This paper re-visits the question of mapping a probability distribution to patient unpunctuality in appointment-driven outpatient clinics, with reference to published empirical arrival data. This data indicates the possibility of interesting aberrations such as local modes and near-modes, asymmetry and peakedness. We examine the form of some published data on patient unpunctuality, and propose a mixed distribution which we call "F3" to provide a richer representation of shape such as in the shoulders of the distribution. The adequacy of this model is assessed in a worked example referencing a classical study, where a comparison is made of F3 against the normal and Pearson VII distributions with reference to summary statistics, graphical probability plots (P-P and Q-Q), a range of goodness of fitness criteria. Under this patient arrival setting, 2P method is proposed for optimal patient interval setting to minimize waiting time of both patient and the doctor and this 2P method is validated with a tentative simulation example. This study argues that frequency distribution of patient unpunctuality shows asymmetry in shape which is resulted from various types of arrival behaviours. Consequently optimal appointment intervals of scheduled patients, which minimize the total waiting time of patients and the doctor is highly related to patient unpunctuality patterns and this makes the optimal appointment intervals for various patient unpunctualities predictable.
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