Mathematical Models in Quality Engineering: Applications to Project Management

1. Introduction

According to the principles of traditional management, three criteria are used to assess the success of a project: time, cost and quality (Dumitru, 2001), (Radu, 2008). Although the quality of the management process can be considered of an abstract nature, in fact it is related to the performance parameters within which a project should operate in order to generate income and to run in optimal conditions (Turner, 2004). The success of a project depends on observing the requirements formulated by the project manager in relation to time and cost (Dumitru, 2001; Radu, 2008; Turner, 2004).

Successful project management is a complex process in which many of the company functions are involved. Project management relies on the application of knowledge and abilities, as well as on the use of adequate tools and techniques for the specific project activities.

In projects, the objectives, outcomes, time, cost and quality-related requirements and performance parameters are well defined (Cochran, 2000; Doran, 1981). However, the time-related constraints are dominant and they have an impact on costs, quality and performance. These constraints are correlated in such a manner that they can lead to either the success or the failure of a project.

The classical indicators, i.e. efficiency, effectiveness and the performance cost which appear in the specialised literature (Dumitru, 2001) are used in mathematical statistics in order to assess the evolution of a project from the point of view of the normal and uniform distribution. In this way, the confidence intervals are established and, in their turn, these help to identify the minimum and maximum limits within which the project implementation is not influenced by disturbing factors.

The analysis presented in this paper is also based on the elements of mathematical statistics and reliability which are currently used to evaluate the quality of products (Popescu, 2003; Craiu, 1999; Badford, 2003; Hardle, 2007), but the novelty it brings resides in the introduction and use of four other economic and performance indicators related to the variations of cost and time. They are used alongside the classical indicators and provide a reliable model for assessing the management process.

In agreement with the aim of this paper, namely that of analysing the project management process with the help of quality indicators in case of time variance, the following research objectives were formulated:

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  Establishing and defining the project management quality indicators;

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  Establishing the work hypotheses for assessing the quality indicators, namely:

  • a.

    The hypothesis of process parameters with random variables and normal distribution;

  • b.

    The hypothesis of process parameters with random variables and uniform distribution;

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  Analysing the project development in case of process parameters with random variables and normal distribution;

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  Analysing the project development in case of process parameters with random variables and uniform distribution;

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  Establishing the confidence intervals by analysing the input and output process variances for the two hypotheses;

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  Establishing the correlation between the results of the two analysed hypotheses;