Precision of scale weight measurements. The Journal of Quality Technology (July 1998) published an article examining the effects of the precision of measurement on the R-chart. The authors presented data from a British nutrition company that fills containers labeled “500 grams” with a powdered dietary supplement. Once every 15 minutes, five containers are sampled from the filling process, and the fill weight is measured. The table to the right lists the measurements for 25 consecutive samples made with a scale that is accurate to .5 gram, followed by the table below, which gives measurements for the same samples made with a scale that is accurate to only 2.5 grams. Throughout the time period over which the samples were drawn, it is known that the filling process was in statistical control with mean 500 grams and standard deviation 1 gram.

a. Construct an R-chart for the data that is accurate to .5 gram. Is the process under statistical control? Explain.

b. Given your answer to part

a, is it appropriate to construct an x@chart for the data? Explain.

c. Construct an R-chart for the data that is accurate to only 2.5 grams. What does it suggest about the stability of the filling process? FILL1 FILL2 Second table for Exercise 13.38 Sample Fill Weights Accurate to 2.5 Grams Range Sample Fill Weights Accurate to 2.5 Grams Range 1 500.0 500.0 502.5 500.0 500.0 2.5 14 500.0 500.0 500.0 500.0 500.0 0.0 2 500.0 500.0 500.0 500.0 500.0 0.0 15 502.5 502.5 502.5 500.0 502.5 2.5 3 500.0 500.0 500.0 500.0 500.0 0.0 16 500.0 500.0 500.0 500.0 500.0 0.0 4 497.5 500.0 497.5 497.5 500.0 2.5 17 497.5 497.5 497.5 497.5 497.5 0.0 5 500.0 500.0 500.0 500.0 500.0 0.0 18 500.0 500.0 500.0 500.0 500.0 0.0 6 502.5 500.0 497.5 500.0 500.0 5.0 19 495.0 497.5 500.0 500.0 500.0 5.0 7 500.0 500.0 502.5 502.5 500.0 2.5 20 500.0 502.5 500.0 500.0 502.5 2.5 8 497.5 500.0 500.0 497.5 500.0 2.5 21 500.0 500.0 500.0 500.0 500.0 0.0 9 500.0 500.0 497.5 500.0 502.5 5.0 22 500.0 500.0 500.0 500.0 500.0 0.0 10 500.0 500.0 500.0 500.0 500.0 0.0 23 500.0 500.0 500.0 500.0 500.0 0.0 11 500.0 505.0 502.5 500.0 500.0 5.0 24 497.5 497.5 500.0 497.5 497.5 2.5 12 500.0 500.0 500.0 500.0 500.0 0.0 25 500.0 500.0 497.5 500.0 500.0 2.5 13 500.0 500.0 497.5 500.0 500.0 2.5 Source: A. Tricker, E. Coates, and E. Okell, “The Effects on the R-Chart of Precision of Measurement,” Journal of Quality Technology, Vol. 30, No. 3, July 1998. Reprinted with permission from the Journal of Quality Technology © 1998 ASQ, www.asq.org. No further distribution allowed without permission.

d. Based on your answers to parts a and

c, discuss the importance of the accuracy of measurement instruments in evaluating the stability of production processes. First table for Exercise 13.38 Sample Fill Weights Accurate to .5 Gram Range 1 500.5 499.5 502.0 501.0 500.5 2.5 2 500.5 499.5 500.0 499.0 500.0 1.5 3 498.5 499.0 500.0 499.5 500.0 1.5 4 500.5 499.5 499.0 499.0 500.5 1.5 5 500.0 501.0 500.5 500.5 500.0 1.0 6 501.0 498.5 500.0 501.5 500.5 3.0 7 499.5 500.0 499.0 501.0 499.5 2.0 8 498.5 498.0 500.0 500.5 500.5 2.5 9 498.0 499.0 502.0 501.0 501.5 4.0 10 499.0 499.5 499.5 500.0 499.5 1.0 11 502.5 499.5 501.0 501.5 502.0 3.0 12 501.5 501.5 500.0 500.0 501.0 1.5 13 498.5 499.5 501.0 500.5 498.5 2.5 14 499.5 498.0 500.0 499.5 498.5 2.0 15 501.0 500.0 498.0 500.5 500.0 3.0 16 502.5 501.5 502.0 500.5 500.5 2.0 17 499.5 500.5 500.0 499.5 499.5 1.0 18 499.0 498.5 498.0 500.0 498.0 2.0 19 499.0 498.0 500.5 501.0 501.0 3.0 20 501.5 499.5 500.0 500.5 502.0 2.5 21 501.0 500.5 502.0 502.5 502.5 2.0 22 501.5 502.5 502.5 501.5 502.0 1.0 23 499.5 502.0 500.0 500.5 502.0 2.5 24 498.5 499.0 499.0 500.5 500.0 2.0 25 500.0 499.5 498.5 500.0 500.5 2.0