Designing Tolerance of Assembled Components Using Weibull Distribution

Document Type: Original Manuscript


1 Department of Industrial Management, Firoozkooh Branch, Islamic Azad University, Firoozkooh, Iran.

2 Department of Industrial Management, Science and Technology Branch, Islamic Azad University, Tehran, Iran.



Tolerancing is one of the most important tools for planning, controlling, and improving quality in the industry. Tolerancing conducted by design engineers to meet customers’ needs is a prerequisite for producing high-quality products. Engineers use handbooks to conduct tolerancing. While use of statistical methods for tolerancing is not a new concept, engineers often use known distributions, including the normal distribution. However, if the statistical distribution of the given variable is unknown, a new statistical method will be employed to design tolerance. Therefore, in this study we want to offer a proper statistical method for determining tolerance. The use of statistical methods to design tolerance is not a new concept; however, flexible use of statistical distributions can enhance its performance. In this regard, Weibull distribution is proposed. To illustrate the proposed method first technical characteristics of production parts were selected randomly, and then manufacturing parameters were determined using maximum likelihood method.  Finally, the Goodness of Fit test was used to ensure the accuracy of the obtained results.

Graphical Abstract

Designing Tolerance of Assembled Components Using Weibull Distribution


  • Nowadays, tolerance of components is determined by using engineering handbooks. Since the process capability is not taken into account for this purpose; tolerance is determined sometimes less and sometimes more than process capability. In the first case, many components are produced as waste or correction is needed; in the second case, components are manufactured with greater precision than needed. As a result, the product cost rises. In any case, the total cost of production will rise.
  • In practice, produced components tend to be assembled together. Therefore, if probabilistic relationships, process capability, and products’ functional needs are simultaneously and properly considered for determining the tolerance of assembled components, we can determine the tolerance of each of assembled components more judiciously and greater than its current value, so that in practice they can be produced more easily whereas they still serve the intended function.
  • Another point that can be stated here is related to the nature of probability distribution function of produced components. For example, if the distribution function of components is normal or at least symmetrical, or if several samples can be picked up from the production line simultaneously, and their average quality characteristics can be considered as a random variable, fewer problems will arise. But if the distribution of quality characteristics is neither normal nor at least symmetrical, or we have individual measurement of variable characteristics, using a flexible distribution such as Weibull distribution, which can embrace several distributions including the normal distribution, would seem appropriate.


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