Read Chapter 9 Schoeder R G Goldstein S M Rungtusanat 290917

Read Chapter 9schoeder Rg Goldstein Sm Rungtusanatham Mj

Read Chapter 9schoeder Rg Goldstein Sm Rungtusanatham Mj

Read Chapter 9 (Schoeder, R.G., Goldstein, S.M., & Rungtusanatham, M.J. (2013). Operations Management in the Supply Chain: Decisions and Cases (6th Ed). McGraw-Hill Irwin, New York, NY ISBN: ) and create a Microsoft Word document with your responses to the following questions. Q1: Golden Gopher Airline issues thousands of aircraft boarding passes to passengers each day. In some cases, a boarding pass is spoiled for various reasons and discarded by the airline agent before the final boarding pass is issued to a customer.

To control the process for issuing boarding passes, the airline has sampled the process for 100 days and determined the average proportion of defective passes is .006 (6 in every 1000 passes are spoiled and discarded). In the future, the airline plans to take a sample of 500 passes that are issued each day and calculate the proportion of spoiled passes in that sample for control chart purposes. A. What is the sample size (n) for this problem? Is it 100, 500, or 1000? Explain the significance of the 100 days used to determine the average proportion defective. B. Calculate the CL, UCL, and LCL, using three standard deviations for control purposes.

Q2: We have taken 12 samples of 400 letters each from a typing pool and found the following proportions of defective letters: .01, .02, .02, .00, .01, .03, .02, .01, .00, .04, .03, and .02. A letter is considered defective when one or more errors are detected. A. Calculate the control limits for a p control chart. B. A sample of 400 has just been taken, and 6 letters were found to be defective. Is the process still in control?

Q3: Each day 500 inventory control records are cycle-counted for errors. These counts have been made over a period of 20 days and have resulted in the following proportion of records found in error each day: .0025, .0075, .0050, .0150, .0125, .0100, .0050, .0025, .0175, .0200, .0150, .0050, .0150, .0125, .0075, .0150, .0250, .0125, .0075, .0100. A. Calculate the center line, upper control limit, and lower control limit for a p control chart. B. Plot the 20 points on the chart and determine which ones are in control. C. Is the process stable enough to begin using these data for quality control purposes? PLEASE NOTE: USE THE ATTACHED EXCEL SPREADSHEET TEMPLATE TO CALCULATE THESE (Q9: The Robin Hood Bank has noticed an apparent recent decline in the daily demand deposits. The average daily demand deposit balance has been running at $109 million with an average range of $15 million over the past year. The demand deposits for the past six days have been 110, 102, 96, 87, 115, and 106. A. What are the CL, UCL, and LCL for the x and R charts based on a sample size of 6? B. Compute an average and range for the past six days. Do the figures for the past six days suggest a change in the average or range from the past year? Q11: PLEASE NOTE: USE THE ATTACHED EXCEL SPREADSHEET TEMPLATE TO CALCULATE THESE: (As cereal boxes are filled in a factory; they are weighed for their contents by an automatic scale. The target value is to put 10 ounces of cereal in each box. Twenty samples of three boxes each have been weighed for quality control purposes. The fill weight for each box is shown below. a. Calculate the center line and control limits for the x and R charts from these data. b. Plot each of the 20 samples on the x and R control charts and determine which samples are out of control. c. Do you think the process is stable enough to begin to use these data as a basis for calculating x and R and to begin to take periodic samples of 3 for quality control purposes? CH9_P11 FILENAME: CH9_P11.xlsx For the charts CHAPTER 9, PROBLEM 11 OPERATIONS MANAGEMENT by ROGER SCHROEDER, et al. Average Range no. obs cl ucl lcl obs cl ucl lcl THIS WORKSHEET CALCULATES CONTROL CHARTS FOR AVERAGE 1.0 0........0000 AND RANGE. ENTER THE DATA FROM THE PROBLEM AND THE CONTROL 2.0 0........0000 LIMIT COEFFICIENTS. THE PROGRAM WILL CALCULATE THE CONTROL 3.0 0........0000 LIMITS AND PLOT THE DATA ON THE AVERAGE AND RANGE CONTROL 4.0 0........0000 CHARTS. 5.0 0.........0 0........0000 TO PRINT A COPY OF THE CALCULATIONS AND CHARTS, PRESS "CTRL" 16.0 0........0000 AND "P" SIMULTANEOUSLY AND CHOOSE "OK". 17.0 0........0000 NAME: CHAPTER 9, PROBLEM 11 SECTION: 41256.0 Observation Sample Sample Sample Average Range = = = = = = 1.0 0.00 0..0 0.00 0..0 0.00 0..0 0.00 0..0 0.00 0..0 0.00 0..0 0.00 0..0 0.00 0..0 0.00 0..0 0.00 0..0 0.00 0..0 0.00 0..0 0.00 0..0 0.00 0..0 0.00 0..0 0.00 0..0 0.00 0..0 0.00 0..0 0.00 0..0 0.00 0..0 0.00 0..0 0.00 0..0 0.00 0..0 0.00 0..0 0.00 0..0 0.00 0..0 0.00 0..0 0.00 0..0 0.00 0..0 0.00 0..0 0.00 0..0 0.00 0..0 0.00 0..0 0.00 0..0 0.00 0..0 0.00 0..0 0.00 0..0 0.00 0..0 0.00 0..0 0.00 0..0 **

Paper For Above instruction

Quality control in manufacturing and service industries relies heavily on statistical process control (SPC) methods to ensure the consistency and reliability of outputs. Control charts are pivotal tools within SPC, enabling organizations to monitor process stability over time. This paper critically examines the application of control charts in various contexts based on the provided case studies and scenarios, emphasizing the importance of sample sizes, control limits, and process stability assessment.

Introduction

Control charts serve as visual tools that help managers and quality engineers determine whether a process is in a state of statistical control. They facilitate early detection of variations caused by assignable causes, preventing defective products or services from reaching customers. The significance of appropriate sampling, accurate calculation of control limits, and correct interpretation of control charts is critical to effective process management.

Analysis of Case Studies

Q1: Aircraft Boarding Passes

The problem involves using process data to monitor the proportion of defective boarding passes issued daily. The sample size (n) selected for control chart analysis is 500 passes per day, aligned with the airline's future sampling plan. Analyzing the historical data collected over 100 days, with an average defect rate (p̄) of 0.006, provides a reliable estimate of the process average (center line, CL) for the control chart.

The use of 100 days as a sampling window offers a robust dataset, reducing the impact of random fluctuations and capturing the process's long-term behavior. This timeframe smoothens out anomalies due to short-term variations, giving confidence in the calculated control limits. The CL is set at the historical average proportion defective (p̄ = 0.006).

Calculations of control limits employ the standard deviation of the proportion defective, which is derived from the binomial distribution:

σp = √[p̄(1 - p̄) / n]

Using three standard deviations, the Upper Control Limit (UCL) and Lower Control Limit (LCL) are computed as:

UCL = p̄ + 3σp


LCL = p̄ - 3σp

Plugging in the numbers:

σp = √[0.006  (1 - 0.006) / 500] ≈ √[0.006  0.994 / 500] ≈ √[0.005964 / 500] ≈ √0.000011928 ≈ 0.00345


UCL ≈ 0.006 + 3 * 0.00345 ≈ 0.006 + 0.01035 ≈ 0.01635


LCL ≈ 0.006 - 0.01035 ≈ -0.00435 (set to zero since proportion cannot be negative)

Implication

The process appears capable of operating within these limits, with the LCL constrained at zero, indicating minimal risk of defect rates exceeding the UCL under normal variation. Continuous monitoring would confirm process stability.

Q2: Typing Pool Defects

In examining the 12 samples, the average proportion defective (p̄) is calculated as:

p̄ = (0.01 + 0.02 + 0.02 + 0.00 + 0.01 + 0.03 + 0.02 + 0.01 + 0.00 + 0.04 + 0.03 + 0.02) / 12 ≈ 0.0183

The control limits for a p control chart are based on the binomial standard deviation, adjusted for the sample size (n = 400):

σp = √[p̄(1 - p̄) / n] ≈ √[0.0183 * 0.9817 / 400] ≈ √[0.01795 / 400] ≈ √0.00004486 ≈ 0.0067


UCL = p̄ + 3σp ≈ 0.0183 + 3 * 0.0067 ≈ 0.0183 + 0.0201 ≈ 0.0384


LCL = p̄ - 3σp ≈ 0.0183 - 0.0201 ≈ -0.0018 (set to zero)

For the latest sample, with 6 defective letters out of 400 (proportion = 0.015), this is within the control limits, indicating the process is in control.

Q3: Inventory Error Counts

The average proportion of error per day over 20 days is computed as:

p̄ = (0.0025 + 0.0075 + 0.0050 + 0.0150 + 0.0125 + 0.0100 + 0.0050 + 0.0025 + 0.0175 + 0.0200 + 0.0150 + 0.0050 + 0.0150 + 0.0125 + 0.0075 + 0.0150 + 0.0250 + 0.0125 + 0.0075 + 0.0100) / 20 ≈ 0.01175

The control limits are calculated as:

σp = √[p̄(1 - p̄) / n] with n=500


σp ≈ √[0.01175 * 0.98825 / 500] ≈ √[0.0116 / 500] ≈ √0.0000232 ≈ 0.00482


UCL ≈ 0.01175 + 3 * 0.00482 ≈ 0.01175 + 0.01446 ≈ 0.0262


LCL ≈ 0.01175 - 0.01446 ≈ -0.0027 (constrained at zero)

Plotting all 20 points, most fall within the control limits, suggesting the process is statistically stable. The process variability aligns with expectations under current control measures.

Discussion

The calculated control limits provide a basis for ongoing process monitoring. When data points lie outside these limits, it indicates potential assignable causes requiring investigation. The stability observed in these processes underscores the importance of regular data collection and analysis. Utilizing control charts enables proactive management of quality attributes, reducing defect rates, and enhancing customer satisfaction.

Moreover, the importance of appropriate sample sizes emerges clearly from these calculations. Larger samples tend to yield more accurate estimates of process parameters, while smaller samples can result in misleading signals due to higher variability.

Additionally, the use of historical data, as in the 100-day sampling window for the airline's boarding pass process, underscores the need for robust data collection before implementing control measures. This ensures that control limits are based on representative data, minimizing false alarms or missed signals.

Conclusion

Control charts are vital tools within quality management systems, facilitating the detection of process variations. Proper application—considering optimal sample sizes, accurate control limit calculations, and regular data review—culminates in improved process stability and product quality. Continuous monitoring and data-driven decision-making remain core principles for operational excellence across industries, as exemplified by the scenarios analyzed.

References

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  • Levine, D. M., Stephan, D. F., Krehbiel, T. C., & Berenson, M. L. (2014). Statistics for Managers Using Microsoft Excel (8th ed.). Pearson.
  • Sokal, R. R., & Rohlf, F. J. (2012). Biometry: The Principles and Practice of Statistics in Biological Research. W. H. Freeman.
  • Ishikawa, K. (1985). What is Total Quality Control? The Japanese Way. Prentice-Hall.
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  • Daleki, A. (2020). Practical Applications of Control Charts in Manufacturing and Service Operations. Journal of Operations Management, 65, 100-113.

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