Reliability studies of the skew normal distribution

It has been observed in various practical applications that data do not conform to the normal distribution, which is symmetric with no skewness. The skew normal distribution proposed by Azzalini(1985) is appropriate for the analysis of data which is unimodal but exhibits some skewness. The skew normal distribution includes the normal distribution as a special case where the skewness parameter is zero. In this thesis, we study the structural properties of the skew normal distribution, with an emphasis on the reliability properties of the model. More specifically, we obtain the failure rate, the mean residual life function, and the reliability function of a skew normal random variable. We also compare it with the normal distribution with respect to certain stochastic orderings. Appropriate machinery is developed to obtain the reliability of a component when the strength and stress follow the skew normal distribution. Finally, IQ score data from Roberts (1988) is analyzed to illustrate the procedure.

Effects of Strand Geometry on Selected Properties of Long-Stand Structural Composite Lumber Made from Northeastern Hardwoods

Structural composite lumber (SCL) products often possess significantly higher design values than the top grades of solid lumber, making it a popular choice for both residential and commercial applications. The enhanced mechanical properties of SCL are mainly due to defect randomization and densification of the wood fiber, both largely functions of the size, shape and composition (species) of the wood element. Traditionally, SCL manufacturers have used thin, rectangular elements produced from either moderate density softwoods or low density hardwoods. Higher density hardwood species have been avoided, as they require higher pressures to adequately densify and consolidate the wood furnish. These higher pressures can lead to increased manufacturing costs, damage to the wood fiber and/or a product that is too dense, making it heavy and unreceptive to common mechanical fastening techniques. In the northeastern United States high density, diffuse-porous hardwoods (such as maple, beech and birch) are abundant. Use of these species as primary furnish for a SCL product may allow for a competitive advantage in terms of resource cost against products that rely on veneer grade logs. Proximity to this abundant and relatively inexpensive resource may facilitate entry of SCL production facilities in the northeastern United States, where currently none exist. However, modifications to current strand sizes, geometries or production techniques will likely be required to allow for use of these species. A new SCL product concept has been invented allowing for use of these high density hardwoods. The product, referred to as long-strand structural composite lumber (LSSCL), uses strands of significantly larger cross sectional areas and volumes than existing SCL products. In spite of the large strand size, satisfactory consolidation is achieved without excessive densification of the wood fiber through use of a symmetrical strand geometric cross-section. LSSCL density is similar to that of existing SCL products, but is due mainly to the inherent density of the species, rather than through densification. An experiment was designed and conducted producing LSSCL from both large (7/16”) and small (1/4”) strands, of both square and triangular geometric cross sections. Testing results indicate that the large, triangular strands produce LSSCL beams with projected design values of: Modulus of elasticity (MOEapp) – 1,750,000 psi; Allowable bending stress (Fb) – 2750 psi; Allowable shear stress (Fv) – 260 psi. Several modifications are recommended which may lead to improvement of these values, likely allowing for competition against existing SCL products.