ENBIS-8 in Athens

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

Process Capability Indices for Weibull Distributed Quality Characteristics and Target Value 0

22 September 2008, 15:20 – 15:40

Abstract

Submitted by
Malin Albing
Authors
Malin Albing
Affiliation
Luleå University of Technology, Sweden
Abstract
Consider a situation in process capability analysis where the smallest possible value of the studied quality characteristic is zero and an upper specification limit only exists. For this situation it is not uncommon that zero is also the best value to obtain. For instance, consider a surface polishing process where the surface should be as smooth as possible or a gearwheel production process, where the deviation from the surface of the gearwheel should be as small as possible. In such situations it is likely to find a skew distribution with a long tail towards large values rather than a normal distribution for the studied quality characteristic. Hence the most commonly used process capability index for an upper specification limit in industry today, Cpu, is not suitable to use when studying process capability.

For the situation described above it is often reasonable to assume that the underlying distribution is a Weibull distribution. Hence, we focus on process capability indices when the studied quality characteristic is distributed according to a highly skewed Weibull distribution and there is an upper specification with a pre-specified target value 0.Under these conditions we consider a previously proposed class of capability indices, designed for skewed zero-bound distributions, and propose an efficient estimator of the index in the studied class. Using this estimated index and its asymptotic distribution we suggest a decision rule to be used for deeming a process capable at a given significance level. We present results from a simulation study, performed to investigate the true significance level, when the sample size, n, is between 50 and 200. An example from a Swedish industry will also be presented to illustrate the proposed ideas.

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