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Quality control with non-normal, censured and truncated data Noghhondarian, Kazem


This research presents a new approach to the computations of control charts for non- Normal data and for those quality characteristics where the exact sampling distributions of statistics for the process mean and standard deviation are not known. We use a class of power transformations due to Box and Cox (1964), to produce data that conform best to the Normal distribution. A statistical test of significance to determine the presence of an additional between-sample variation is introduced and an appropriate control chart to control this extra variation is developed. The Likelihood Ratio (LR), statistic which has been found useful in areas such as testing of hypothesis and estimation of confidence intervals, is used to design the control charts in the original scale of measurements that are natural for the product. The major advantage of LR method is its relatively rapid convergence to its chi-square asymptote. We present a specific application in the wood industry, by constructing appropriate control charts for the final Moisture Content (MC) of kiln-dried lumber. Comparison with a previous study which used the original non-Normal MC data showed the importance of an appropriate transformation and the inclusion of the additional between-sample variation in the calculations of the control chart limits. Without these necessary steps the control chart may lose its validity and falsely signal an out of control situation. Confidence intervals and control charts for the process mean and standard deviation are developed based on the LR statistic for the Weibull and Gumbel distributions. A control chart for the percentile of strength data to maintain a rninimum strength at a desired level, is also presented. Probability plots to check the Normality assumption of the censored and truncated data are presented. Appropriate control charts for the sample estimates of mean and standard deviation for the non-Normal censored and truncated data are developed. A procedure is given to re-express the control charts for the censored and truncated data in the original scale of measurements. Complex calculations were performed without the need to program using the Mathcad™ computer analysis package. This is a highly desirable property for the non-statistically oriented user.

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