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The use of tolerance limits in production and operations management

Product quality has become highly important in today's competitive world, and the use of tolerance limits has become a common method of specifying the quality of a manufactured product. Even when the usual quality control and reliability procedures have been applied, it is still desirable to know with what confidence one can assert what percentage of the resultant population consists of the relevant product having the required quality. Furthermore, tolerance limits provide a simple, relatively inexpensive, measure to ensure that production will not be outside given specifications. This paper discusses both nonparametric and parametric methods of setting tolerance limits, from which it can be determined with a specified confidence what percentage of a product made under commercial conditions may be expected to have a quality falling between the tolerance limits. The satisfactory application of tolerance limits requires that assignable causes of variability be determined and eliminated so that the remaining variability may be considered random. Tolerance limits are also practical and useful in “unconventional” areas where they are not usually applied, such as warranties, failure-free operational hours of complex machines used in large machine shops, and availability of equipment, etc. The methods for determining tolerance limits are simple yet powerful, and are easily understood and implemented by production engineers and managers. Several examples of the potential application of conventional and unconventional types of tolerance limits are given.