An electric company produces incandescent light bulbs. The following data on the

Question

An electric company produces incandescent light bulbs. The following data on the number of lumens for 40-watt bulbs were collected when the process was in control: Number of Observations Sample 604 581 620 590 601 570 605 588 607 585 595 608 600 603 592 588 604 1. What is the mean (x) for each sample? a. Sample 1? (601] b. Sample 2? [602] c. Sample 3? [582] d. Sample 4? (602] e. Sample 5? [6041| 2. What is the range (R) for each sample? a. Sample 1? [24] b. Sample 2? [10] c. Sample 3? [22] d. Sample 4? [32] e, Sample 5? [24] What is the grand mean ()? [598.2] What is the average range (R)? [22.4] 5. What are the three sigma control limits for 3. 4. Mean control chart when standard deviation is unknown? [UCL= 614.552 and LC 581.848] b. Range control chart? [UCL 51.072 and LCL-0] 6, Based on the mean control chart and the sample means identified in question #1, is the process in or out of control? [yes, values for 1a-1e all fall within the mean control limit boundaries] 7. Based on the range control chart and the range values identified in question #2, is the process in our out of control? [yes, values for 2a-2e all fall within the range control limit boundaries] 8. Since these data were collected, some new employees were hired and a new sample was taken. The observations were 570, 603, 623, and 583. What are the mean (x) and range (R) for this sample? [sample mean 594.75; sample range 53] 9. Using the same control limits calculated in question #5, is the process still in control? [No, the sample mean falls within the mean control chart, but the range of 53 exceeds the range control chart UCL]

Explanation / Answer

Sample 570 603 623 583 Sum 2379 Mean=Sum/4 594.75 It is within control limits Largest Value in sample 623 Smallest value in sample 570 Range=Difference between the two 53 it is not in control limits

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