EBK OM
6th Edition
ISBN: 9781305888210
Author: Collier
Publisher: YUZU
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Chapter 16, Problem 13PA
Summary Introduction
Interpretation: process capability indexes are to be computed and interpreted.
Concept Introduction: A statistical tool used for measuring the process’ ability for producing the output within the limits of the specification.
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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 5 pistons produced each day, the mean and the range of this diameter have
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158
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What is the UCL using 3-sigma?(round your response to two decimal places).
1.
2.
4.
For 50 consecutive days, a process engineer has measured the weight of acomponent after it has been coated with a special paint. Each day, she takes a sampleof 10 components. The average across all 500 components (50 days, 10 componentsper day) is 45.343018 grams. The standard deviation across all parts is 0.0076382 gram.When constructing an X-bar chart, what would be the center line and what would be thelines for the upper and lower control limits?
At Webster Chemical Company, lumps in the caulking compound could cause difficulties in dispensing a smooth bead from the tube. Testing for the presence of lumps destroys the product, so an analyst takes random samples. The following results are obtained:
Tube No.
Lumps
Tube No.
Lumps
Tube No.
Lumps
1
6
5
6
9
0
2
7
6
5
10
5
3
2
7
5
11
2
4
4
8
8
12
3
Determine the c-chart
two-sigma
upper and lower control limits for this process. Is the process in statistical control?
The
UCLc
equals
------
and the
LCLc
equals
------
(Enter
your responses rounded to two decimal
places.)
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- c) A process manufactures ball bearing whose diameters are normally distributed with mean 2.505cm and standard deviation 0.008cm.Specifications call for the diameter to be in the interval 2.5 ‡ 0.01 cm. estimate the proportion of the ball bearings will meet the specification?arrow_forwardManagement at Webster Chemical Company is concerned as to whether caulking tubes are being properly capped. If a significant proportion of the tubes are not being sealed, Webster is placing its customers in a messy situation. Tubes are packaged in large boxes of 135. Several boxes are inspected, and the following numbers of leaking tubes are found: View an example Sample 1 2 3 Get more help. 4 Tubes 7 7 8 5 1 5 6 7 Calculate p-chart three-sigma control limits to assess whether the capping process is in statistical control. The UCL, equals 1 Sample 8 8 9 10 11 12 13 14 Tubes 7 2 4 8 6 9 MacBook Pro 3 Sample 15 16 17 18 19 20 Total Tubes 8 3 3 5 and the LCL equals (Enter your responses rounded to three decimal places. If your answer for LCL, is negative, enter this value as 0.) 3 6 104 Clear all Check answer Oarrow_forwardWe want to determine the AOQ for an acceptance samplingplan when the quality of the incoming lots in percent defectiveis 1.5%, and then again when the incoming percent defective is 5%.T he sample size is 80 units for a lot size of 550 units. Furthermore,Pa at 1.5% defective levels is 0.95. At 5% incoming defective levels,the Pa is found to be 0.5. Determine the average outgoing qualityfor both incoming percent defective levels.arrow_forward
- < Refer to Table S6.1 - Factors for Computing Control Chart Limits (3 sigma) for this problem. Sampling 4 pieces of precision-cut wire (to be used in computer assembly) every hour for the past 24 hours has produced the following results: Hour X 1 2 3 4 5 6 R 3.25" 0.65" 3.00 1.23 3.32 1.43 3.39 1.26 3.07 1.17 2.96 0.37 Hour X R Hour R Hour 7 2.95" 0.48" 13 X 3.11" 0.90" 2.73 1.36 19 20 8 2.55 1.18 14 9 0.71 3.12 1.11 21 3.12 2.85 15 16 10 1.38 2.74 0.50 22 11 2.83 1.22 17 2.86 1.38 23 12 3.07 0.45 18 2.64 1.29 24 X 4.51" 2.89 2.65 3.18 3.04 2.54 R 1.56" 1.14 1.13 0.51 1.58 1.02 Based on the sampling done, the control limits for 3-sigma x chart are (round all intermediate calculations to three decimal places before proceeding with further calculations): Upper Control Limit (UCL) = inches (round your response to three decimal places).arrow_forwardNeed help on calculating control limits for x-bar and r-chart based on the samples below: Sample No X-BAR (Sample Mean) R (Sample Range) X-BAR R 1 28.2151942 9.5450186 2 30.5767201 11.1032318 3 29.0253789 5.52221327 4 29.9431791 6.27087883 5 29.947177 12.7568255 6 29.6848334 11.4927456 7 29.2539019 4.72514932 8 29.6694257 13.9330532 9 30.1590205 6.33461804 10 28.6867307 6.49522527 11 30.5960109 8.13717125 12 29.4390565 5.80286433 13 31.863426 3.40227918 14 32.3716448 8.62217828 15 29.7052597 10.0026916 16 30.0060069 4.25003967 17 32.8491753 4.6515662 18 33.5023103 9.62764088 19 28.1876404 9.6980397 20 30.5043768 6.46724539 21 29.6856417 7.65071069 22 32.5728395 9.2483604 23 28.2363719 7.54975234 24 29.6579999 11.3224787 25 28.1319897 13.213391 26 28.8811004 8.08405181 27 31.6730765 12.9865678 28 28.2078142 5.96315947 29 27.9430689 7.39518992 30 29.6269815 9.48802129 31 34.3599108 7.66563648 32 28.2423234 7.34122645…arrow_forward4: A production manager at a Contour Manufacturing plant has inspected the number of defective plastic molds in 5 random samples of 20 observations each. Following are the number of defective molds found in each sample: Sample N Number of observations Number of defections 1 1 20 2 2 20 3 2 20 4 1 20 5 0 20 a) Construct a 3-sigma control chart (P-chart) with this information.arrow_forward
- A process that produces computer chips has a mean of .04 defective chip and a standard deviationof .003 chip. The allowable variation is from .03 to .05 defective.a. Compute the capability index for the process.b. Is the process capable?arrow_forwardEach of the processes listed is noncentered with respect to the specifications for that process.Compute the appropriate capability index for each, and decide if the process is capable.Process Mean Standard Deviation Lower Spec Upper SpecH 15.0 0.32 14.1 16.0K 33.0 1.00 30.0 36.5T 18.5 0.40 16.5 20.1arrow_forwardConstruct a 3-sigma X-bar chart for the length in centimeters of a part from the following tabble . What is the upper controt limit? sample observation 1 observation 2 observation 3 observation 4 1 0.486 0.499 0.493 0.511 2 0.499 0.506 0.516 0.494 3 0.496 0.5 0.515 0.488 4 0.495 0.506 0.483 0.487 5 0.472 0.502 0.526 0.469 6 0.473 0.495 0.507 0.493 7 0.495 0.512 0.49 0.471 8 0.525 0.501…arrow_forward
- The time to replace vehicle wiper blades at a service center was monitored using a mean and a rangechart. Six samples of n = 20 observations were obtained and the sample means and ranges computed:Sample Mean Range Sample Mean Range1 3.06 .42 4 3.13 .462 3.15 .50 5 3.06 .463 3.11 .41 6 3.09 .45 a. Using the factors in Table 10.3, determine upper and lower limits for mean and range charts.b. Is the process in control?arrow_forwardTen samples of 15 parts each were taken from an ongoing process to establish a p-chart for control. The samples and the number of defectives in each are shown in the following table. SAMPLE LNMAS6789G 1 2 3 4 5 10 n 15 р Sp UCL LCL S555555555 15 15 15 15 15 15 15 15 15 NUMBER OF DEFECTIVE ITEMS IN THE SAMPLE 2 WONW/wwwON 3 3 3 1 3 2 0 3 a. Determine the p, Sp, UCL and LCL for a p-chart of 95 percent confidence (1.96 standard deviations). (Leave no cells blank. Round up any negative LCL value to "O". Round your answers to 3 decimal places.) 0.133 0.088 0.305 (0.039) b. What comments can you make about the process? O Process is out of statistical control ● Process is in statistical controlarrow_forwardExplain how a person using 2-sigma control charts will more easily find samples “out of bounds” than 3-sigma control charts. What are some possible consequences of this fact?arrow_forward
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