This paper develops a logistic approximation to the cumulative normal distribution. Although the literature contains a vast collection of approximate functions for the normal distribution, they are very complicated, not very accurate, or valid for only a limited range. This paper proposes an enhanced approximate function. When comparing the proposed function to other approximations studied in the literature, it can be observed that the proposed logistic approximation has a simpler functional form and that it gives higher accuracy, with the maximum error of less than 0.00014 for the entire range. This is, to the best of the authors' knowledge, the lowest level of error reported in the literature. The proposed logistic approximate function may be appealing to researchers, practitioners and educators given its functional simplicity and mathematical accuracy.

The healthcare arena, much like the manufacturing industry, benefits from many aspects of the Toyota lean principles. Lean thinking contributes to reducing or eliminating nonvalue-added time, money, and energy in healthcare. In this paper, we apply selected principles of lean management aiming at reducing the wasted time associated with drug dispensing at an inpatient pharmacy at a local hospital. Thorough investigation of the drug dispensing process revealed unnecessary complexities that contribute to delays in delivering medications to patients. We utilize DMAIC (Define, Measure, Analyze, Improve, Control) and 5S (Sort, Set-in-order, Shine, Standardize, Sustain) principles to identify and reduce wastes that contribute to increasing the lead-time in healthcare operations at the pharmacy understudy. The results obtained from the study revealed potential savings of> 45% in the drug dispensing cycle time.

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One way to understand the Parkinson’s disease (PD) population is to investigate the similarities and differences among patients through cluster analysis, which may lead to defined, patient subgroups for diagnosis, progression tracking and treatment planning. This paper provides a systematic review of PD patient clustering research, evaluating the variables included in clustering, the cluster methods applied, the resulting patient subgroups, and evaluation metrics. A search was conducted from 1999 to 2021 on the PubMed database, using various search terms including: Parkinson’s disease, cluster, and analysis. The majority of studies included a variety of clinical scale scores for clustering, of which many provide a numerical, but ordinal, categorical value. Even though the scale scores are ordinal, these were treated as numerical values with numerical and continuous values being the focus of the clustering, with limited attention to categorical variables, such as gender and family history, which may also provide useful insights into disease diagnosis, progression, and treatment. The results pointed to two to five patient clusters, with similarities among the age of onset and disease duration. The studies lacked the use of existing clustering evaluation metrics which points to a need for a thorough, analysis framework, and consensus on the appropriate variables to include in cluster analysis. Accurate cluster analysis may assist with determining if PD patients’ symptoms can be treated based on a subgroup of features, if personalized care is required, or if a mix of individualized and group-based care is the best approach.