Other Univariate Statistical Process Monitoring and Control Techniques Chapter 9 Other Univariate Statistical Process Monitoring and Control Techniques Introduction to Statistical Quality Control, 4th Edition

9-1. Statistical Process Control for Short Production Runs 9-1.1 and R Charts for Short Production Runs Deviation from nominal (DNOM) control chart can be used for short production runs. The procedure is: Calculate xi = Mi – Tk, the deviation from nominal for each observation. (Where Mi is the ith actual measurement and Tk is the target value for a particular group or part.) Calculate and R for each sample using the deviations. Construct standard and R charts for the deviations calculated. Introduction to Statistical Quality Control, 4th Edition

9-1. Statistical Process Control for Short Production Runs 9-1.1 and R Charts for Short Production Runs Using data in Table 9-1, the control charts are Introduction to Statistical Quality Control, 4th Edition

9-1. Statistical Process Control for Short Production Runs 9-1.1 and R Charts for Short Production Runs Important points about relative to the DNOM approach: An assumption is that the process standard deviation is approximately the same for all parts. If this assumption is invalid, use standardized and R charts. This procedure works best when the sample size is constant for all part numbers Deviation from nominal control charts have intuitive appeal when the nominal specification is the desired target value for the process. Introduction to Statistical Quality Control, 4th Edition

9-1. Statistical Process Control for Short Production Runs 9-1.1 Standardized and R Charts If process standard deviations are different for different part numbers, the deviation from nominal control charts will not work effectively. Standardized control charts can effectively handle the situation of different process standard deviations. Introduction to Statistical Quality Control, 4th Edition

9-1. Statistical Process Control for Short Production Runs 9-1.1 Standardized and R Charts - average range for ith part Ti – nominal value of x for the ith part For all samples from this part number is plotted on a standardized R chart with LCL = D3 and UCL = D4 Introduction to Statistical Quality Control, 4th Edition

9-1. Statistical Process Control for Short Production Runs 9-1.1 Standardized and R Charts - average range for ith part Ti – nominal value of x for the ith part For all samples from this part number is plotted on a standardized chart with LCL = -A2 and UCL = A2 Introduction to Statistical Quality Control, 4th Edition

9-1. Statistical Process Control for Short Production Runs 9-1.2 Attribute Control Charts for Short Production Runs Standardized control charts for attribute data can be used for short production runs. These charts are discussed in Chapter 6. Table 9-2 provides a summary of the standardized attribute control charts for short production runs. Introduction to Statistical Quality Control, 4th Edition

9-1. Statistical Process Control for Short Production Runs 9-1.2 Attribute Control Charts for Short Production Runs Introduction to Statistical Quality Control, 4th Edition

9-2. Modified and Acceptance Control Charts When a high level of process capability has been achieved, it may be useful to relax the level of surveillance provided by standard control charts. Modified control limits for charts or acceptance control charts can be employed for this situation. Introduction to Statistical Quality Control, 4th Edition

9-2. Modified and Acceptance Control Charts 9-2.1 Modified Control Limits for the Chart Modified control limits commonly used in the case Cp or Cpk > 1. The modified control chart is concerned only with detecting whether the true process mean  is located such that the process is producing a fraction nonconforming in excess of some specified value, .  can vary over the range L    U Introduction to Statistical Quality Control, 4th Edition

9-2. Modified and Acceptance Control Charts 9-2.1 Modified Control Limits for the Chart The upper and lower control limits for the modified control chart are Introduction to Statistical Quality Control, 4th Edition

9-2. Modified and Acceptance Control Charts Acceptance control charts take into account both the -risk and the -risk. Two approaches to designing the acceptance control chart Design the chart based on a specified n and process nonconforming  that we would like to reject with probability 1 - . Choose a sample size for an acceptance control chart so that specified values of   , and  are obtained. Introduction to Statistical Quality Control, 4th Edition

9-2. Modified and Acceptance Control Charts Approach 1: The control limits are Introduction to Statistical Quality Control, 4th Edition

9-2. Modified and Acceptance Control Charts Approach 2: A sample size of will yield the required values of   , and . Introduction to Statistical Quality Control, 4th Edition