Assume that Allied Manufacturing Co. produces sheet metal, with a target thickness of 0.750 inch. Below are the observed thicknesses of output each day over the past 30 working days. Because the company has only recently begun operations and is eager to compete effectively in the market for specialty rolled-steel products, it is interested in developing and implementing an effective quality-control system. As the management accountant for Allied, you have been invited to participate in the design of this system.

Day                               Output Thickness (inch)
1.......................................................................0.734
2.......................................................................0.754
3.......................................................................0.755
4.......................................................................0.727
5.......................................................................0.722
6.......................................................................0.708
7.......................................................................0.734
8.......................................................................0.749
9.......................................................................0.728
10.....................................................................0.731
11....................................................................0.744
12....................................................................0.761
13....................................................................0.731
14....................................................................0.776
15....................................................................0.693
16....................................................................0.754
17....................................................................0.786
18....................................................................0.833
19....................................................................0.761
20....................................................................0.795
21....................................................................0.766
22....................................................................0.771
23....................................................................0.781
24....................................................................0.749
25....................................................................0.755
26....................................................................0.789
27....................................................................0.812
28....................................................................0.766
29....................................................................0.801
30....................................................................0.821

Required

1. Prepare a histogram using the 30 observations presented above. (Hints: In conjunction with the Histogram option under Charts, choose Axis Options, Bins, No. of bins = 12, and choose to show Numbers on the horizontal axis to 2 decimal places; resize the resulting chart to increase its clarity.) Show the sample mean and sample standard deviation for the 30 observations. (Round answers to 3 decimal places.)

2. What information is conveyed in the histogram you prepared, and what information (of interest to the present discussion) is not conveyed by the histogram? In general, what cautions might you offer (or, what questions might you ask) when attempting to interpret information from a histogram, similar to the one you prepared in requirement 1?

3. The time interval between each of the 30 observations above is equal. Therefore, the sample number (1, 2, 3, etc.) can be used to as a surrogate for “time.” Use Excel to prepare a “run chart” [i.e., a line graph in which observations are plotted over time; the vertical axis is the observed quality characteristic (thickness), while the horizontal axis represents the time scale]. (Hints: Prepare an XY scatter chart, with Smooth Lines and Markers. For the vertical axis, use 0.65 for the minimum bound and 0.85 for the maximum bound, under Format Axis, Axis Options.) What can you conclude from a visual examination of the chart you prepared? What is the mean value of the first 16 observations (to 3 decimal places), and what is the mean value of the last 14 observations (to 3 decimal places)?

4. Statistical control chart: Assume that, after collecting additional data over time, the company concludes that the process is in control, with a mean thickness of rolled steel (in inches) of 0.750 and a standard deviation of 0.025 inch. Given these characteristics, what is the upper control limit and the lower control limit for the process of producing rolled steel by Allied, assuming a 95% confidence level? (Round answers to 3 decimal places. For example, 0.7846 = 0.785.)

5. Assume that the data presented above represent a new sample of observations, collected after the construction of the statistical control limits set in requirement 4 above. Use conditional IF statements in Excel to scan the set of 30 observations to isolate any observations outside the statistical control limits determined in requirement 4. What conclusion(s) can you draw based on this analysis?

6. Suggest follow-up activities that might be pursued, as a result of the findings from requirements 1 through 5.