A Scalable Health Information System with Appointments Scheduling Facility (A Case Study of National Health Insurance Scheme (NHIS)).

Waiting time problem, especially for out-patients, is an exceptionally serious issue in public hospitals across the globe. This study observes that with a system that allows subscribers of NHIS to seek medical attention in any NHIS designated hospitals, the waiting time problem will be a major challenge. A perusal of the literature shows that this problem stems substantially from the practice of fixing patients appointments without regard to specific time periods a patient is likely to receive attention on the designated day. The problem is further exacerbated by the practice of fixing such appointments without recourse to the number of doctors who will be available and in some cases, the time to be spent at some facilities. To address this problem, this study modelled an appointment scheduling system that took into consideration the number of doctors, the number of patients and the likely time it will take to complete consultations and the time it will take to complete some procedures or checks at available facility, in some instances. The study then translated this conceptual solution into a formal design using an object-oriented analysis and design methodology. The designed solution was implemented using suitable programming and scripting languages (Hypertext Preprocessor (PHP), JavaScript, HTML5, and CSS), different software tools (MySQL DBMS, Apache Tomcat Webserver) and third party Application Programming Interfaces (API’s). The test results of the developed system vividly demonstrated the proper functioning of the desired features and functions specified. Keywords: National Health Insurance Scheme, Integrated Information System, Out Patients Appointment Scheduling, Object Oriented Analysis and Design.

On a generalization of a waiting time problem and some combinatorial identities

In this paper we give an extension of the results of the generalized waiting time problem given by El-Desouky and Hussen (1990). An urn contains m types of balls of unequal numbers, and balls are drawn with replacement until first duplication. In the case of finite memory of order k, let ni be the number of type i, i = 1, 2, …, m. The probability of success pi = ni/N, i = 1, 2, …, m, where ni is a positive integer and Let Ym,k be the number of drawings required until first duplication. We obtain some new expressions of the probability function, in terms of Stirling numbers, symmetric polynomials, and generalized harmonic numbers. Moreover, some special cases are investigated. Finally, some important new combinatorial identities are obtained.

On a generalization of a waiting time problem and some combinatorial identities

In this paper we give an extension of the results of the generalized waiting time problem given by El-Desouky and Hussen (1990). An urn contains m types of balls of unequal numbers, and balls are drawn with replacement until first duplication. In the case of finite memory of order k, let ni be the number of type i, i = 1, 2, …, m. The probability of success pi = ni/N, i = 1, 2, …, m, where ni is a positive integer and Let Ym,k be the number of drawings required until first duplication. We obtain some new expressions of the probability function, in terms of Stirling numbers, symmetric polynomials, and generalized harmonic numbers. Moreover, some special cases are investigated. Finally, some important new combinatorial identities are obtained.

On Generating Functions of Waiting Times and Numbers of Occurrences of Compound Patterns in a Sequence of Multistate Trials

In this paper we study two distributions, namely the distribution of the waiting times until given numbers of occurrences of compound patterns and the distribution of the numbers of occurrences of compound patterns in a fixed number of trials. We elucidate the interrelation between these two distributions in terms of the generating functions. We provide perspectives on the problems related to compound patterns in statistics and probability. As an application, the waiting time problem of counting runs of specified lengths is considered in order to illustrate how the distributions of waiting times can be derived from our theoretical results.

On Generating Functions of Waiting Times and Numbers of Occurrences of Compound Patterns in a Sequence of Multistate Trials

In this paper we study two distributions, namely the distribution of the waiting times until given numbers of occurrences of compound patterns and the distribution of the numbers of occurrences of compound patterns in a fixed number of trials. We elucidate the interrelation between these two distributions in terms of the generating functions. We provide perspectives on the problems related to compound patterns in statistics and probability. As an application, the waiting time problem of counting runs of specified lengths is considered in order to illustrate how the distributions of waiting times can be derived from our theoretical results.

Waiting time distributions of competing patterns in higher-order Markovian sequences

Competing patterns are compound patterns that compete to be the first to occur pattern-specific numbers of times. They represent a generalisation of the sooner waiting time problem and of start-up demonstration tests with both acceptance and rejection criteria. Through the use of finite Markov chain imbedding, the waiting time distribution of competing patterns in multistate trials that are Markovian of a general order is derived. Also obtained are probabilities that each particular competing pattern will be the first to occur its respective prescribed number of times, both in finite time and in the limit.