Identify the type of method for sampling is associated with equal probabilities for each selection, even with small sample sizes .

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Chapter 7.1, Problem 1.2LC

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Identify the type of method for sampling is associated with equal probabilities for each selection, even with small sample sizes.

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Question 5 A fraction nonconforming control chart with center line 0.10, UCL = 0.19, and LCL = 0.01 is used to control a process. (a) If three-sigma limits are used, find the sample size for the control charte 2 (b) Use the Poisson approximation to the binomial to find the probability of type I error. (c) Use the Poisson approximation to the binomial to find the probability of type II error if the process fraction defective is actually p = 0.20.

Question 8 Ten parts are measured three times by the same operator in a gauge capability study. The data are shown in Table 4. (a) Describe the measurement error that results from the use of this gauge. I (b) Estimate total variability and product variability. (c) What percentage of total variability is due to the gauge? (d) If specifications on the part are at 100±15, find the P/T ratio for this gauge. Comment on the adequacy of the gauge. 3 Table 4: Measurement Data for Question 8 Part Number Measurement 1 Measurement 2 Measurement 3 1 2 100 95 101 100 93 97 3 101 103 100 4 96 95 97 5 98 98 96 6 99 98 98 7889 95 97 98 100 99 98 100 100 97 10 100 98 98 99

Question 6 The data shown in Table 3 are and R values for 24 samples of size n = 5 taken from a process producing bearings. The measurements are made on the inside diameter of the bearing, with only the last three decimals recorded (i.e., 34.5 should be 0.50345). Perform a process capability analysis using and R charts for the data from Table 3. Table 3: Data for Question 6 Sample Number R | Sample Number I Ꭱ 1 34.5 3 13 35.4 8 2 34.2 4 14 34.0 6 ∞∞ 31.6 15 37.1 5 4 31.5 4 16 34.9 7 56789 35.0 5 17 33.5 4 34.1 6 18 31.7 3 32.6 4 19 34.0 8 33.8 3 20 35.1 4 34.8 7 10 33.6 8 11 31.9 3 12 38.6 9 2232 21 33.7 2 32.8 1 33.5 24 34.2 2 32 3