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Calculate the degrees of freedom for error:dfError=Total df−Treatment df=24−4=20\text{df}_{\text{Error}} = \text{Total df} - \text{Treatment df} = 24 - 4 = 20dfError​=Total df−Treatment df=24−4=20

Calculate the sum of squares for error:ssError=Total ss−Treatment ss=643−333=310\text{ss}_{\text{Error}} = \text{Total ss} - \text{Treatment ss} = 643 - 333 = 310ssError​=Total ss−Treatment ss=643−333=310

Calculate the mean squares:

MSTreatment=ssTreatmentdfTreatment=3334=83.25\text{MS}_{\text{Treatment}} = \frac{\text{ss}_{\text{Treatment}}}{\text{df}_{\text{Treatment}}} = \frac{333}{4} = 83.25MSTreatment​=dfTreatment​ssTreatment​​=4333​=83.25 MSError=ssErrordfError=31020=15.5\text{MS}_{\text{Error}} = \frac{\text{ss}_{\text{Error}}}{\text{df}_{\text{Error}}} = \frac{310}{20} = 15.5MSError​=dfError​ssError​​=20310​=15.5

Calculate the F-statistic:

F=MSTreatmentMSError=83.2515.5≈5.37F = \frac{\text{MS}_{\text{Treatment}}}{\text{MS}_{\text{Error}}} = \frac{83.25}{15.5} \approx 5.37F=MSError​MSTreatment​​=15.583.25​≈5.37

A tree diagram is a tool used to break down broad goals into increasingly detailed levels. It starts with a central concept and branches out into finer levels of detail, similar to the structure of a tree. This helps in understanding the various components of a goal and how they relate to one another, facilitating a step-by-step approach to achieving the objective.

References:

ASQ (American Society for Quality). (n.d.). Tree Diagram. Retrieved from https://asq.org/quality-resources/tree-diagram

Tague, N.R. (2004). The Quality Toolbox. ASQ Quality Press.

The situation described is an example of an unintended consequence. Each module functions as intended individually, but when combined, the overall system's performance is suboptimal. This situation often arises when interactions between modules are not fully considered, leading to unforeseen issues that degrade overall system performance.

Standardized work involves documenting and following the best practices for performing tasks on the production line.

Job aids that outline step-by-step instructions ensure consistency and quality in task performance.

This practice helps in maintaining uniformity and reducing variability in the production process.

References: Lean manufacturing literature, such as "The Lean Manufacturing Pocket Handbook," describes standardized work as a core principle for ensuring efficiency and quality.