Statistical Tolerance Limits for Process Capability

The problem of constructing one-sided exact statistical tolerance limits on the kth order statistic in a future sample of m observations from a distribution of log-location-scale family on the basis of an observed sample from the same distribution is considered. The new technique proposed here emphasizes pivotal quantities relevant for obtaining tolerance factors and is applicable whenever the statistical problem is invariant under a group of transformations that acts transitively on the parameter space. The exact tolerance limits on order statistics associated with sampling from underlying distributions can be found easily and quickly making tables, simulation, Monte Carlo estimated percentiles, special computer programs, and approximation unnecessary. Finally, numerical examples are given, where the tolerance limits obtained by using the known methods are compared with the results obtained through the proposed novel technique, which is illustrated in terms of the extreme-value and two-parameter Weibull distributions.

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Simulation-Based Maximum Likelihood Median Pragmatic A-Basis and B-Basis Statistical Tolerance Limits Given Fatigue Datum Values with No Censoring or with Potential or Actual Type I Censoring

Journal of Testing and Evaluation ◽

10.1520/jte102648 ◽

2010 ◽

Vol 38 (4) ◽

pp. 102648

Author(s):

M. R. Mitchell ◽

R. E. Link ◽

R. E. Little

Keyword(s):

Maximum Likelihood ◽

Type I ◽

Tolerance Limits ◽

Type I Censoring ◽

Simulation Based ◽

Actual Type ◽

Statistical Tolerance

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Advanced Tolerancing Based on Product Performance by Using Statistical Tolerance Index Cpk and Cc

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.523-524.781 ◽

2012 ◽

Vol 523-524 ◽

pp. 781-786 ◽

Cited By ~ 1

Author(s):

Akimasa Otsuka

Keyword(s):

Normal Distribution ◽

Mass Production ◽

Manufacturing Industry ◽

Process Capability ◽

Product Performance ◽

Precision Machining ◽

Tolerance Index ◽

Control Performance ◽

Functional Dimension ◽

Statistical Tolerance

In this paper, the improvement of performance design for mass production are shown by using statistical tolerance index Cpk and Cc. Recently, the demand for product performance is getting higher. Meanwhile, precision machining and measurement are also developing in manufacturing industry. To satisfy consumer in terms of product performance, we have proposed advanced tolerancing method by using statistical tolerance index (STI). In this study, it is assumed that the performance of each product can be quantified and depends on the only functional dimension. It is also assumed that the dimension distribution of each machined part follows normal distribution. Consequently, performance of mass production can be quantified statistically. To control performance, we introduce STI which is composed of process capability limitation. After all, performance design is to calculate STI so as to satisfy the demand for performance. There are two problems in performance design. One is a synthesis of STI and another is an allocation of STI. These problems are just like the conventional tolerance synthesis and allocation problems. In this paper, the former problem is formulated algebraically.

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