SCOTT D.GRIMSHAW AND FRANK B.ALT and y which is exponentially distributed with mear ten the characteristics and pr 1.Both have equal means and standard deviations. ed using either moments or the probability den but t distrib di tion shapes as sho sity function. the quantile plots where it is po ossible to select values inverse cumulative dist Q(u)=F-1(u)={:F()=uh,0<u<1 This paper proposes a control chart which uses values of the quantile function These charts ar in de e percentiles,Q(p/100 and R charts.Using historical data,values of an in controlquarntilefir ion can be established peration can be tion, evalated through a test statistic which compares the sample to the in-control quantile function values )=n(21-）x网 Control Charts for Quantile Function Values +n(u-2 for the 25-1≤us25+1 2n 2n i=1,2,n-1 whereX(1:n)≤X(2:m)≤ ≤X(nn）)denote the order statistics.Q(u）is for u< 2元0ru >1 This quantile function given by Parzen(1979).It app ars to behave better in small samples,which is often the o,than the piece The first step in constructing the control chart is unction whic -1 effective use of this control chart is when there are and the likely out-of-control distributions.Anothe nay be elect values of u that co (b) 02 04 06 08 For example,monitoring the box plots and Hoaglin (1987)c FIGURE 1.(a)Probability Density Functions and (b) nlot A third ann oach is to select values Quantile Functions for Normally Distributed X and Expo correspond to characteristics which are of most con nentially Distributed Y cern in the process.For example,if a change in th Journal of Quality Technology Vol.29.No.1.January 1997 Reproduced with permission of the copyright owner.Further reproduction prohibited without permission Reproduced with permission of the copyright owner. Further reproduction prohibited without permission