Abstract
Our purpose is to indicate a new method for determining the control limits of univariate control charts to show the effectiveness of golden ratios search. We examine a solution to a problem when signals from mean and variance charts differ. Lack of concordance in the signals from mean and variance (or standard deviation) control charts bring confusion to Quality Control managers which in turn may lead to sub optimal management quality practices. To achieve better quality management practice, we provide a solution to the problem of finding different decision signals for in-control processes for quality control charts for mean and variability. We construct the control charts in experimental conditions for in-control average run length using the methods of simulation. Finally, we employ the golden ratio search method to identify the control limit parameters which differ from standard methods for constructing quality control charts. Last, we minimize the length of time in computation in the construction of these new quality control charts.
Highlights
AND PURPOSEIn SQC, a key measure for control chart performance is average run length (ARL)
We need an efficient search method and we propose using golden ratio search to achieve this goal
We find mathematical studies of golden ratio search in Wilde and Beightler (1987), Livio (2002), among others
Summary
AND PURPOSEIn SQC, a key measure for control chart performance is average run length (ARL). Its computation is usually determined by [1] Monte Carlo simulation, [2] Markov Chains, or [3] the calculus of integral equations. Some SQC simulation studies often require extensive computing time and frequent trials. In these cases, efficiency in the Monte Carlo approach is still a vital issue. In another study Pan, Jarrett and Mangiamelli (2001) explored the use of the geometric distribution to calculate the mean and standard deviation of run length. Promising, this attempt did not explain why the average runs length (ARL) changes
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