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Please read the instructions throughly before starting the assignment.

In this individual assignment, you will be playing the role of a quality manager for a new manufacturing plant – Gainsborough Manufacturing Company. As part of your job, you will use the Quality Analytics simulation to simulate the process stability and capability of the plant before handing it over to operations. The CEO also wants to know the lowest possible total cost of quality.

Connection to the course learning outcomes

- Calculate the control limits and the capability indexes of a process
- Use control limits in real time to maintain control of a process
- Analyze control charts post hoc to determine whether a process is capable
- Examine quality control investment decisions to minimize total cost of quality
- Use data analytics to examine a process capability and examine various costs of quality
- Examine the relationship between internal failure costs, external failure costs, appraisal costs and prevention costs and how they contribute to the total cost of quality
- Differentiate between a process that is statistical control and a process that is capable

**Instructions**

Your task in this assignment is to ensure that the manufacturing process at Gainsborough Brewery is both stable and capable and that the total cost of quality is as low as possible. To achieve this, you will face the following challenges:

**Challenge 1 (20%):** You will calculate control limits for X-bar and R charts. Simulate daily production, one batch at a time, by clicking “Run Next Batch” repeatedly. With each click, the simulation will generate the next batch processed, draw a random sample from the batch, and calculate the mean and range of the sample. Run your cursor over the points on the X-bar and R charts to see the explicit values. Be sure to copy the sample means and ranges to **Minitab** in order to calculate the control limits for this process. Remember to save your file. You’ll need to use these control limits in Challenge #2. *Note that a production shift – an entire day of production -- starts at 7:00 a.m. and ends at 10:00 p.m.*

You can manually calculate control limits for the means and the ranges using the formulas from the attached terminology primer sheet, or you can calculate them with Minitab. The results will be approximately the same. You will need to use the data from the 6th production shift (the data you will copy and paste into Minitab to calculate the control limits).

- Use the ranges to calculate the control limits of the range chart

- Stat>Control Charts>Variable Charts for Subgroups>R

- Use the means to calculate the control limits of the mean chart

- Stat>Control Charts>Variable Charts for Subgroups>Xbar

** Note: **The subgroup size is 5.

**Challenge 2 (20%)**: In this challenge, you will use the control limits that you calculated in Challenge #1. Enter their values in the boxes at the upper right of the X-bar and R charts. As the sample means and ranges are plotted, you will use the control charts to determine whether or not the process is in control. If you find that the process is out of control, you can recalibrate the equipment or make a labor substitution in order to bring the process back into control. ** Your goal is to minimize the number and cost of internal and external defects by keeping the process in control**. Adjusting a process is costly, but will improve the quality of the process through changing the underlying process mean or standard deviation. Experiment with Challenge #2 as many times as you would like.

**Challenge 3 (20%)**: In Challenge #3, you will receive data that describes the frequency of defects for four different processes. Use this information to calculate the process capability index for each process and interpret it. Your goal in this challenge is to determine whether or not each process is capable of producing to specifications. Please include a table that contains a row for each company and the data for the following items: USL, LSL, Process Mean, Process Standard Deviation, UCL, LCL, Process Capability Index, Centered? and Capable? To determine the Process Mean, Process Standard Deviation and Process Capability Index you can use the formula in the Technology Primer which is the Quality Analytics simulation or you can use Minitab 19. The following link:

will bing you to a YouTube entitled: "How to Access Process Capability in MiniTab 17". In your submission include the formulas that you used to calculate each process mean, process standard deviation and process capability index if you manually calculated or a copy of your Minitab results if you used Minitab.

**Challenge # 3 is independent of Challenges 1 and 2**.

**Challenge 4 (40%)**: In Challenge #4, you can experiment with investments in prevention and appraisal. Investments in prevention include labor training, new equipment, and switching suppliers. Each of these investments is expensive, but will improve the quality of the process by changing the underlying process mean or variance. Investments in appraisal include larger SPC sample sizes and increased frequency with which samples are taken and inspected. Larger and more frequent inspections will increase appraisal costs, while providing more opportunities to detect defects internally. Each time you make an investment in prevention and/or appraisal, press “Run to End” to view the effect of this investment in the long term. You may run this challenge as many times as you’d like as you try to minimize the total cost of quality.

**Please make sure to copy your results from all the four challenges into one PowerPoint file and submit it through the link below.**

Performance measurement: How your performance will be measured?

Your performance will be measured as follows:

**Challenge 1**: Your ability to accurately calculate the control limits of control charts.**Challenge 2**: Your ability to control and minimize the total cost (TC) of quality of a process.**Challenge 3**: Your ability to examine the capability of a process and calculate the capability index of a process.**Challenge 4**: Your ability to make the appropriate investment decisions related to quality assurance and quality control, to minimize the total cost (TC) of quality of a process.

**How to get the most out of this assignment?**

To access the simulation, you must purchase it using the link provided below. This is a unique link generated for this section of the class. Make sure you are enrolled in your section of PJM6135 simulation. Here is the correct link: https://hbsp.harvard.edu/import/710477 .

Once you have access to the simulation, the first thing to do is to review the preparatory materials, which include:

- The preparation Tab
- Click on the Question Mark (?), next to Prepare tab, it shows you how to play the simulation.

To achieve the highest score; that is, to be the best quality manager you can be, you need to follow a structured approach. The first step is Preparation – Click on the Prepare tab on the simulation to read about your task. This is an important step to understand the quality challenges that you have to face. See the “How to Play” PDF file in attachment.

** **

**Grading Scheme**

Your grade will be based on the following benchmarks:

**Challenge 1**: The upper and lower control limits for the R-chart and X-bar chart are accurate (100%). A ± 5% deviation from the true values will be acceptable.**Challenge 2**: Your total cost of quality is less than or equal to $4,000 (TC <= $4,000). This is a benchmark. Students have achieved lower total cost of quality. If you achieve a total cost of quality of $4,000 or less, you will earn 100% of the grade. If you achieve a TC higher than $4,000, for example, a TC of $4,500, your grade will be calculated as follows:

[100% - ($4,500 - $4,000)/4,000] = 88% of the grade.

**Challenge 3**: You will graded on the overall accuracy of the data in the table that contains a row for each company and the data for the following items: USL, LSL, Process Mean, Process Standard Deviation, UCL, LCL, Process Capability Index, Centered? and Capable?**Challenge 4**: Your total cost of quality should be less than or equal to $8,000 (TC <= $8,000). This is a benchmark. Students have achieved lower total cost of quality. If you achieve a total cost of quality of $8,000 or less, you will earn 100% of the grade. If you achieve a TC higher than $8,000, for example, a TC of $8,500, your grade will be calculated as follows: [100% - ($8,500 - $8,000)/8,000] = 94% of the grade.

**Submission guidelines**

This assignment is due no later than (NLT) Monday at 11:59 p.m. EST, 05/04 of the FOURTH week of the class. Copy and Paste the results for ALL four challenges into a PowerPoint file and submit it through the link below.

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