1. An industrial engineer is investigating the effect of four assembly methods (
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1. An industrial engineer is investigating the effect of four assembly methods (A, B, C, D) on the assembly time for a colour television component. Four operators are selected the study. Furthermore, the engineer knows that each assembly method produces such fatigue that the time required for the last assembly may be greater than the time required for the first, regardless of the method. That is, a trend develops in the required assembly time. To account for nuiscance sources of variability, the engineer uses the design shown with the results below. tor C-10 B=7 A-5 D=10 2 D-14 C=18 B=10 A=10 3 A=7 D=11 C=11 B=12 B-8 A=8 D=9 C=14 3 (a) What kind of design is this? (b) Obtain the ANOVA table using the computer. (c) Obtain appropriate diagnostic plots and comment on the assumptions of normality and equal variances. (6) (d) Assess the null hypothesis of no differences among the methods (a -0.01) i. State the hypotheses. ii. Give the value of the test statistic. ii. What is the distribution of the test statistic? iv. Obtain the P value. v. Make a decision. vi. State a conclusion in the context of the problem. (e) What should the engineer report about the effects of assembly order? Do these effects increase due to fatigue as the engineer suspects? Explain clearly (3 (f) What should the engineer report about the influence of the operator? Eaplain clearly (g) Obtain simu laneous 99% confidence intervals for the differences between the method means, using Bonferroni.Explanation / Answer
1. An industrial engineer is investigating the effect of four assembly methods (A, B, C, D) on the assembly time for a colour television component. Four operators are selected the study. Furthermore, the engineer knows that each assembly method produces such fatigue that the time required for the last assembly may be greater than the time required for the first, regardless of the method. That is, a trend develops in the required assembly time. To account for nuiscance sources of variability, the engineer uses the design shown with the results below. tor C-10 B=7 A-5 D=10 2 D-14 C=18 B=10 A=10 3 A=7 D=11 C=11 B=12 B-8 A=8 D=9 C=14 3 (a) What kind of design is this? (b) Obtain the ANOVA table using the computer. (c) Obtain appropriate diagnostic plots and comment on the assumptions of normality and equal variances. (6) (d) Assess the null hypothesis of no differences among the methods (a -0.01) i. State the hypotheses. ii. Give the value of the test statistic. ii. What is the distribution of the test statistic? iv. Obtain the P value. v. Make a decision. vi. State a conclusion in the context of the problem. (e) What should the engineer report about the effects of assembly order? Do these effects increase due to fatigue as the engineer suspects? Explain clearly (3 (f) What should the engineer report about the influence of the operator? Eaplain clearly (g) Obtain simu laneous 99% confidence intervals for the differences between the method means, using Bonferroni.
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