714 CHAPTER 14 Statistical Process Control Notation p = estimate of the proportion of defective items in the process = total number of defects found among all items sampled total number of items sampled q = estimate of the proportion of process items that are not defective = 1 - p n = size of each individual sample or subgroup Graph Points plotted: proportions from the individual samples of size n Centerline: p Upper control limit: p + 3Apq n (Use 1 if this result is greater than 1.) Lower control limit: p - 3Apq n (Use 0 if this result is less than 0.) CAUTION Note this distinction in the calculations: When evaluating p, divide the total number of defects by the total number of items sampled. The computations for UCL and LCL, however, require division by n, the size of each individual sample. We use p for the centerline because it is the best estimate of the proportion of defects from the process. The expressions for the control limits correspond to 99.7% confidence interval limits for the confidence intervals described in Section 7-1. (Section 7-1 did not include any 99.7% confidence intervals, but the z score used for a 99.7% confidence interval is z = 2.97, which is rounded to 3 in the expressions used for the LCL and UCL in this section.) Defective Aircraft Altimeters EXAMPLE 1 The accuracy of aircraft altimeters is important because pilots rely on this instrument to maintain safe altitudes at all times. Pilots and passengers have been killed in crashes caused by wrong altimeter readings that led pilots to believe that they were safely above the ground when they were actually flying dangerously low. Because aircraft altimeters are so critically important to aviation safety, their accuracy is carefully controlled by government regulations. Federal Aviation Administration (FAA) Regulation 91.411 requires periodic testing of aircraft altimeters, and those altimeters must comply with specifications included in Appendix E to Part 43 of the FAA regulations. One of those FAA specifications is that an altimeter must give a reading with an error of no more than 30 ft when tested for an altitude of 2000 ft. The Orange Avionics Company manufactures altimeters in batches of 100, and each altimeter is tested and determined to be acceptable or defective. Listed below are the numbers of defective altimeters in successive batches of 100. Construct a control chart for the proportion p of defective altimeters and determine whether the process is within statistical control. If not, identify which of the three out-of-control criteria apply. Defects:2013122435127
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