The viability of Weibull analysis of small samples in process manufacturing

Abstract

This research deals with some Statistical Quality Control (SQC) methods, which are used in quality testing. It investigates the problem encountered with statistical process control (SPC) tools when small sample sizes are used. Small sample size testing is a new area of concern especially when using expensive (or large) products, which are produced in small batches (low volume production). Critical literature review and analysis of current technologies and methods in SPC with small samples testing failed to show a conformance with conventional SPC techniques, as the confidence limits for averages and standard deviation are too wide. Therefore, using such sizes will provide unsecured results with a lack in accuracy. The current research demonstrates such problems in manufacturing by using examples, in order to show the lack and the difficulties faced with conventional SPC tools (control charts). Weibull distribution has always shown a clear and acceptable prediction of failure and life behaviour with small sample size batches. Using such distribution enables the accuracy needed with small sample size to be obtained. With small sample control charts generate inaccurate confidence limits, which are low. On the contrary, Weibull theory suggests that using small samples enable achievement of accurate confidence limits. This research highlights these two aspects and explains their features in more depth. An outline of the overall problem and solution point out success of Weibull analysis when Weibull distribution is modified to overcome the problems encountered when small sample sizes are used. This work shows the viability of Weibull distribution to be used as a quality tool and construct new control charts, which will provide accurate result and detect nonconformance and variability with the use of small sample sizes. Therefore, the new proposed Weibull deduction control charts shows a successful replacement of the conventional control chart, and these new charts will compensate the errors in quality testing when using small size samples.