effectively preventing the implant osseointegration.
Most important negative influence of the surgery stage can be creation of excessive heat with rotary instruments. It has been shown that bringing of the temperature of bone to 47°C for 1 minute is enough to kill osteogenic cells which can compromise necessary healing. As a safety measure, several sharp drills must be used at low speeds with low hand pressure and proper irrigation for cooling the site [31].
Following surgery if no infection or inflammatory response takes place to prevent healing, primary wound healing defines the long-term properties of surrounding tissues. Regardless of the dental implant material, the general outcome of bone healing around an implant is osseointegration which is defined by Brånemark as “a direct structural and functional connection between ordered, living bone and the surface of a load-carrying implant [11].” Throughout several weeks of healing, woven bone which forms during early stages of healing starts to become more compact lamellar bone. This formation can be observed both from the cut bone and from the implant surface [32].
Titanium’s corrosion rate in tissues is well documented [33]. In older studies, the presence of titanium has been detected in peri-implant tissues and internal organs, presumed to be caused by corrosion, mechanical wear, and peri-implant inflammation, but the compositions of the implant alloys were not strictly controlled, and in same studies, the diffusion is very slow and since titanium has little to no toxicity, it should be considered biocompatible [34, 35]. In a recent study, titanium particles have been detected in healthy and inflamed mucosa and even in patients with no titanium implants [36]. The increased amount of particles is likely the effect of the inflammation rather than its cause. Since then, higher strength alloys of titanium have emerged [37]. Recently, applications of these materials have been successful and have not resulted in significant negative effects. Titanium allergy has been studied and is known to be rare, but research is insufficient to give an accurate incidence rate [38].
The oxide surface of titanium as previously discussed exists through reacting with oxygen at normal temperatures and will rapidly reform if removed mechanically. It minimizes biocorrosion in tissues [15]. The oxide layer consists of mostly TiO2 and to a lesser degree Ti2O3 and TiO [39]. While in normal temperatures, the oxide layer is less than 20 nm in thickness, when processed at high temperatures or anodized at high voltages, the layer can be 10–100 times thicker in a crystalline structure [40]. The macro and micro architecture of dental implants achieved via sand blasting, acid etching, or mechanical milling has no significant effect over the thickness of the oxide layer [41]. Naturally occurring oxidants in tissues such as hydrogen peroxide has been shown to form a complex gel with titanium on a molecular level. This layer is found to have a very low toxicity, anti-inflammatory, and bactericidal properties [42].
Coating titanium implants by hydroxyapatite via plasma spraying is a method developed to help minimize ion transfer and accelerate bone formation between the bone-implant interface [43]. The disadvantages of this coating are its possibility of partial resorption during bone remodeling, after in vivo function, or in inflammation areas [44]. A recent study tested titanium and cobalt implants coated with zirconium nitride and found the product to be cytocompatible and the red color range can potentially minimize the visibility of implants under the gingiva [45].
Aluminum oxide ceramics are used as implant bulk materials one advantage is having the oxide layer properties throughout the entire body of the implant. As a result, any removal of surface has no effect on the electrochemical properties underneath the surface. Ceramic coatings aim to give the same biocompatibility advantages to metals or alloys to be coated [46]. A systematic review including six randomized controlled trials (RCTs) studied implants consisting of 85% Ti and 15% Zr found that narrow Ti-Zr implants have comparable performance to regular diameter Ti implants noting further research is necessary [47]. Some studies tested alloys consisting of Ti-Nb and found the material to be cytocompatible and a good candidate for implantology in future research due to its very low elasticity modulus [48, 49].
There have been different criteria for measuring success of dental implants. The two most commonly used in literature is survival and success. Survival of an implant states whether the implant is simply still functioning in the mouth or it has been removed. Success on the other hand is concerned with the condition of peri-implant tissues and teeth as well as patients comfort and satisfaction [50].
A systematic review evaluating 23 published articles and 7711 implants over a minimum of 10 and a mean of 13.4 years found a survival rate of 94.6% and a mean bone loss of 1.3 mm around implants [51].
An article on zirconia dental implants stated zirconium dioxide is a promising alternative for titanium, but studies found significantly more early failures compared to titanium. Technical advances and innovation are found to be promising; however, there is insufficient evidence for a final verdict at present [52]. An ITI consensus report from 2018 states one-piece zirconia implants are safe in appropriate conditions but cautions against two-piece zirconia implants due to insufficient data. Same report stated that throughout different implant loading protocols and implant materials, survival rates are above 96% [53]. A meta-analysis evaluating 17 studies reviewing clinical outcomes of zirconium dioxide implants states that the survival rate was 95% over 1–7 years of follow-up [54]. A study on properties of porous tantalum found the materials similarity to bone in terms of mechanical properties and that it has less cytotoxicity than titanium. The authors claim bone growth into the implant surface to form a unique interface pattern but state tantalums safety and performance as an implant material should be further tested [55].
The lack of long-term follow-ups for zirconia implants result in researchers advising caution and stating the information in insufficient even when high survival rates are found and zirconium dioxide implants are becoming a viable alternative to metal implants.
Titanium implants in contrast have very well-documented success with follow-ups exceeding 25 years [56]. The current research in titanium implants is not concerned of success of the material but rather its viability and applications in diabetics, smokers, patients who underwent radiotherapy or anti-resorptive drugs as well as timing of implantation and loading.
Titanium and its alloys have been widely and safely used in the field of oral implantology for 40 years. In the early years, researchers have argued that titanium is a bio-inert material, but with recent studies, it has been found that titanium degradation, as particle or ion release may penetrate surrounding tissues. This degradation can occur during implantation, during the prosthesis stage, or many years after loading, during maintenance. The surface of an implant is covered with many atomic-sized titanium oxide layers for its benefit in osseointegration and corrosion resistance. Degradation of this layer over time may cause ion release from the implant surface. The compressive and frictional forces generated during osteotomy in surgical phase may disrupt this structure and cause titanium particle release. It is also possible that the biofilm formed in the abutment-implant connection, which is the weakest component of an implant, acts as a lubricant, and thus results in micro-movement and wear on the inner surface of the implant. Finally, with the exposure of the implant surface during maintenance, chemical changes may occur on the surface of the implant with factors such as saliva and bacteria. Cleaning of implants surface with various instruments may also cause titanium release [57]. Titanium release, which may occur due to the reasons listed above, has been held responsible for peri-implant diseases such as mucositis and periimplantitis in recent years. Oliviera et al. reported that titanium particles increase osteoclast activity and cause mutational changes in cells. As a result, it was argued that titanium release from the implant surface is responsible for peri-implant tissue destruction with its cytotoxic and genotoxic effect [58]. In many studies, titanium nanoparticles phagocytosed by macrophages were found in histological examination of specimens taken from the surrounding infected tissue. In a study by Wennerberg et al., implants with moderately rough surfaces emit much more titanium than other implant surfaces. The same study argues that the titanium oxide layer oscillates more easily in additive surfaces than the surfaces formed by subtraction [59]. In the light of all this information, it is not possible to say that titanium used in dental implant applications is bio-inert. Due to the surface structure of the implant, bone density, overloading, and various many different factors, potential influences in degradation of the implant surface come in sight and harmful effects on the surrounding tissues can occur [60]. On the other hand, the peripheral organ impacts of titanium are still controversial. Although it is not possible to completely eliminate the titanium particle release, there are some ways to minimize titanium release. Today, the use of different materials that are more resistant to abrasion (such as zirconium, tantalium, etc.) has come to the fore in order to protect against the possible harmful effects of titanium.
Implant macrogeometry, which can also be defined as implant design, has been one of the most researched topics in recent years. However, before examining thoroughly into this topic, it is necessary to know the two popular hypotheses that implant success and survival are based on. The first one is the “Biological Hypothesis” which declares, marginal bone loss mostly depends on bacterial plaque and the host response. “Biomechanical Hypothesis,” which became a current factor, advocates the effect of occlusal excessive forces on the bone surrounding implants and compression, tension, and shear forces during and after osseointegration are crucial in implant survival and success. According to the biomechanical hypothesis, implant design is the key that provides primary stability of the implant and resistance of the implant to forces during and after osseointegration. Primary and secondary osseointegration degrees and durations of the implant have been correlated with macrogeometry in many studies. The reason for this fact is that implant macrogeometry affects the host-implant response [61]. According to these studies, the healing time of implants was shortened with the development of implant macrogeometries, and the possibility of immediate or early loading of implants came to the fore. Especially in recent years within the scope of macrogeometry, many studies have been examining implant abutment connection, implant neck design, and their effects on long-term preservation of crestal bone. Nowadays, the aim should be to achieve an ideal implant macrogeometry to put the implants into function in the shortest time and to ensure their long-term function. The body shape, groove design, or groove geometry (groove shape, groove spacing, groove depth, groove width, implant groove surface angle, and helix angle), prosthetic interface, and implant neck design forms the macrogeometry of an implant.
The concept of implant microgeometry was first described by Geng et al. in 2004 consists of implant surface topography, implant surface coating, and implant material [62]. In addition, Albrektsson et al. identified six factors for reliable osseointegration. Surface quality is one of the six factors that plays a key role in the host’s response to the implant.
The term implant surface refers to an outer layer of 1–2 nm which includes several outermost atomic layers different from the body material. This outermost layer is seen as the thickness of the titanium oxide layer and the structure that can be responsible for the reactions that occur on the surface. Implant surface modification can be performed in two ways by forming concave or convex surface tissue. Various methods such as sandblasting, turning, chemical and electrochemical pickling, laser application, and anodizing are used for roughening of surfaces. The amount of roughness of the resulting surface can range from nanometers to millimeters [63]. A number of studies have shown that rough surface implants have a stronger connection with bone; this structure stops the migration of epithelial attachment to the apical, thus preventing crestal bone resorption [64].
The discipline of oral implantology has come a long way from its state in 1960s. This is largely due to the rapid evolution of biomaterials discipline in 1970s. With new biomaterials and advances in surgical techniques, dental implantology is a highly successful field, consistently publishing articles reporting success rates of 90% and above over long follow-ups. Biomaterials are now manufactured and provided as sterile, standardized devices with high predictability which is essential in the field of medicine. This requirement of predictability is the reason titanium implants with widely used, well-documented surface properties are the gold standard and are the most common biomaterial of choice in dental implant devices. In recent years, zirconium implants have been rising in popularity and dependable short-term clinical outcomes look promising, but future research of long-term clinical outcomes is necessary to safely recommend and expand the indications of zirconia implants.
The authors declare no conflict of interest.
Project schedule can often be shortened by assigning excess crews (labor and equipment) to critical activities. However, the ultimate cost consequences to the project are often difficult to estimate. This schedule compression strategy may adversely impact project cost performance because the overstaffing of critical activities may result in wasted or idle time in these activities. Trade-offs between elapsed time and the associated cost of crew is required to determine the best crew configurations [1]. This is not a trivial issue because of the complex relationships between elapsed time, crew configurations, and their associated costs.
Monte Carlo simulation (MCS) has been used widely to solve probabilistic uncertainty in range estimating for projects [2]. It has been extensively used for generating many scenarios by considering the random sampling of each probability distribution. In practice, the probability of an event can be estimated according to the frequency of that event occurring in a number of experiments [3]. However, if the number of experiments is not large enough to be significant, and more experiments cannot be performed, it is not possible to accurately estimate the event’s probability. In these circumstances, we can engage human experts who are usually good at supplying the required information. Some researchers try to convert experts’ knowledge into probabilistic distributions. However, this can lead to pointless and unreliable results since the results are obtained based on experts’ subjective judgments and assumptions [4]. Fuzzy Logic has been used successfully for representing such uncertainties in experts’ judgments [5].
This research proposes a fuzzy Monte Carlo simulation (FMCS) model that provides the capability of considering fuzzy and probabilistic uncertainty simultaneously to help improve decisions regarding crew configurations.
Monte Carlo simulation (MCS), or probability simulation, is a technique used to understand the impact of risk and uncertainty cost, time, and other forecasting models [4]. MCS estimates the expected value based on historical data, or expertise in the field, or experience. While this estimate is useful for creating a model, it contains some intrinsic uncertainties, because it is an estimate of unknown values [4].
In project management, you could use expert knowledge to estimate the time it will take to complete a particular job, you can also estimate the maximum time it might take, in the worst possible case, and the minimum time, in the best possible case. The same could be done for project costs. The Monte Carlo simulation method is used for estimating the output Y of a function (M) with random input variables (R1, R2, …, Rn) (Figure 1).
The output Y of a function M with random inputs can be calculated using Monte Carlo simulation.
In a Monte Carlo simulation, an arbitrary value is selected for each of the activities, based on the range of estimates. The model is calculated based on this arbitrary value. The result of the model is recorded, and the process is repeated [6]. A traditional Monte Carlo simulation calculates the model hundreds/thousands of times, each time using different randomly selected values. When the simulation is complete, we have a large number of outcomes, each based on random input values. These outcomes are used to describe the likelihood, or probability, of reaching various results in the model [6] (Figure 2).
A probability density function (PDF) developed based on historical data.
Fuzzy logic is a technique that offers a clear conclusion from unclear and inaccurate data. The Fuzzy Set concept was first introduced by Zadeh in 1965 [7]. He was inspired by witnessing that human thinking could utilize ideas that do not have precise borders [8]. Fuzzy logic and fuzzy hybrid methods have been used to capture and model risk, thereby improving workforce and project management [8]. Fuzzy logic can effectively capture expert knowledge and engineering judgment and combine these subjective elements with project data to improve construction decision making, performance, and productivity [9]. The triangular fuzzy number (TFN) is a common shape of fuzzy logic (Figure 3). The α-cut method is a common technique to do arithmetic operations on a Triangular Membership Function [10]. The α-cut signifies the degree of risk that the project managers are ready to take (i.e., no risk to full risk). Because the value of α could significantly affect the solution, it should be wisely chosen by project managers [11].
Triangular fuzzy set developed based on experts’ judgment.
The proposed FMCS is a joint propagation method based on both the probability theory of MCS and the possibility theory of fuzzy arithmetic. A generalized problem in which we have both types of uncertainty, fuzzy and probabilistic. Here, we need to determine the output Y of a function (M) that has R1, R2, …, Rn being random variables and represented by probabilistic distributions and F1 (triangular values), F2 (triangular values), …, Fm being fuzzy sets (Figure 4).
Converting fuzzy sets to PDF before performing Monte Carlo simulation.
The first stage of the model is to defuzzify the fuzzy variables to get crisp values. The centroid method is one of the most common methods for defuzzification, in which the defuzzified value is calculated by finding the center of the area under the membership function.
The second stage of the model is to transfer the crisp sets of numbers that we got in step one to random variables. To that, the confidence level of the intervals is estimated using the probability of that interval. This probability is equal to the area under the PDF that is bounded within that interval. Among different intervals of the same confidence level, the most informative interval is the one with minimal length [8].
The third stage of the model is to use an optimization algorithm for finding a set of optimal values minimizing or maximizing the given object function [MIN F(X) or MAX F(X)] subjected to minimum-maximum intervals. Then, the uncertainty quantifications propagated using the obtained optimal values are represented as a plausibility distribution and a belief distribution. Figure 5 shows Fuzzy Monte Carlo simulation (FMCS) process.
Fuzzy Monte Carlo simulation (FMCS) process.
To illustrate an implementation of the FMCS model, the researcher analyzes the behavior of FMCS framework in comparison with traditional Monte Carlo simulation using a time range estimating example. Consider a sample application by [12] of a time range estimating problem for an excavation project. The time and cost needed for the project equipment are shown in Table 1, and probabilistic distributions are used to express the uncertainty regarding those variables.
Activity | Triangular duration (min) | Triangular cost ($/min) |
---|---|---|
20 cu yd hauler: haul, unload, return | (18,33,48) | 2.39 |
15 cu yd hauler: haul, unload, return | (15,28,41) | 2.29 |
Activity time and cost data.
These uncertainties may result from uncertainty regarding different scenarios that may happen in the field during construction. For example, uncertainty in the activity duration may be a result of uncertainty associated with the productivity of workers or variability in weather conditions.
The case study evaluated seven alternatives using Monte Carlo simulation (MCS), to compare the presented FMCS model with the traditional MCS that is used by [12], we will evaluate the same alternatives to see if the outcomes of the new FMCS model will be different. The seven equipment configurations alternatives are shown in Table 2.
Alternatives | Configurations |
---|---|
Alt 1 | 4 of 20-cu yd haulers |
2 of 15-cu yd haulers | |
Alt 2 | 5 of 20-cu yd haulers |
2 of 15-cu yd haulers | |
Alt 3 | 4 of 20-cu yd haulers |
Alt 4 | 3 of 20-cu yd haulers |
Alt 5 | 2 of 20-cu yd haulers |
2 of 15-cu yd haulers | |
Alt 6 | 8 of 20-cu yd haulers |
3 of 15-cu yd haulers | |
Alt 7 | 6 of 20-cu yd haulers |
3 of 15-cu yd haulers |
Alternatives of equipment configurations.
Using Fuzzy logic toolbox in MATLAB the FMCS generates the results shown in Table 3.
Alternatives | Shift duration (days) | Shift cost ($) |
---|---|---|
Alt 1 | 26 | 77,438 |
Alt 2 | 26 | 86,667 |
Alt 3 | 27 | 63,780 |
Alt 4 | 31 | 67,549 |
Alt 5 | 33 | 61,170 |
Alt 6 | 17 | 98,014 |
Alt 7 | 17 | 79,050 |
FMCS results.
From Table 3, we can conclude that the best alternative is number seven with shift duration of 17 days and shift cost of $79,050. By comparing this result with the result published by [12], we find out that [12] concluded that the best alternative is also alternative seven with shift duration of 18 days and shift cost of $82,665.
This chapter proposes a new FMCS model. This model can consider both fuzzy and probabilistic uncertainty in the resource planning problem. The model provides decision-makers with the ability to reduce risk in the output in the form of fuzziness and probabilistic uncertainty, and he/she can use subjective judgment and experience to make the final decision. A case study has been analyzed to evaluate the robustness of the FMCS model. The outcomes show that the proposed FMCS model could help reduce the duration and cost of a certain task, which will help reduce the cost and duration of the project.
The research leading to the publication of this chapter was partially supported by the Department of Civil Engineering at Marshall University in Huntington, West Virginia, United States of America.
The authors declare that there are no conflicts of interest regarding the publication of this chapter.
Supporting women in scientific research and encouraging more women to pursue careers in STEM fields has been an issue on the global agenda for many years. But there is still much to be done. And IntechOpen wants to help.
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