ENBIS-8 in Athens

21 – 25 September 2008 Abstract submission: 14 March – 11 August 2008

Process Capability Analysis for Zero-bound Process Data with Zero-values Present

22 September 2008, 15:40 – 16:00

Abstract

Submitted by
Kerstin Vannman
Authors
Kerstin Vännman and Malin Albing
Affiliation
Luleå University of Technology, Luleå, Sweden
Abstract
When a studied quality characteristic is zero-bound it is common that its distribution is skewed and that the specification limit is one-sided. Furthermore it is not unusual that the best value to obtain is zero and hence, the target value is zero. The traditional process capability indices based on the normality assumption cannot be used in such situations. A class of capability indices, designed for this case, has previously been suggested and studied under the assumption that the distribution of the quality characteristic is continuous. However, if the quality characteristic can attain values of exactly zero a continuous distribution is not a proper model to use. A typical situation when this might occur is during a process that handles materials where cracks can occur. No crack is the best situation, but if cracks occur they should be short or cover a small area. Then the quality characteristic can obtain the value 0, corresponding to no crack, or some strictly positive number describing the length of the crack or the size of the crack area. Furthermore, the specification interval is an upper specification limit and the target value is 0. We study this situation by using a nonstandard mixture of distributions, involving a Weibull distribution, to model the quality characteristic. Under this assumption we suggest an estimator of the index in the class of indices previously suggested. We study the asymptotic statistical properties of this estimator and suggest a suitable decision rule to be used for deeming a process capable at a given significance level. This decision rule is constructed to be simple to use for practitioners. By using simulation studies we investigate the suggested rule for moderate sample sizes. Examples will also be given to illustrate the presented result.

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