OPERATIONS MANAGEMENT IN THE SUPPLY CHAIN: DECISIONS & CASES (Mcgraw-hill Series Operations and Decision Sciences)
7th Edition
ISBN: 9780077835439
Author: Roger G Schroeder, M. Johnny Rungtusanatham, Susan Meyer Goldstein
Publisher: McGraw-Hill Education
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Chapter 9, Problem 2P
a)
Summary Introduction
To determine: The control limits for a p-chart.
b)
Summary Introduction
To determine: Whether the process is under control.
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We have taken 12 samples of 400 book pages found the following proportions of defective pages: .01, .02, .02, .00, .01, .03, .02, .01, .00, .04, .03, and .02. A page is considered defective when one or more errors are detected.a. Calculate the control limits for a p control chart.b. A new sample of 400 pages is taken, and 6 pages are defective.Is the process still in control?
Five data entry operators work at the data process-ing department of the Birmingham Bank. Each day for 30 days,
the number of defective records in a sample of 250 records typedby these operators has been noted, as follows:
a) Establish 3s upper and lower control limits.b) Why can the lower control limit not be a negative number?
c) The industry standards for the upper and lower control lim-its are 0.10 and 0.01, respectively. What does this imply about
Birmingham Bank’s own standards?
Twenty samples of 100 items each were inspected when a process was considered to be operating satisfactorily. In the 20 samples, a total of 140 items were found to be
defective.
(a) What is an estimate of the proportion defective when the process is in control?
(b) What is the standard error of the proportion if samples of size 100 will be used for statistical process control? (Round your answer to four decimal places.)
(c) Compute the upper and lower control limits for the control chart. (Round your answers to four decimal places.)
UCL =
LCL =
Chapter 9 Solutions
OPERATIONS MANAGEMENT IN THE SUPPLY CHAIN: DECISIONS & CASES (Mcgraw-hill Series Operations and Decision Sciences)
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- 6. The defect rate for your product has historically been about 4.50%. For a sample size of 500, the upper and lower 3-sigma control chart limits are: Part 2 UCLp = _______ (enter your response as a number between 0 and 1, rounded to four decimal places). The Standard deviation of defect rate of product is given __________. The Upper and Lower 3-sigma control charts limits are: UCLp ________ LCLp ________arrow_forwardUsing samples of 200 credit card statements, an auditor found the following: Sample 1 2 3 4 Number with errors 4 2 5 9 a. Determine the fraction defective in each sample. b. If the true fraction defective for this process is unknown, what is your estimate of it? c. What is your estimate of the mean and standard deviation of the sampling distribution of fractions defective for samples of this size? d. What control limits would give an alpha risk of .03 for this process? Page 457 e. What alpha risk would control limits of .047 and .003 provide? f. Using control limits of .047 and .003, is the process in control? g. Suppose that the long-term fraction defective of the process is known to be 2 percent. What are the values of the mean and standard deviation of the sampling distribution? h. Construct a control chart for the process, assuming a fraction defective of 2 percent, using two-sigma control limits. Is the process in control? Can you show me the steps and formulas using excelarrow_forwardWe have taken 12 samples of 400 book pages found the following proportions of defective pages: .01, .02, .02, .00, .01, .03, .02, .01, .00, .04, .03, and .02. A page is considered defective when one or more errors are detected. Calculate the control limits for a p control chart. A new sample of 400 pages is taken, and 6 pages are defective. Is the process still in control?arrow_forward
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- 1. The data shown in Table 1 are x and R values for 20 samples of size n= 5 taken from a process producing bearings. The measurements are made on the inside diameter of the bearing, with only the last three decimals recorded (i.e., 31.6 should be 0.50316). Please show all your work for full credit. (a) Set up x and R charts on this process. Does the process seem to be in statistical control? If necessary, revise the trial control limits. (b) Assume that diameter is normally distributed. Estimate the process standard deviation. Sample R Sample R 1 31.6 4 11 29.8 4 33.0 3 12 34.0 4 35.0 4 13 33.0 10 4 32.2 4 14 34.8 4 5 33.8 38.4 31.6 15 35.6 7 3 16 30.8 7 4 17 33.0 5 8 36.8 10 18 31.6 3 9. 35.0 15 19 28.2 9 10 34.0 6 20 33.8 Table 1: Bearing Diameter Dataarrow_forwardTwelve samples, each containing five parts, were takenfrom a process that produces steel rods at Emmanuel Kodzi’sfactory. The length of each rod in the samples was determined.The results were tabulated and sample means and ranges werecomputed. The results were: a) Determine the upper and lower control limits and the overallmeans for x -charts and R -charts.b) Draw the charts and plot the values of the sample means andranges.c) Do the data indicate a process that is in control?d) Why or why not?arrow_forwardThe defect rate for data entry of insurance claims hashistorically been about 1.5%.a) What are the upper and lower control chart limits if you wishto use a sample size of 100 and 3-sigma limits?b) What if the sample size used were 50, with 3s ?c) What if the sample size used were 100, with 2s ?d) What if the sample size used were 50, with 2s ?e) What happens to snp when the sample size is larger?f) Explain why the lower control limit cannot be less than 0.arrow_forward
- Management 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_forward17. Over a period of 12 consecutive production hours, samples of size 50 resulted in the following proportions of defective items: Proportion Defective Proportion Defective Sample Number Sample Number 1 .04 7 .10 .02 .06 .08 8 .10 3 9 10 .06 4 .08 5 6 .08 .04 .04 .04 11 12 a. What are the three-sigma control limits for this process? b. Do any of the sample points fall outside of the control limits? c. The company claims a defect rate of 3 percent for these items. Are the observed proportions consistent with a target value of 3 percent defectives? What diffi- culty would arise if the control limits were based on a target value of 0.03? In view of the company's claims, what difficulty would arise if the control limits computed in part (a) were used?arrow_forwardory 5 Media telo Alan's Shop Once each day, a sample of 96 components is randomly taken and the # of defective components (out of 96), is recorded. Given the following results from 14 samples: Sample 1 2 3 4 5 6 7 0.1889 36812 0,2566 # Defects 8 4 11402 5 6 Ⓒ01366 7 4 5 Sample 8 What is the upper control limit for the most appropriate control chart? 9 10 11 12 13 14 # Defects 7 5 9 3 8 5 8arrow_forward
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