a b s t r a c tGompertz curve has been used to estimate the number of residual faults in testing phases of software development, especially by Japanese software development companies. Since the Gompertz curve is a deterministic function, the curve cannot be applied to estimating software reliability which is the probability that software system does not fail in a prefixed time period. In this article, we propose a stochastic model called the Gompertz software reliability model based on non-homogeneous Poisson processes. The proposed model can be derived from the statistical theory of extreme-value, and has a similar asymptotic property to the deterministic Gompertz curve. Also, we develop an EM algorithm to determine the model parameters effectively. In numerical examples with software failure data observed in real software development projects, we evaluate performance of the Gompertz software reliability model in terms of reliability assessment and failure prediction.

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Introduction: There are complex interactions between pain and perceptions of the painful body part in musculoskeletal disorders, and disruption of various body representations in people with chronic pain. Objectives: The purpose of this study was to investigate how frequently people with knee osteoarthritis (OA) complain of swelling without objective evidence of swelling, and describe the clinical characteristics of this population. Methods: Forty-six people with knee OA (68.1 6 8.8 years) participated in this cross-sectional study. Subjective and objective swelling was evaluated by knee-specific body perception questionnaire and ultrasonography, respectively. Pain intensity, disability, pain-related beliefs, 2-point discrimination threshold, and quadriceps muscle strength were also evaluated.Results: Approximately 1/3 of participants (n 5 15) had subjective feelings of knee swelling in the absence of objective swelling (S only). Fifteen participants had both subjective and objective knee swelling (S 1 O group) and 16 had neither subjective nor objective knee swelling (No S/O group). Participants in the S only group had similar pain or disability as those in the S 1 O group but had more severe pain or disability than those with in the No S/O group. Those in the S only group also had larger 2-point discrimination distance threshold at the medial knee (impaired tactile acuity) than those in the S 1 O group and had more dysfunctional pain catastrophizing and pain-related self-efficacy than both other groups. Conclusion: Our results suggest that about 30% of people with knee OA perceive swelling of the knee in the absence of any objective swelling and that this is accompanied by severe pain and functional disability. Considering altered body image of the knee may reveal relevant treatment-based subgroups in people with knee OA.

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