SINGLE-SUBGROUP PERFORMANCE-MEASURES AND DIAGNOSTIC PROCEDURES FOR X-BAR CONTROL CHARTS

Although Shewhart control charts have had a tremendous impact on quali ty improvement, the inability to precisely measure chart performance h as limited their role, and subsequently overall effectiveness in the c ontrol of manufacturing processes. Measures of performance in terms of operational characteristics (OC) are defined on two distinct levels: (a) single-subgroup level, which examines the probability of a rule vi olation at any given subgroup (b) multiple-subgroup level, which consi ders the probability of one or more rule violations throughout process monitoring. Single-subgroup performance measures for X-bar charts tha t employ four rules are formulated. These measures are exact expressio ns of operational characteristics, except for the numerical approximat ion to the integral of the normal distribution. Applications of these models to simulated data demonstrate their accuracy in predicting char t performance. In addition, a diagnostic methodology is described whic h utilizes the derived performance measures to predict the mean of a s hifted distribution. The proposed diagnostic procedure is illustrated in validation and application examples.