The exponentially growing online reviews have become a great wealth of information into which many researchers have started tapping. Using online reviews as a source of customer feedback, product designers are able to better understand customers’ preferences and improve product design accordingly. However, while predicting future product demand as a function of product attributes and customer heterogeneity has proved to be effective, not many literatures have studied the impact of non-product-related features, such as number of reviews and average ratings, on product demand using a large-scale dataset. As such, this paper proposes a data-driven methodology to investigate the influence of online ratings and reviews in purchase behavior by using discrete choice analysis. In the absence of information about the true customer choice set, we generate an estimated customer choice set based on a probability sampling using customer clustering and product clustering. In order to examine the effect of number of reviews and average rating, we have computed, for all the laptops in the choice set of each customer, the number of reviews and thus average rating at the date of this particular customer’s review. Using laptops for our case study, our experiment has shown that the number of reviews and average ratings are statistically significant, and the inclusion of these features will greatly improve the predictive ability of the model.

This paper presents the gravity balancing reliability and sensitivity analysis of robotic manipulators with uncertainties. The gravity balancing reliability of the robot is defined as the probability that the reduction torque ratio of the robot reduces below a specified threshold. This index is of great importance for assessing and guaranteeing the balancing performance of the robot in the presence of uncertainties in input parameters. In this work, the balancing design for an industrial robot using the gear-spring modules (GSMs) is proposed with the adoption of a simulation-based analysis of the gravity effect of the robot. The Monte Carlo Simulation (MCS) method with normally distributed variables (i.e., link dimensions, masses, and spring stiffness coefficients) is employed to analyze and simulate the reliability. A case study with an industrial robot is then given to illustrate the reliability performance and the sensibility of the uncertain parameters. It is found that the gravity balancing behavior is achieved even when the uncertainties are applied. The uncertainties could deteriorate the balancing performance when increasing the standard deviations by more than seven percent of their means. The dimensional parameters enjoy the most critical influence on the balancing performance.

Global concerns about climate change and resource management have escalated the need for sustainable consumer products. In light of this, sustainable design methodologies that supplement the product design process are needed. Current research focuses on developing sustainable design curricula, adapting classical design methods to accommodate environmental sustainability, and sustainability tools that are applicable during the early design phase. However, concurrent work suggests that sustainability-marketed and innovative products still lack a reduction of environmental impact compared to conventional products. Life cycle assessment (LCA) has proven to be an exceptional tool used to assess the environmental impact of a realized product. However, LCA is a reactive tool that does not proactively reduce the environmental impact of novel product concepts. Here we develop a novel methodology, the PeeP method, using historical product LCA data with kernel density estimation to provide an estimated environmental impact range for a given product design. The PeeP method is tested using a series of case studies exploring four different products. Results suggest that probability density estimations developed through this method reflect the environmental impact of the product at both the product and component level. In the context of sustainable design research, the PeeP method is a viable methodology for assessing product design environmental impact prior to product realization. Our methodology can allow designers to identify high-impact components and reduce the cost of product redesign in practice.

Due to normal variations in dimensions inherent in the manufacture of the components of a mechanism, there is a small probability of not meeting the accuracy predicted by a deterministic representation of the mechanism. The reliability of a mechanism can be defined as the probability of deviation from its specified function. This paper presents a Monte Carlo simulation approach for the reliability analysis of function generating mechanisms. The approach is illustrated by considering the reliability analysis of a four-bar straight-line mechanism. The effect of the probability distribution of the random parameters on the overall reliability is also investigated. The Monte Carlo approach can be coupled with the known statistical properties of the production techniques to significantly increase the production yield of mechanisms that satisfy specified reliability requirements.

Structural analysis and synthesis of linkages is a very important aspect. Detection of isomorphism (equivalent structural topology) is essential to determine structurally distinct chains. Some methods to detect distinct chains and mechanisms have already been developed. These methods besides being falliable, require enormous computational effort and as such necessitate development of an easy and efficient method. This paper presents a new method based on graph theory, for detection of isomorphism among kinematic chains. A probability scheme is attached with the chains and relative loop positions are determined for the chains having identical probability schemes. Isomorphism is detected between planar kinematic chains having single degree of freedom.

The performance of a flexible assembly system consisting of a set of work stations linked by a set of transporter stations is modeled by a Markovian queueing network in steady state. Its optimal behavior is characterized such that the throughput rate from the system is maximized, while the probability of finding an arbitrary workpiece waiting inside either each work station or each transporter station in addition to an allowable lenght of time will be sufficiently close to zero.

A technique to perform design calculations on imprecise representations of parameters using the calculus of fuzzy sets has been previously developed [17]. An analogous approach to representing and manipulating uncertainty in choosing among alternatives (imprecision) using probability calculus is presented and compared with the fuzzy calculus technique. We find that the fuzzy calculus is well suited to representing and manipulating the imprecision aspect of uncertainty, and probability is best used to represent stochastic uncertainty.

The problem of designing mechanical systems or components under uncertainty is considered. The basic idea is to ensure quality control at the design stage by minimizing sensitivity of the response to uncertain variables by proper selection of design variables . This formulation is applied to the design of a brass sleeve which is press fitted over a steel shaft in an uncertain thermal environment. The contact pressure is determined using finite element analysis. By optimizing the shape of the sleeve, the sensitivity of contact pressure with respect to operating temperature is reduced. The minimum sensitivity approach offers a straightforward procedure for robust design and can be implemented in a general manner. It is shown that reduction in sensitivity leads to increase in probability of safety.

An exact constraint scheme based on the physical contacting constraints of real part mating features is used to represent the process of assembling the parts. To provide useful probability information about how assembly dimensions are distributed when the parts are assembled as intended, the real world constraints that would prevent interference are ignored. This work addresses some limitations in the area of three dimensional assembly tolerance analysis. As a result of this work, the following were demonstrated: 1. Assembly of parts whose assembly mating features are subjected to variation; 2. Assemble parts using a real world set of exact constraints; 3. Provide probability distributions of assembly dimensions.

The Taguchi method of product design is a statistical experimental technique aimed at reducing the variance of a product performance characteristic due to uncontrollable factors. The goal of this paper is to provide a monotonicity analysis based methodology to facilitate the solution of N-type parameter design problems. The obtained design is robust , i.e., the least sensitive to variations on uncontrollable factors (noise). The performance characteristic is unbiased in the sense that its expected value equals a target or specification. The proposed loss function is based on the absolute deviation of the characteristic with respect to the target, instead of the common square error approach. Conditions, like those imposed by monotonicity analysis, on the monotonic characteristics of the performance function are proven, despite the objective function is not monotonic and contains stochastic parameters. These conditions allow the qualitative analysis of the problem to identify the activity of some constraints. Identification of active sets of constraints allows a problem reduction strategy to be employed, where the solution to the original problem is obtained by solving a set of problems with fewer degrees of freedom. Results for the case of one uncontrollable factor are independent of the probability measure on the factor. However, conclusions for the multi-parametric case must take into account the characteristics of the probability space on which the random parameters are defined.

The present investigation aims to develop a general probabilistic approach for the prediction of potential damage configurations of structure under modal oscillations. The multiple-crack distribution of the as-predicted damage configurations were characterized by the associated probability measure in terms of crack patterns, crack locations and crack depths. It is postulated that the structure is damaged at a prevailing modal response and the cracking process is sequential. The first passage probability of critical structural parameter exceeding the characteristic material allowable was evaluated to predict the mean time to failure, crack initiation, and crack propagation. In conjunction with the multiple-crack interactive stress relief effects, the probabilistic distributions of damage configuration were established for some representative modal shapes. The analysis results indicate that the damage configurations are highly affected by the modal shape wherein modal stress peak regions provide the most probable locations for cracking. Multiple-crack configuration is more likely to occur at higher mode of vibration. A single crack pattern is dominant at lower mode of vibration.

Engineered products are designed for manufacture using nominal values and tolerances. As such, finished products will more or less satisfy design specifications depending on the actual materials and manufacturing processes used. Design feasibility, therefore, depends on how these variations impact specified constraints. Probabilistic feasibility analysis can be used to extend conventional feasibility analysis. By using moment matching and simulation, the probability of points occurring in the design space can be evaluated. The resulting values establish the limits of feasibility and the amount of feasibility in between. The nature of variation in mechanical design is introduced along with concepts of variation propagation in functions of random variables. Moment matching methods are applied to illustrative cases consisting of deterministic and probabilistic constraint equations, resulting in three dimensional feasibility mappings of each design space.

In the presented paper the response of nonlinear random oscillators is calculated by the numerical solution of the associated Fokker-Planck-Equation. This approach can be used to approximate the invariant probability density of chaotic nonlinear oscillators or to calculate the response of a nonlinear oscillator, driven by additive white noise. A weighted residual approach is proposed to solve the Fokker-Planck-Equations numerically. By this method the partial differential equation is transformed to a coupled set of linear ordinary differential equations. These equations can be derived easily, because the integrals associated to the Galerkin procedure can be solved analytically. Considering stationary densities the solution is given by a generalized Eigenproblem. Utilizing sparse matrix techniques the solution can be calculated very efficiently.

This paper presents an analysis method for reliability measures of a system with step changes in failure and repair rates. Both failure and repair time have exponential function of time. Such a system is called a stepwise exponential distribution system. This kind of failure process can take place in various equipments. This paper deals with the system having components in series arrangement. Bayesian statistics is used in defining prior and posterior probability density functions of failure and repair rates. These functions provide information for the estimation of reliability measures: 1) failure and repair rates, 2) mean time to failure, 3) mean time to repair, 4) reliability function and 5) availability. A sample problem is given to illustrate the methodology. The Bayesian estimation of the stepwise exponential distribution model is useful in the planning of equipment predictive maintenance.

A method for calculating a component’s design survivability by incorporating finite element analysis and probabilistic material properties was developed. The method evaluates design parameters through direct comparisons of component survivability expressed in terms of Weibull parameters. The analysis was applied to a rotating disk with mounting bolt holes. The highest probability of failure occurred at, or near, the maximum shear stress region of the bolt holes. Distribution of material failure as a function of Weibull slope affects the probability of survival. Where Weibull parameters are unknown for a rotating disk, it may be permissible to assume Weibull parameters, as well as the stress-life exponent, in order to determine the effect of disk speed on the probability of survival.

Probabilistic wind loads likely to occur on a structure during its design life are predicted. This article describes a suitable multifactor interactive equation (MFIE) model and its use in the Composite Load Spectra (CLS) computer program to simulate the wind pressure cumulative distribution functions on four sides of a building. The simulated probabilistic wind pressure load was applied to a building frame, and cumulative distribution functions of sway displacements and concepts of reliability were demonstrated by computing the probability of overturning using NESSUS (Numerical Evaluation of Stochastic Structure Under Stress), a stochastic finite-element computer code. The geometry of the building and the properties of building members were also considered as random in the NESSUS analysis. The uncertainties of wind pressure, building geometry, and member section property were quantified in terms of their respective sensitivities on the structural response.

The strength distribution of reaction bonded silicon carbide tubes that failed by internal pressurization was predicted from strength distributions obtained from simple laboratory test specimens at room temperature. The strength distributions of flexure bars, C-rings tested in tension, C-rings tested in compression, diametrally compressed O-rings, and internally pressurized short tubes were compared to the strength distribution of internally pressurized long tubes. The methodology involved application of Weibull statistical theory using elasticity theory to define the stress distributions in the simple specimens. The flexural specimens did not yield acceptable results, since they were ground prior to testing, thereby altering their flaw population in comparison with the processing induced flaw populations of the tubular specimens. However, the short tube internal pressure test, the c-ring tested in tension and the diametrally compressed o-ring test configurations yielded accurate predictions, since these specimens more accurately represent the strength limiting flaw population in the long tubes.

In order to study the behavior of fatigue crack propagation and fatigue reliability of a structural or mechanical component under random loading, a numerical simulation scheme and other analytical prediction models are proposed in this paper. The paper consists of (1) digital generation of random loading from random process theory; (2) numerical simulation of fatigue crack growth based on fracture mechanics concept; (3) a modified rain-flow cycle counting method for the identification of stress cycles and stress amplitudes; (4) Weibull probability density fit and other statistical analyses for the stress amplitudes as well as the crack growth curves; and (5) probabilistic models for the prediction of fatigue crack growth, fatigue life and fatigue reliability. Some conclusions are drawn at the end of this paper which can be used as references in the design of a structural or mechanical component under random loading.

Computing the reliability of structural components with uncertainties in both stress and resistance variables is investigated. The NESSUS™ probabilistic software is used to perform the reliability computations using both Fast Probability Integration (FPI) and Monte Carlo methods. Results are compared for an example reliability analysis using both closed-form expressions and finite elements. The Advanced Mean Value probabilistic algorithm is used and is shown to yield highly accurate results, even for highly nonlinear response functions. The results show clearly the effectiveness of the newly incorporated algorithms available in the NESSUS software for computing structural reliability.

Probabilistic optimization using the moment matching method and the simulation optimization method are discussed and compared to conventional deterministic optimization. A new approach based on successively approximating probability density functions, using recursive quadratic programming for the optimization process, is described. This approach incorporates the speed and robustness of analytical probability density functions and improves accuracy by considering simulation results. Theoretical considerations and an example problem illustrate the features of the approach. The paper closes with a discussion of an objective function formulation which includes the expected cost of design constraint failure.