8. Control charts for X and R are maintained on the shear strength of spot welds. Onehundred observations divided into subgroups of size five are used as a baseline toconstruct the charts, and estimates of u and o are computed from these observa-tions. Assume that the 100 observations are X1, X2, . . . , X100 and the ranges of the20 subgroups are R1, R2, . . . , R20. From these baseline data the following quanti-ties are computed:10020ΣΧ- 97,500, ΣR- 1,042.Using this information, compute the values of three-sigma limits for both charts.

X bar chart - X bar chart determines whether process is in control with respect to process mean. X…

Answered: 8. Control charts for X and R are…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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Compute CL, UCL, and LCL of MR and X Control Charts for the following data. Batch Number Flowrate X Moving Range MR 1 49.6 2 47.6 3 49.9 4 51.3 5 47.8 6 51.2 7 52.6 8 52.4 9 53.6 10 52.1
Vilfredo Pareto was a famous engineer/economist in the 19th and early 20th centuries. He reportedly expressed this 80/20 Rule: 80% of all progress results from 20% of the actions taken. The Pareto Diagram, also called a Juran Diagram, depicts a variant 80/20 Rule: 80% of all production problems come from 20% of the problem areas. a. What kind of statistical chart is the Pareto Diagram? ____ (enter H for histogram, P for probability distribution, T for a Taguchi chart, A for all three of these. N for none of these. b. The value of the Pareto Diagram is its highlighting the areas causing 80% of quality problems. ____ (enter T for true or F for false)
A travel agency is concerned with the accuracy and ap-pearance of itineraries prepared for its clients. Defects caninclude errors in times, airlines, flight numbers, prices, carrental information, lodging, charge card numbers, and res-ervation numbers, as well as typographical errors. As thepossible number of errors is nearly infinite, the agency mea-sures the number of errors that do occur. The current processresults in an average of three errors per itinerary.a. What are the two-sigma control limits for these defects?b. A client scheduled a trip to Dallas. Her itinerary containedsix errors. Interpret this information
Find the minimum sample size n needed to estimate μ for the given values of c, σ, and E. c=0.98, σ=6.9, and E=1 Assume that a preliminary sample has at least 30 members.
The output from a process contains a 0.02 defective unit. Defective units that go undetected into final assemblies cost $25 each to replace. An inspection process, which would detect and remove all defectives, can be established to test these units. However, the inspector, who can test 20 units per hour, is paid $8 per hour, including fringe benefits. Should an inspection station be established to test all units?a. What is the cost to inspect each unit?b. What is the benefit (or loss) from the inspection process?
Amertron, discussed in the given problem, has established a policy of passing rolls of wire having five or fewer defects.a. Based on the exact Poisson distribution, what is the proportion of the rolls that pass inspection? b. Estimate the answer to part (a) using the normal approximation to the Poisson.
Refer to Table S6.1 - Factors for Computing Control Chart Limits (3 sigma) for this problem. Sample Size, n Mean Factor, A2 Upper Range, D4 Lower Range, D3 2 1.880 3.268 0 3 1.023 2.574 0 4 0.729 2.282 0 5 0.577 2.115 0 6 0.483 2.004 0 7 0.419 1.924 0.076 8 0.373 1.864 0.136 9 0.337 1.816 0.184 10 0.308 1.777 0.223 12 0.266 1.716 0.284 Auto pistons at Wemming Chung's plant in Shanghai are produced in a forging process, and the diameter is a critical factor that must be controlled. From sample sizes of 10 pistons produced each day, the mean and the range of this diameter have been as follows: Day Mean Bold x overbarx (mm) Range R (mm) 1 154.9154.9 4.04.0 2 151.2151.2 4.44.4 3 153.6153.6 3.93.9 4 155.5155.5 5.05.0 5 158.6158.6 4.3 a) What is the value of x? X = ____ mm b) What is the value of R? R =…
A pallet manufacturer has measured the output of a board cutting operation. Theboards have a specification of 24 inches {0.5 inch. A sample of the boards isshown below. Calculate the capability of the board cutting operation. What suggestions would you give to the operator?24.0 24.1 24.2 23.8 24.3 23.9 24.0 24.123.8 24.3 24.2 23.9 24.4 24.0 23.9 24.2
As the supervisor in charge of shipping and receiving,you need to determine the average outgoing quality in a plantwhere the known incoming lots from your assembly line havean average defective rate of 3%. Your plan is to sample 80 unitsof every I ,000 in a lo t. The number of defects in the sample isnot to exceed 3. Such a plan provides you with a probabilityof acceptance of each lot of . 79 (79%). What is your averageoutgoing quality?
The following table contains the measurements of the key length dimension from a fuel injector. These samples of size five were taken at one-hour intervals. Use three-sigma control limits. Use Exhibit 10.13. SAMPLE NUMBER OBSERVATIONS 1 2 3 4 5 1 0.486 0.499 0.493 0.511 0.481 2 0.499 0.506 0.516 0.494 0.529 3 0.496 0.500 0.515 0.488 0.521 4 0.495 0.506 0.483 0.487 0.489 5 0.472 0.502 0.526 0.469 0.481 6 0.473 0.495 0.507 0.493 0.506 7 0.495 0.512 0.490 0.471 0.504 8 0.525 0.501 0.498 0.474 0.485 9 0.497 0.501 0.517 0.506 0.516 10 0.495 0.505 0.516 0.511 0.497 11 0.495 0.482 0.468 0.492 0.492 12 0.483 0.459 0.526 0.506 0.522 13 0.521 0.512 0.493 0.525 0.510 14 0.487 0.521 0.507 0.501 0.500 15 0.493 0.516 0.499 0.511 0.513 16 0.473 0.506 0.479 0.480 0.523 17 0.477 0.485 0.513 0.484 0.496 18 0.515 0.493 0.493 0.485 0.475 19 0.511 0.536 0.486 0.497 0.491 20 0.509 0.490 0.470 0.504 0.512 Calculate the mean and range for the above samples.…
Aspen Plastics produces plastic bottles to customer order. The quality inspector randomly selects four bottles from the bottle machine and measures the outside diameter of the bottleneck, a critical quality dimension that determines whether the bottle cap will fit properly. The dimensions (inch) from the last six samples are: BOTTLE Sample 1 2 3 4 1 0.694 0.622 0.698 0.69 2 0.687 0.611 0.697 0.613 3 0.671 0.680 0.695 0.602 4 0.610 0.615 0.685 0.678 5 0.680 0.624 0.618 0.614 6 0.685 0.693 0.607 0.669 What would be the center line of a 3-sigma S chart? Answer:
The operations manager of a Soft drink company is concerned about Machine No.3 in the assembly line. In order to make sure that the machine is operating correctly, samples are taken, and the average and range for each sample is computed. Each sample consists of 10 items produced from that machine. Recently, 12 samples were taken and the sample range and average computed for each are as follows: Sample Number Sample Range Sample Mean 1 1.00 45 2 1.21 44 3 0.81 45 4 1.00 46 5 1.11 47 6 0.72 46 7 0.76 49 8 1.01 48 9 1.02 50 10 0.89 51 11 0.76 49 12 1.10 51 During installation, the supplier set an average of 46 for the process with an average range 0.9. (a) Draw the appropriate control charts for machine No. 3. (b) Comment on your results.

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