General control charts for attributes

Traditional Shewhart-type control charts ignore the skewness of the plotted statistic. Occasionally, the skewness is too large to be ignored, and in such cases the classical Shewhart chart ceases to deliver satisfactory performance. In this paper, we develop a general framework for constructing Shewhart-like control charts for attributes based on fitting a quantile function that preserves all first three moments of the plotted statistic. Furthermore, these moments enter explicitly into the formulae for calculating the limits. To enhance the accuracy of these limits the value of the skewness measure used in the calculations is inflated by 44%. This inflation rate delivers accurate control limits for diversely-shaped attribute distributions like the binomial, the Poisson, the geometric and the negative binomial. A new control chart for the M/M/S queueing model is developed and its performance evaluated.

[1]  H. Shore.  General control charts for variables , 2000 .

[2]  Haim Shore.  A new approach to analysing non-normal quality data with application to process capability analysis , 1998 .

[3]  William H. Woodall,et al.  Control Charts Based on Attribute Data: Bibliography and Review , 1997 .

[4]  F. Alt,et al.  Control Charts for Quantile Function Values , 1997 .

[5]  Neil C. Schwertman,et al.  OPTIMAL LIMITS FOR ATTRIBUTES CONTROL CHARTS , 1997 .

[6]  Haim Shore,et al.  Fitting a distribution by the first two moments (partial and complete) , 1995 .

[7]  Ds Bai,et al.  X and R Control Charts for Skewed Populations , 1995 .

[8]  Steven A. Yourstone,et al.  Non‐Normality and the Design of Control Charts for Averages* , 1992 .

[9]  James C. Benneyan,et al.  Statistical Control Charts Based on a Geometric Distribution , 1992 .

[10]  Charles P. Quesenberry,et al.  SPC Q charts for a Poisson parameter (lambda): Short or long runs , 1991 .

[11]  Charles P. Quesenberry,et al.  SPC Q charts for a binomial parameter p: Short or long runs , 1991 .

[12]  Haim Shore,et al.  Simple Approximations for the GI/G/c Queue-II: The Moments, the Inverse Distribution Function and the Loss Function of the Number in the System and of the Queue Delay , 1988 .

[13]  H. Shore.  Approximate Closed Form Expressions for the Decision Variables of Some Tests Related to the Binomial Distribution , 1986 .

[14]  Haim Shore.  Simple general approximations for a random variable and its inverse distribution function based on linear transformation of a nonskewed variate , 1986 .

[15]  Haim Shore.  Simple Approximations for the Inverse Cumulative Function, the Density Function and the Loss Integral of the Normal Distribution , 1982 .

[16]  Peter R. Nelson,et al.  The Effect of Non-Normality on the Control Limits of X-Bar Charts , 1976 .