Skewed zero-bound distributions and process capability indices for upper specifications

A common practical situation in process capability analysis, which is not well developed theoretically, is when the quality characteristic of interest has a skewed distribution with a long tail towards relatively large values and an upper specification limit only exists. In such situations, it is not uncommon that the smallest possible value of the characteristic is 0 and this is also the best value to obtain. Hence a target value 0 is assumed to exist. We investigate a new class of process capability indices for this situation. Two estimators of the proposed index are studied and the asymptotic distributions of these estimators are derived. Furthermore, we suggest a decision procedure useful when drawing conclusions about the capability at a given significance level, based on the estimated indices and their asymptotic distributions. A simulation study is also performed, assuming that the quality characteristic is Weibull-distributed, to investigate the true significance level when the sample size is finite.

[1]  Kerstin Vännman,et al.  Process capability indices for one-sided specification intervals and skewed distributions , 2007, Qual. Reliab. Eng. Int..

[2]  Wen Lea Pearn,et al.  An algorithm for calculating the lower confidence bounds of CPU and CPL with application to low-drop-out linear regulators , 2003, Microelectron. Reliab..

[3]  W. L. Pearn,et al.  Testing process capability for one-sided specification limit with application to the voltage level translator , 2002, Microelectron. Reliab..

[4]  Guo Jin-li,et al.  A New Measure of Process Capability , 2008 .

[5]  D. Cox,et al.  An Analysis of Transformations , 1964 .

[6]  Kerstin Vännman,et al.  Process Capability Plots for One-Sided Specification Limits , 2007 .

[7]  Fred A. Spiring,et al.  A Bibliography of Process Capability Papers , 2003 .

[8]  Taiwan Roc,et al.  AN APPLICATION OF NON-NORMAL PROCESS CAPABILITY INDICES , 1997 .

[9]  Ashok Sarkar,et al.  ESTIMATION OF PROCESS CAPABILITY INDEX FOR CONCENTRICITY , 1997 .

[10]  W. Pearn,et al.  Capability indices for non-normal distributions with an application in electrolytic capacitor manufacturing , 1997 .

[11]  Samuel Kotz,et al.  Process Capability Indices , 1993 .

[12]  Richard D. Deveaux,et al.  Applied Smoothing Techniques for Data Analysis , 1999, Technometrics.

[13]  F. P. Lawrence,et al.  C pk index estimation using data transformation , 1995 .

[14]  Kerstin Vännman,et al.  Families of Capability Indices for One-Sided Specification Limits , 1998 .

[15]  Kerstin Vännman,et al.  A uniformed approach to capability indices , 1995 .

[16]  Fred A. Spiring,et al.  A New Measure of Process Capability: Cpm , 1988 .

[17]  W. Nelson.  Statistical Methods for Reliability Data , 1998 .

[18]  Youn Min Chou,et al.  Transforming Non-Normal Data to Normality in Statistical Process Control , 1998 .

[19]  Ing Rj Ser.  Approximation Theorems of Mathematical Statistics , 1980 .

[20]  J. Bert Keats,et al.  Statistical Methods for Reliability Data , 1999 .

[21]  Kerstin Vännman,et al.  A Graphical Method to Control Process Capability , 2001 .

[22]  Samuel Kotz,et al.  Process Capability Indices—A Review, 1992–2000 , 2002 .

[23]  Yu-Sheng Hsu,et al.  Asymptotic analysis of estimators for C Np (u, v) based on quantile estimators , 2003 .

[24]  Kerstin Vännman,et al.  Process capability plots—a quality improvement tool , 1999 .

[25]  Douglas C. Montgomery,et al.  PROCESS CAPABILITY INDICES AND NON-NORMAL DISTRIBUTIONS , 1996 .

[26]  Kuen-Suan Chen,et al.  One‐sided capability indices CPU and CPL: decision making with sample information , 2002 .