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## Sample Size, Control Distance, and Type I and Type II Errors in Control Charts

Type I and Type II errors in control charts (or in statistics) are difficult to explain concepts. When trying to explain the impact of the sample size and the control distances in the magnitude of Type I and Type II errors, it becomes exponentially more difficult to explain.

The embedded visualization shows three distributions:

• A population distribution (PDF: g(x)) with the average m = 12 and the s.d. S = 0.5. The process target is t = 12.
• A sampling distribution (PDF: f(x)) with the sample size n = 4 and the standard error = S/sqrt(n)
• A sampling distribution (PDF: h(x)) with a “derailed mean” c = 12.32

It uses the following control charts specifications.

• A control chart with the control distance of k = 1.96, ucl = t + k*s, and lcl = t – k*s

If you are familiar with the sampling distribution, the size of k will determine the size of both the Type I error and Type II error, and the size of n will determine the size of Type II error.

You can refer to the attached in-class exercise note to adapt it to your teaching/learning needs. This visualization to helps you to see how Type I error and Type II error changes as you:

• Change the sample size n
• Change the control distance k
• Change the mean of the process m

Go to the visualization: https://www.desmos.com/calculator/hccg2zkpon

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## What could go wrong with a product design?

This is what happens when you do not respect the voice of your customers.

This illustration can also be used in the project management context to emphasize the importance of the client requirements gathering and the project scope mismanagement and what it can cause to the project deliverables.

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## From Factory to Market: Distribution Problem (Linear Programming Approach)

This exercise introduces an important topic in the operations and supply chain management – distribution problem. Essentially, it deals with a problem where you need to match the supply and demand with the least transportation cost.

To understand the impact of this kind of approach in the real world, please refer to the following talk by Jack Levis, the guy who led the optimization effort in UPS.

Holland, C., Levis, J., Nuggehalli, R., Santilli, B., & Winters, J. (2017). UPS optimizes delivery routes. Interfaces47(1), 8-23. https://doi.org/10.1287/inte.2016.0875

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## Service Level, Fill Rate, and Newsvendor Model

Service level is the frequency of the stockout, while the fill rate means the proportion of demands satisfied.

Newsvendor model determines the desired service level, not the fill rate.

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## Inventory Simulation Using Excel Solver (linear programming approach)

This technique offers an Excel solver solution on the previous inventory simulation problem I posted.

This exercise can serve as a bridging topic between the inventory planning and the optimization technique. The inventory planning chapter from the textbook our university is using (Jacob, the core, 5th edition), does not introduce the idea of optimization before it jumps into the Newsvendor modeling. It introduces the idea of the optimization in the logistics management chapter where it uses a network optimization problem to introduce the distribution problem.

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## Inventory Simulation (newsvendor)

In this modeling exercise, you are asked to determine an inventory level that would minimize the grand total cost for a two-hundred-month planning period.

• For each month, the demand follows the same pattern described below.
• Demand: normally distributed with a mean of 100, sd of 30
• Overage cost: 10 unit/USD
• Shortage cost: 5 unit/USD
• Once determined, you will not change the inventory level during the two-hundred-month period.

This problem exists a clear analytical solution using a newsvendor model. Students will have to do a brute-force approach to determine the cost minimizing inventory level.

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## Research Article Collection for Quality Management Class

Shah, R., Ball, G. P., & Netessine, S. (2017). Plant operations and product recalls in the automotive industry: An empirical investigation. Management Science63(8), 2439-2459. (https://doi.org/10.1287/mnsc.2016.2456)

• Using samples from auto manufacturing plants, this article demonstrates the positive relationship between the plant utilization and the likelihood of resulting a recall.

Corbett, C. J., Montes-Sancho, M. J., & Kirsch, D. A. (2005). The financial impact of ISO 9000 certification in the United States: An empirical analysis. Management science51(7), 1046-1059. (https://doi.org/10.1287/mnsc.1040.0358)

• Using event study fashion, this article seeks to identify both short-term and long-term implications of receiving an ISO-9000 certification.

Guajardo, J. A., Cohen, M. A., Kim, S. H., & Netessine, S. (2012). Impact of performance-based contracting on product reliability: An empirical analysis. Management Science58(5), 961-979. (https://doi.org/10.1287/mnsc.1110.1465)

• This article suggests that even the type of contract (time and material contracts and performance-based contracts) with the manufacturer can have impact over the product reliability.

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## Variation Reduces Capacity Utilization

There is a well-known story about how to “properly” fill a jar with sand, rocks, and water. For the detailed story, please refer to the video below. The story is often used as an analogy to inspire people about the importance of priority.

But from the operations management perspective, the story also tells us an important principle about the capacity utilization. The fact that it still had space to fill sand and water after the rocks are filled first, is because the irregular shape (variation) of the rocks were inhibiting the space from being utilized efficiently!

Efforts to reduce variations can be seen everywhere! Workstations in the factory is moving in “cycle times”, packages follow certain design specifications so that the container (or truck) spaces can be maximally utilized.

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## Quality Control in Factory Level: OnePlus Factory Tour by Linus Tech Tips

In this video, a tech Youtuber, Linus, is showing us around the OnePlus factory. You do not have much factory experience or have never toured a manufacturing plant before, this is a good material.

It explicitly shows how the quality control is done in the factory level. Processes, Purposes, People, and Tasks of quality management are demonstrated clearly. (Although Linus never intended to make the video as a quality management case study. 🙂 )