MATH1316: Practical package utilisation and report writing on control charting

Overview of Assignment and Assessment Criteria

1. This Assignment will assess your knowledge of Total quality management, your skill in utilising the software package to monitor and improve the quality of service or industrial processes, assess the ability of a process to meet customer expectations, develop an appropriate quality assurance plan to assess the ability of the service to meet its required national and international quality standard and your communication skill to report the status of the process to laypersons such as the public or line managers and provide the recommendation to improve the process.
2. The detailed Rubrics are attached at the end of the assignment.

MATH1316: Practical package utilisation and report writing on control charting

 Learning Outcomes

3. Elucidate techniques and concepts of Statistical Quality Control,
4. Construct the appropriate Quality Control charts / Forecasting and critically discuss the role of such charts/models in monitoring a process.
5. Assess the ability of a process to meet customer expectations.
6. Develop an appropriate quality assurance plan to assess the ability of the service to meet its required national and international quality standards.
7. Explain technical material, without unnecessary jargon, to laypersons such as the public or line managers.

Feedback and grades

Feedback on your assignment and your grade will be released via the Grades item in the left menu. 

1. Surface temperature of the pavement at various locations of the state highway is an important characteristic to control when studying the pavement deflection adjustment factor.  The data below are temperature readings  at 80 locations. (Read the data down from left row by row, so reading number 9 is 945 (first entry on row 2 and reading 17 is 972, i.e, first entry in row 3). You should enter the data in a single column by entering the first row, followed by the second row and …..

(a) Analyse these data using Individual, Moving Range and Cumulative Control charts.  What can you say about the process variability? 

• Interpret Individual, Moving Range, and Cusum Charts, Comment on the patterns/trend in each chart.  What behavior in the process may have produced these trends?
• Utilize an EWMA chart with  to control these data. Compare both EWMA charts with the Cusum V mask (imposed on sample 80) and the Individual chart obtained in part (a).  Then explain the effect on the EWMA chart when we use  close to 1 and  close to zero.

((1.0+1.0)+(1.0+1.0)+(1.0+1.0)= 6 marks)

Note:

Use MINITAB only.  Take sample size one, µ = 951.37 and σ = 14.51.  For Cusum use h = 4 and k = 0.25.

2.   Control charts are to be constructed for a process producing still rings for bridge construction.  The diameters have specifications of  meters.

      Consider 35 samples of size n=5, the value of  is 157.85175 meters and  meters.

(a) Assume that the Shewhart Charts for  and R shows the process is in good statistical control. Suppose this process continues to be in control and can be approximated by the normal distribution. What percent of the parts produced will be within specification limits?

(b) What percent will be within the specifications if the process were to be centered at the prescribed nominal mean?

MATH1316: Practical package utilisation and report writing on control charting

(c)  What are the values of PCR and  for the process?

(d) Use the information in part (c) and the available tables in your lecture notes to estimate the process fallout per million. The calculation is not required.

(e) How can we reduce the process fallout?  Explain.

((0.5+0.5+0.5)+(1.0)+(1.0+1.0)+(0.5)+(2.0)= 7 marks)

3.  The producer of a particular cheese cube has decided to perform quality assurance on the products before shipping the cheese cubes to the customers. Cheese cubes are shipped in lots of size 5000. A single sampling plan with n=50 and C=1 is being used for inspection.

• Obtain and draw the OC curve for this plan when p= 0.01, 0.02, and 0.05.
• Management has objected to the use of the above sampling procedure and wants to use a sampling plan with an acceptance number C=0 where the sample size n is 30, arguing that this is more consistent with their zero-defects program. What is the producer’s risk of submitting the lots with the proportion of defects p=0.01 to this sampling plan?
• Find the level of lot quality that will be rejected 90% of the time under the sampling plan in part (b).
• Suppose that the submitted lots are 5% defective. Which of the two sampling plans (mentioned in parts (a) and (b)) would protect the customer better? Give reason(s) for your answer.
• For the sampling plan in part (b), find the AOQ at P=0.01 and AOQL at p=0.04. Interpret both values in plain English.

(2+2+2+(1+1)+(1+1) = 10 marks)

• What are the steps involved in performing a process capability study? Be specific in outlining the data collection, analysis, and evaluation process.

                                                                                                                                                                                                                                                                        (4 marks)

= 8 marks

• A manufacturer has asked you to design a single sampling plan with a maximum type I error of 5% and type II error of 10%. The manager claims that the Acceptance Quality Level (AQL) for his products is 0.015 and the Lot Tolerance Percentage of Defect (LTPD) is 0.053.

1. Which sampling plan would you recommend? Explain your choice.

2. If the lot size is 4000 and the percentage of defect is 4%, what is the average Total Inspection for a sampling plan with sample size n=175 and acceptance number C=2?
3. Is the plan in part (b) a more economical plan than the plan in part (a) for the supplier? Explain your answer.
4. What are the problems associated with a zero defect policy (i.e., C = 0),

• From the point of view of the customer?
• From the point of view of the supplier?

(2+2+2+ (2+2) =10 marks)

)

• A drug company has produced a new COVID vaccine. The government requires quality assurance on the vaccine before it is released to health centers across the nation. The vaccine bottles are packed in boxes of size 100. The company claims that the products are 99.9% non-defective. Therefore, they would like to minimize inspections to the minimum level before shipping them. Design an appropriate sampling plan for this company.

(3 marks)

(3 marks)

Assignment 2 Rubrics

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