Concept explainers
The control limits.
Answer to Problem 4.69P
The Upper control limit for averages, lower control limit for averages, upper control limit for ranges and lower control limit for ranges is
Explanation of Solution
Given:
The number of sample subsets are
The number of measured values in each subset are
Formula used:
The expression for average of sample subset is given as,
Here,
The expression forrange of sample subset is given as,
Here,
The expression for average of averages is given as,
The expression for average of ranges is given as,
The expression for upper control limit for the averages is given as,
Here,
The expression for lower control limit for the averages is given as,
The expression for upper control limit for the ranges is given as,
Here,
The expression for lower control limit for the ranges is given as,
Here,
Calculation:
Refer to table 4.2 “Constant for control charts” for sample size 4 values obtained,
The average of the first subset can be calculated as,
The range of the first subset can be calculated as,
The average of the second subset can be calculated as,
The range of the second subset can be calculated as,
The average of the third subset can be calculated as,
The range of the third subset can be calculated as,
The average of the fourth subset can be calculated as,
The range of the fourth subset can be calculated as,
The average of the fifth subset can be calculated as,
The range of the fifth subset can be calculated as,
The average of the sixth subset can be calculated as,
The range of the sixth subset can be calculated as,
The average of averages can be calculated as,
The average of ranges can be calculated as,
The upper control limit for the averages can be calculated as,
The lower control limit for the averages can be calculated as,
The upper control limit for the ranges can be calculated as,
The lower control limit for the ranges can be calculated as,
Conclusion:
Therefore, the Upper control limit for averages, lower control limit for averages, upper control limit for ranges and lower control limit for ranges is
Want to see more full solutions like this?
Chapter 4 Solutions
Manufacturing Processes for Engineering Materials (6th Edition)
- Kindy answer correctly. Please show the necessary steps (the template is provided)arrow_forwardWhat is relation between product tolerance (engineering tolerance) and process variation.? Explain in some details showing some representation. Analyze the following study in terms: Components of variations and their contributions X Chart and R Chartarrow_forwardWhat do you mean by fixed cost and variable cost? Provide at least three examples of each item. (Write within 4-5 lines).arrow_forward
- Thanks for your work. Can you please repost with pictures or any other way because my computer doesn't display all the solution steps (error showing equation)arrow_forwardWith complete and clear units/conversion factors please thank you. Please label also the final answerarrow_forwardComplete the following comparison table with the possible answers indicated in each comparison factor:arrow_forward
- Observe the given values carefully and give me right solution with clear calculationsarrow_forwardExplain what the different variable(x-bar and r-bar) and attribute(c, p, np, etc) control charts mean and what they tell about a process.arrow_forwardThe table provided is table 10.1, therefore table 10.1 and table 5.1 are the same table. Please show all your work. :D thank youarrow_forward
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY