Abstract
A measurable quality characteristic is assumed to follow Inverse Rayleigh Distribution. Variable control charts based on extreme values of each subgroup are constructed. The technique of analysis of means (ANOM) is adopted to workout the decision lines of Inverse Rayleigh Distribution(IRD). The preferability of the proposed ANOM decision lines over that of Ott(1967) is illustrated by some examples.
Highlights
The probability density function of a Inverse Rayleigh Distribution (IRD) with scale parameter σ is given by f (x)
Because of this paper aims at exploring Analysis of Means (ANOM) using control limits of extreme value statistics we have considered only the control chart aspects but not any recently developed ANOM tables or techniques
On the other hand when the ANOM tables of our model (IRD) are used for data sets we get the number of homogeneous means to be 5,3,4 respectively without exhibiting deviation of any mean from homogeneity
Summary
The probability density function (pdf) of a Inverse Rayleigh Distribution (IRD) with scale parameter σ is given by f (x). The test statistic on extreme value control chart is the original sample vector X (x1, x2 ,..., xn ) from the ongoing production. Analysis of Means (ANOM) is a technique originally developed by Ott (1967) [11] for comparing a group of treatment means to see if any one of them differs significantly from the overall mean. This procedure is carried out by comparing the sample mean values to the overall grand mean, about which decision lines have been constructed.
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