A comparison of the effectiveness of statistical process control charts

With consumer demands for a more consistent quality product, manufacturers have turned away from the concept of acceptance sampling to the concept of controlling processes to assure acceptable products. One method of controlling processes is through the generation and interpretation of control charts. Since Shewhart first introduced control charts in 1924, alternative control chart methodologies have been introduced that have stated an increased efficiency of correctly determining that a process parameter has changed.; The analyses for this dissertation examined the efficiency of the Shewhart control chart employing the most common rules for interpretation. Alternative control charts were also examined to investigate any increase in effectiveness in determining a change in process parameters as compared to the most commonly used Shewhart control chart. Analyses performed by other experts in the field using numerical methods was recreated and their work extended in an effort to analyze the effectiveness of existing control chart methodologies in correctly identifying a change in a process parameter. A computer simulation model was developed and was used as an extension of the numerical methods to analyze cases that were too complex for the numerical methods. These cases included the effectiveness of the control charts using data from various statistical distributions including skewed and autocorrelated data.; Analysis was performed to show that the distribution of the run lengths of the control chart methodologies was geometric and could be approximated by the use of an exponential distribution. For each pair of control chart methodologies, the hypothesis that their effectiveness was equal was tested for various shifts in the process mean. The analysis performed for this dissertation showed that the hypothesis that the effectiveness of different control chart techniques was equal could be rejected using a χ2 test indicating a significant difference in the control chart methodologies to detect process shifts.; The relationship of Type I (α) error and Type II (β) error proved to be a major factor in determining the relative effectiveness of the control chart methodologies. Further analysis lead to the ability to modify the published control limits of control chart techniques to equate the Type I (α) error to allow for direct comparison.; It was also shown in this analysis that the knowledge of an underlying process distribution is a factor in determining the most effective control to be used. Although a Shewhart control chart was determined to be most effective for an underlying normal distribution, a CUSUM control chart is most effective if the distribution is skewed and a Zone control chart is most effective for autocorrelated data. The effect of sample size was shown to be an important factor in determining the relative effectiveness of control chart methodologies when the data is from a skewed distribution.