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Statistical tolerancing through discretization of variables

Tirthankar Ghosh (Department of Statistics, Visva‐Bharati University, Santiniketan, India)
Dilip Roy (The University of Burdwan, Burdwan, India)

International Journal of Quality & Reliability Management

ISSN: 0265-671X

Article publication date: 25 January 2011



The main purpose of this paper is to consider the role of discretization of random variables in analyzing statistical tolerancing, and to propose a new discretizing method along with a study on its usefulness.


The approach for discretization of a continuous distribution is based on the concept of moment equalization with the original random variable, conditionally given a set of points of realization. For the purpose of demonstration the normal distribution has been discretized into seven points. Application of the discretization method in approximating the distribution/survival function of a complex system has also been studied. Numerical analysis on two important engineering items has been undertaken and the closeness between the values of the distribution/survival functions obtained by simulation and the proposed method has been examined to indicate the advantage of the proposed approach.


A comparative study with the earlier reported discretizing methods indicates that the proposed method, which is easy to implement, provides better results for most of the cases studied in this work.

Research limitations/implications

Using the proposed approach one can approximate the probability distribution of a complex system with random component values, which cannot be analytically expressed.

Practical implications

This paper is able to provide a new direction in reliability management research, because it can be used for product design of many important engineering items such as solid‐shaft, hollow cylinder, torsion bar, I‐beam etc.


This research gives a new linear method of discretization. It gives better results than the existing discretization methods of Experimental design, Moment equalization, and Discrete Concentration for reliability (survival probability) determination of solid‐shaft and power resistor.



Ghosh, T. and Roy, D. (2011), "Statistical tolerancing through discretization of variables", International Journal of Quality & Reliability Management, Vol. 28 No. 2, pp. 220-232.



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