TITLE:
Process Capability Indices for Shape Parameter of Weibull Distribution
AUTHORS:
Suboohi Safdar, Ejaz Ahmed
KEYWORDS:
Regression Coefficient; Non-Normal Distribution; Delta Method; Bootstrapping
JOURNAL NAME:
Open Journal of Statistics,
Vol.4 No.3,
April
24,
2014
ABSTRACT: Process capability analysis is used to
determine the process performance as capable or incapable within a specified
tolerance. Basic indices Cp, Cpk, Cpm, Cpmk initially developed for normally distributed processes showed inappropriate for
processes with non-normal distributions. A number of authors worked on
non-normal distributions which were most notably those of Clements, Pearn and
Chen, Montgomery and Johnson-Kotz-Pearn (JKP). Obtaining PCIs based on the
parameters of non-normal distributions are completely disregarded and ignored.
However parameters of some non-normal distributions have significance for
knowing the status of process as capable or incapable. In this article we
intend to work on the shape parameter of Weibull distribution to calculate
PCIs. We work on two data sets for verification and validation purpose.
Efficacy of the technique is assessed by bootstrapping the results of estimate
and standard error of shape parameter.