Eric is the design engineer at West Battery Corp. He examined the sample data below (Table 1, the same as the data used in the previous problems) vs. the original document of battery design specifications (instead of inspection guideline) where the nominal value of battery voltage is 50.5 volt and the tolerance is +/- 5.5 volt. The document also shows that the company was targeting three-sigma performance (2.7 parts or less in 1,000 to be "out of spec") when the production for this type of batteries was designed. Provide your analysis for Eric (based on the data and calculation result, not your personal opinion):

(1) Plot the histogram showing the disbution of the production output of battery voltage based on all collected sample entries (in Table 1);

(2) Eric stated that the process is not a three-sigma capable process. Justify his statement by measuring process capability.

(3) Eric had worked with other engineers, hoping to achieve three-sigma performance. The team came up with some plan of corrective actions and put it into experiment. Table 2 shows the testing data of voltages of produced batteries after the plan was incorporaetd into production processes. After re-measuring process capability, is it a successful plan for achieving three-sigma performance? If not, discuss the issue in terms of the centering and variability of the process for further corrective actions.

Problem 1 -- 4 pts Due to the complaints from retailers, West Battery Corp. decided to study the battery voltage for the batteries produced at the plant located in upstate New York. The manager has taken a sample of 16 batteries each hour for 24 hours. The data of the voltage (in volts) of each battery is shown in the table below. The battery is used for a medium-size electric lawn mower and the voltage of a new battery should be higher than 46, but no more than 54 volts. The manager would like to label each battery by A, B, C, D and F (ranking the battery voltage output quality) according to the new inspection guideline: -- Grade A (i.e. excellent) if the voltage is higher than 49 but no more than 52 -- Grade B (i.e. good) if the voltage is higher than 52 but no more than 53 -- Grade C (i.e. average) if the voltage is higher than 53 but no more than 54 -- Grade D (i.e. marginal) if the voltage is higher than 46 but no more than 49 -- Grade F (i.e. bad) otherwise Plot an appropriate chart to show the frequency distribution over the above grades for all batteries collected during these 24 hours. Note that in the chart, the frequencies should be shown in a descending order and thus the chart visually decipts which grades are more likely produced from the current system. Then, the cumulative output (in terms of % out of all 384 sample entries collected) for each grade (meaning the portion of batteries for that grade and the grades with a higher frequency than it) should be indicated in the chart as well. Hour sample taken Sample of 16 batteries Min Table of the distribution of battery grades Max Frequenc 1 2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 50.2 53.7 48.6 49.3 51.1 52.3 47.3 50.1 50.5 50.2 52.3 46.9 50.1 50.5 52.3 49.9 50.8 48.8 52.8 48.6 45.4 50.6 49.9 46.1 53.6 46.2 50.6 49.9 56.1 50.2 49.9 47.9 voltage voltage Grade y 49 52 A 158.0 52 53 B 60.0 3 50.2 48.3 52.6 46.9 53.3 49.2 47.9 54.1 50.6 52.1 54.0 50.6 48.8 53.8 47.9 53.3 53 54 C 35.0 4 5 6 49.5 48.8 54.9 53.2 53.6 51.1 52.6 52.6 49.5 51.8 47.8 52.3 48.3 52.6 53.3 53.1 52.3 51.7 50.5 50.5 50.5 43.7 45.7 50.6 50.5 50.2 48.3 52.6 48.5 50.2 49.9 53.6 50.6 49.9 46.1 53.6 53.6 52.6 50.6 50.9 44.4 51.9 45.7 50.2 51.1 52.3 47.9 52.3 46 49 D 88.0 F 43.0 7 46.4 54.1 50.6 49.2 52.3 48.3 45.3 49.9 46.1 53.6 49.9 46.1 50.6 49.9 50.3 52.6 8 52.5 52.6 46.9 50.2 50.6 49.9 49.9 47.9 54.7 50.6 52.6 51.1 49.9 46.1 50.3 53.6 Battery Voltage Chart 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 51.5 50.3 50.5 46.7 49.2 47.9 48.6 52.6 52.6 46.3 50.2 45.7 56.1 55.3 49.9 52.6 49.3 45.1 50.6 48.3 52.6 53.3 52.6 49.6 50.2 52.3 45.7 47.9 54.5 51.2 50.6 47.9 49.9 46.1 57.3 53.1 53.2 53.1 55.3 48.3 52.6 53.3 52.6 46.6 50.2 50.6 49.9 49.2 48.6 48.9 50.6 49.9 46.1 53.6 52.6 52.6 46.9 51.8 51.5 49.8 50.5 46.7 49.9 51.1 45.7 50.5 50.5 46.2 51.1 52.3 47.9 50.9 50.5 50.2 46.7 49.2 47.9 46.7 51.1 43.7 47.7 50.2 56.1 50.2 45.1 50.6 49.9 46.1 53.6 46.2 48.3 52.6 53.3 52.3 45.7 52.6 48.1 50.8 48.8 53.8 53.3 49.2 47.9 54.0 50.6 52.1 48.1 49.5 50.5 51.1 51.7 48.3 52.9 55.3 48.3 52.6 52.6 49.1 50.5 52.1 48.3 52.6 49.9 46.1 53.6 47.8 53.6 49.9 48.6 50.3 50.6 49.9 46.1 52.3 48.8 52.2 50.5 49.1 46.4 53.1 49.2 47.9 54.4 46.4 51.9 48.5 50.2 52.2 50.1 50.6 49.9 46.1 53.6 52.6 52.5 52.6 44.3 50.8 55.3 52.5 49.3 51.1 52.3 49.6 47.9 54.7 50.6 48.1 50.3 50.5 51.1 52.3 45.7 46.1 53.6 46.9 49.3 50.6 49.9 50.6 47.7 47.8 52.3 52.7 48.3 48.8 48.9 50.6 49.9 50.6 49.2 50.5 50.6 49.9 46.1 50.2 56.1 45.9 49.2 52.3 49.4 48.3 49.9 46.1 53.6 53.6 52.6 53.6 49.2 47.9 54.2 53.3 52.6 48.1 50.8 48.8 52.8 46.7 54.6 50.6 49.2 52.3 45.7 50.6 49.3 51.1 52.3 45.7 50.8 50.5 43.7 52.8 48.6 52.7 49.9 46.1 52.3 45.7 50.1 50.2 54.1 45.7 49.9 50.5 50.2 45.8 50.2 56.1 49.9 56.1 50.1 50.5 46.7 49.2 47.9 51.9 180.0 160.0 100% 158.0 140.0 Frequency 120.0 100.0 80.0 60.0 40.0 20.0 0.0 D B 80% 60% 88.01 40% 60.0 43.0 35.0 20% 0.0 0% F Battery Grade Frequency