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The chapter reviews and extends the theory of exact and superlative index numbers. Exact index numbers are empirical index number formula that are equal to an underlying theoretical index, provided that the consumer has preferences that can be represented by certain functional forms. These exact indexes can be used to measure changes in a consumer's cost of living or welfare. Two cases are considered: the case of homothetic preferences and the case of nonhomothetic preferences. In the homothetic case, exact index numbers are obtained for square root quadratic preferences, quadratic mean of order r preferences, and normalized quadratic preferences. In the nonhomothetic case, exact indexes are obtained for various translog preferences.

The most frequently used attribute sampling plan in MIL‐STD 105 D. In cases, however, when the quality level of incoming lots is generally sufficiently good, MIL‐STD 105 D often leads to unnecessarily high sampling cost. This can be avoided by using α‐optimal sampling plans. The authors outline the α‐optimal sampling scheme along with a simple procedure to determine α‐optimal sampling plans at workshop level. These plans depend on three parameters which have to be estimated from recorded data. In this article the effects of estimation errors in these parameters are investigated.

A newly developed model for performing reliability and availability analysis of mechanical devices subject to multiple failure modes is presented. Using this model, reliability analyses of mechanical devices such as brakes, bearings, engines, fans, gears, generators, heat exchangers and pumps are developed. Real life failure rate data for these devices are obtained from various sources and are used in their reliability analyses. Principal failure modes of these devices are identified and expressions for reliability, state probabilities, mean time to failure and variance of time to failure are developed. For known field failure data reliability and state probability plots are shown.

When the process probability distribution is non‐normal or is unknown, the process mean and standard deviation may not properly describe the distribution’s shape. Consequently, the traditional process capability indices (PCI) C_p, C_pk, C_pm and C_pmk cannot express the actual process capability. This paper presents a procedure to construct lower confidence limits for PCIs when the process distribution is unknown. First, the order statistics are utilized to find the estimators of C_p, C_pk, C_pm and C_pmk. Bootstrap simulation method is then utilized to construct the lower confidence limits of PCIs, thereby allowing the process’s capability to be evaluated. A numerical example demonstrates the effectiveness of the proposed procedure.

We analyze stochastic volatility effects in the context of the bond market. The short rate model is of Vasicek type and the focus of our analysis is the effect of multiple scale variations in the volatility of this model. Using a combined singular-regular perturbation approach we can identify a parsimonious representation of multiscale stochastic volatility effects. The results are illustrated with numerical simulations. We also present a framework for model calibration and look at the connection to defaultable bonds.

Our objective was to compare the physical health status of adult prisoners with and without a mental illness. Mental illness was diagnosed in a sample of 557 Australian prisoners using the Composite International Diagnostic Interview (CIDI). Physical health measures included self‐reported chronic health conditions, recent health complaints and symptoms, self‐assessed health using the Short‐Form 36 Health Survey (SF‐36), and markers of infectious diseases known to be highly prevalent among prisoner populations (hepatitis A, hepatitis B, and hepatitis C). Men and women with a mental illness had lower scores on the SF‐36 compared with those without a mental illness indicating poor overall health. Adjusting for age and sex, a diagnosis of any mental illness (symptoms of psychosis, anxiety or affective disorder) was positively associated with a history of head injury, back problems, asthma, peptic ulcers, cancer, and epilepsy/seizures. There was a significant association between post traumatic stress disorder and asthma, a history of head injury, peptic ulcers, and cancer. There was no significant difference in the proportion of current tobacco smokers in the mentally ill and nonmentally ill groups (81% vs. 77%, p = 0.33). However, those with a mental illness were less likely than those with no diagnosis to exercise in the past 4 weeks (79% vs. 89%, p = 0.002). Mentally ill prisoners also have significant physical co‐morbidity compared with the non‐mentally ill. These findings suggest that those providing mental health services to prisoners should adopt a holistic approach embracing both mental and physical health.

This article discusses static hedges for installment options, which are finding broad application in cases where the option‐buyer may reduce up‐front premium costs via early termination of an option. An installment option is a European option in which the premium, instead of being paid up front, is paid in a series of installments. If all installments are paid, the holder receives the exercise value, but the holder has the right terminate payments on any payment date, in which case the option lapses with no further payments on either side. The authors summarize pricing and risk management concepts for these options, in particular, using static hedges to obtain both no‐arbitrage pricing bounds and very effective hedging strategies with almost no vega risk.

This article provides tables based on the Poisson model for selection of chain sampling plans of type ChSP‐(0,1). The Indifference Quality Level and the Maximum Allowable Percent Defective are the criteria used for fixing the ChSP‐(0,1) plan. Procedures for selection of plans for given (IQL,AOQL) and (MAPD,AOQL) are also discussed.

We compare potential‐based (ø‐U‐P0) and displacement‐based finite element methods for static analysis of contained fluids. A general transient formulation may be specialized to static analysis in both cases. In the potential‐based method velocity potentials (ø) and a single pressure (P0) variable are the unknowns in the fluid region. Displacements are the unknowns in the fluid for displacement‐based methods. Higher‐order displace‐ment‐based elements may produce singular matrices for some static analyses, restricting us to four‐node elements for reliability. While both methods can yield excellent results when compared with experimental data, potential‐based methods appear to have computational advantages over displacement‐based methods.

Most current modeling approaches identify very small gains from trade reform. In this chapter, we examine recent developments in the literature to assess whether standard modeling approaches are mis-specifying, understating, or overstating the gains from trade reform. Key areas where the impacts of trade barrier reduction appear to be understated include the measurement of barriers; the aggregation of these barriers; process productivity gains, particularly those resulting from reallocation of resources between firms; product quality improvements and expansion of product variety; factor supply; and investment of gains from trade.