Attribute Control Charts Binomial Count Charts P Chart - Fraction defective data, subgroup size could vary or stay constant. NP Chart - Number of defective data, subgroup size has to be constant Area of Opportunity Charts C Chart - Number of defects/unit data when there is a constant area of opportunity U Chart - Number of defects/unit data when area of opportunity changes from subgroup to subgroup

Subgroup Size Determination As a rule of thumb, control charts based on binomial count data should have sample sizes large enough so that the average count per subgroup is at least 2. Example:

P Chart for Variable Subgroup Size Control limits vary proportional to the sample size Three alternatives Construct control charts based on average subgroup size Compute new control limits for every subgroup based on that subgroup’s size. Compute a wide and narrow set of control limits based upon the largest and smallest values of n

Alternative 1: Alternative 2: Most applicable when the variation in subgroup size is ± 25% If a point falls close to the control limits, exact control limits should be used Average value of n should be periodically recalculated Alternative 2: Most applicable when the variation in subgroup size is more than ± 25% Accurate but time consuming hard to read and interpret

Alternative 3: Most applicable when the variation in the subgroup size is ± 25% Determine the outer and inner sets of control limits based on the smallest and largest subgroup sizes, respectively If a sample falls outside the outer control limits it clearly indicates a lack of statistical control If a sample falls inside the inner control limits it indicates presence of statistical control. Exact control limit values need to be calculated for those points falling between the inner and outer control limits

NP Chart Number of defective data, subgroup size has to be constant Control limits: