Evaluating the quality of manufactured products can be straightforward because they are tangible. But the evaluation of services, which are intangible, can be more involving. According to the Evans and Lindsay, existing research suggest the following five principal dimensions that influence customer’s perception on service quality.

As you can see, the level of effort the Japanese moving company is showing is very impressive. Can you comment on what/how the company has done in each of five dimensions listed above?

Number of different ways to choose sample_size from number. For example, 3 choose 2 = 3, there are three different ways of choosing 2 combination out of 3.

This is written in the mid-march of 2020 when the Novel coronavirus (COVID19) started to spread across the United States. Many universities decided to move their in-person classes to online fashion in very short notice. This is written as a tip for the instructors who need the right solutions for their online classes.

I introduce 8 useful tools that can make your virtual presence much more powerful!

Zoom is a very powerful online conferencing solution. To many friends of mine, Zoom is their first choice for the online conferencing tool, not Skype.

Some of the very useful options including (even with the free tier):

The participants can join via a link or meeting ID,

The host can mute/unmute the participants,

Multi-directional screen sharing (both the host and the participants can share their screen),

Participants can raise their virtual “hands” in order to start a discussion.

While there is no time restriction for one to one meetings, there are 45 minutes restriction for group conferences. For the tiers and the pricings, please see the chart below.

It is more seamless than Skype. Skype consumes incredibly large amount of system resources to run, and the interface is very confusing.

It is hard to describe what notion.so is in one sentence because it is very powerful and versatile. So, it could be considered as an online content creation/sharing tool. I have never seen something of this sort.

When used properly, it is quite indispensable. Currently, it is my

Web clip archive,

To-do list,

Markdown (and Latex Code) supported writer,

Kanban for collaborative projects,

Online database

It is free up to 1000 blocks but charges $5 for personal users. It offers a free upgrade to the Personal tier for students and educators. Here is their statement:

Do you offer student discounts? Notion Personal plans are free for students and educators! Simply sign up with your school email address and you’ll immediately gain access to those features.If you’re already on a personal plan, change the email associated with your account to your school email address to get it for free.

Slack is a widely used online collaborative workspace. You can open up public/private communication channels for your work team. It also supports free Slack video conferencing for a 1-to-1 meeting.

Think of this as Facebook for your work project. People share/interact within the Slack environment, therefore, it helps people sending less email. It highlights and “pins” key contents/documents to the chatting windows so team members won’t get lost.

I set up my entire class as a team and invite students to join the Slack. Then, I establish separate communication channels for upcoming major assignments so students can discuss/comment to exchange their opinions.

One downside of the Slack is that the users need to overcome a little bit of the learning curve. It assumes that you have enough patience to go through all the progress update/messages being exchanged within the environment.

It is free to a certain extent. You can use the majority of what it offers for free. It does not inject/embed/promote advertisements. So that is very good.

Microsoft Teams is a competing product. However, our university restricts usage so that not all people can create their own team. So to me, it is useless. If your work organization does not have the restriction, you can try that first. At least, the learning curve will be less steep for Microsoft Teams.

(Update: I was informed that now we are allowed to use the Teams, the condition is that the central IT needs to create a team for you. If your university allows the Teams, considering the learning curves students have to overcome, you should go with the Teams, not Slack.)

Students often need to make an appointment with an instructor. It could be a matter of two or three sentences in face-to-face communication. It is easiest when two parties (students and instructors) lay down their schedule and find a common working time. Imagine if you have to do this over emails. It could be ended up as a dead loop that frustrates both parties.

Calendly can solve the problem by synchronizing your calendar schedule to the Calendly, then letting students choose a time from your free time (or designated time). When you add a schedule to your calendar, it automatically updates the Calendly side so students know the time is not available for them to book.

For example, students can try to book one (or multiple) 30 minutes session with me. (You can have more event types in paid plans).

Calendly shows all my available time (excluding those occupied time on my calendar). Students can book based on those times. When confirmed, I receive an email from Calendly regarding the upcoming appointment.

There are numerous options in the market for screen recording. The most powerful one I have used is Camtasia Studio. However, its three digits price tag scares me.

Screencast-o-Matic allows up to 15 minutes of free recording. It’s paid plan is also very reasonable at $1.65 per month. (But it is billed annually.) The free version leaves a not-so-ugly watermark on the recordings.

The tool basically captures everything happens on your desktop screen. My school provides echo360. But is not very convenient and the recording is also low in the resolution. I prefer to record a better quality video using my own tools such as this one.

This is a cross-platform collaborative whiteboard. Yes, you heard me, a whiteboard. This can be downloaded free from Windows 10 AppStore and other places where you get apps for your (iOS, Android) device.

The idea of the Whiteboard is that, as you draft something in your own Whiteboard app, other people, whom you gave permission to, can see the draft in their respective devices simultaneously.

Microsoft has been diligently updating/upgrading the app over the years. I first discovered the app perhaps a couple of years ago, but back then, there was a huge time lag between drawing from my end to updating to students’ end, which made it almost impossible to use.

Because the time lag is so small, I found another way to take advantage of the Microsoft Whiteboard.

I open up a Microsoft Whiteboard app on my computer screen for demonstration purpose,

Instead of drawing on my computer screen to mess up with all other applications, I use my iPad and Apple Pencil as the actual drawing tools.

Although I like my Surface Pro laptop a lot, letting it handle all the tasks (drawing, video playing, Excel, PowerPoint, screen recording, etc.) can be computationally challenging. You will also have to manage the cognitive complexity of switching between apps. Separating the memory-intensive tasks such as on-screen drawing can reduce both computational challenges on the computer and the cognitive challenge on you, at the same time.

If your school is using Blackboard as the Learning Management System, there is a good chance that they have this under subscription. It is a comprehensive online classroom environment.

It offers

Video conferencing

Screen sharing (entire screen or specific application screen)

Whiteboard

Session recording

Participants hands-up to ask question

In-class quiz

This is the only product I have not been used for my class. But given the Blackboard style (boring and sophisticated, but stable and useful), this should serve as a pretty stable solution for most people for the virtual classrooms.

Since I plan to use both pre-recorded lectures and online conferencing, I still need other tools/solutions.

Carnac (Displaying Keystrokes on Screen)

One question I often receive while demonstrating the Excel work in class is “What did you type?”

In an online teaching environment, students will have the same question. But they cannot ask you immediately. Would it not be nice if the screen constant displays all your keystrokes? Carnac does that.

Sampling distribution is an important concept in statistics. We rely on sampling distributions (e.g., sample mean and sample proportion) to make decisions about whether to accept or to reject the hypotheses about the population properties.

Students usually have tough time understanding the concept due to its highly theoretical nature. The attached Excel spreadsheet can help visualize the process of obtaining a sampling distribution of population mean. Specifically, it allows you to specify a sample size n and the number of sample groups of k. Thus, you will have k number of sample averages can be used to construct a distribution. This Excel applet allows the process of obtaining the sampling distribution more visible.

Note:

Original file has a population of 10,000 observations that follow a normal distribution with mu = 500 and sigma = 50. If you wish to demonstrate the law of large numbers, you can replace the population data with your own.

When you specify a very big k, for example 400, Excel will freeze for a moment to process the request. Please monitor your CPU usage.

My website does not allow me to upload Macro enabled Excel file as/is. That is reason why you are seeing a zip file.

When use in Windows 10, please enable Macro, Data Analysis ToolPak, and Data Analysis ToolPak – VBA. Otherwise, it will report a run time error.

For Mac, please see this link. Essentially you need to enable the developer ribbon.

I developed this lecture note spring 2020 using R markdown for the first time. It supports the compilation of R, Markdown, and LaTex code at the same time! I was really impressed.

Chapter 6. Statistical Techniques in Quality Management
========================================================
author: Z. Wen (OSCM 3340, Spring 2020)
date: 02/12/2020, Thursday
autosize: true
font-import: https://fonts.googleapis.com/css?family=Fira+Sans
font-family: 'Fira Sans', sans-serif
width: 1440
height: 900
Learning Objeectives
========================================================
- Review of Sampling Distribution
- Confidence Interval
- Testing Hypothesis
- Various Distributions
- Sample Size Determination
Estimation
========================================================
Conceptually, the following relationship holds in any type of estimation.
$$ \theta = \hat{\theta} + M.E.$$
In quality management, we are often interested in the process mean. (e.g., Does our machines need alignments?)
$$ \mu = \bar{x} + M.E. $$
We are also interested in the process standard deviation. (e.g., Does our machines need calibrations?)
$$ \sigma = s + M.E. $$
Margin of Error
========================================================
**Since a lot of times we have information about $\bar{x}$ and $s$, we need to develop our knowledge on $M.E.$**
There are three components in developing the confidence interval
- Your level of confidence ($1-\alpha$)
- Sample size ($n$)
- Best estimate of the population s.d. ($\sigma$ or $s$, whichever available)
Here is the formal relationship of these three in forming the margin of error:
$$M.E. = z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$$
Confidence Interval
========================================================
**With the knowledge of M.E., we can construct an interval where the true parameter is located with $1-\alpha$ level of confidence.**
$$C.I. = \bar{x} \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$$
There are many different types of variations. For example,
$$C.I. = \bar{x} \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$$
$$C.I. = \bar{p} \pm z_{\alpha/2}\sqrt{\frac{\bar{p}*(1-\bar{p})}{n}}$$
And many more... $C.I.$ for F distribution, $\chi^2$ distribution, etc. **As long as it is an estimation result, you will always see the reporting of $C.I.$**
Confidence Interval (Example)
========================================================
See the following calculated examples:
| Level of $\alpha$ | $n$ | $z$ | $\sigma$ | M.E. | $\bar{x}$ | C.I. | Interval Length |
|:-----------------:|:---:|:--------:|:--------:|:--------:|:---------:|:-------------------:|:---------------:|
| 0.01 | 100 | 2.58 | 4 | 1.03 | 34 | [32.97, 35.03] | 2.06 |
| 0.05 | 100 | 1.96 | 4 | 0.78 | 34 | [33.22, 34.78] | 1.57 |
| 0.1 | 100 | 1.64 | 4 | 0.66 | 34 | [33.34, 34.66] | 1.32 |
| 0.01 | 64 | 2.58 | 4 | 1.29 | 34 | [32.71, 35.29] | 2.58 |
| 0.05 | 64 | 1.96 | 4 | 0.98 | 34 | [33.02, 34.98] | 1.96 |
| 0.1 | 64 | 1.64 | 4 | 0.82 | 34 | [33.18, 34.82] | 1.64 |
<small>Although the name could be confusing, Excel formula **=CONFIDENCE.NORM(alpha, standard_dev, size)** and **=CONFIDENCE.T(alpha, standard_dev, size)** will give you the **M.E.** value. </small>
One Very Important Application (1/4) - Confirming Doubts
========================================================
**How to find out someone who had your total trust betrayed you?**
<br>
*I am almost certain that he/she won't do that...*
But what if he/she got caught in doing that thing. Is he/she still trustworthy?
**You heartfully believed the mean is 7. But, what if your 95% confidence interval does not contain 7? Will you still believe the mean is 7?**
In this case, you either have to update your belief on the mean, or you must have encountered a rare chance event.
One Very Important Application (2/4)
========================================================
**Example:** <br>
A cylinder manufacturer claims that their process mean is 12.5 mm. Historically, their process standard deviation was .08 mm and there is no reason to think that the s.d. has changed. Upon drawing a random sample of 9, the sample average was 12.22. Please test the claim under 5% of error tolerance level.
*Questions*
1. First, please use a visual aid to determine the answer. <br>
2. Please use a formal approach to determine the probability of obtaining such sample average, given the true mean is 12.5 mm. <br>
3. What is the conclusion?
One Very Important Application (3/4)
========================================================
If what the company claiming is true, this will be the distribution of the population.
- Population mean $\mu = 12.5$
- Population standard deviation $\sigma = 0.08$
<center>
![plot of chunk unnamed-chunk-1](Confidence Interval PowerPoint-figure/unnamed-chunk-1-1.png)
</center>
***
<small>
If what the company claiming is true, for $n=25$, we have...
- Hypothesized mean of $\mu_0 = 12.5$
- Standard Error of $\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}} = \frac{.08}{5} = 0.016$
- 95% C.I. $\bar{x} \pm ME = [12.19, 12.25]$
</small>
<center>
![plot of chunk unnamed-chunk-2](Confidence Interval PowerPoint-figure/unnamed-chunk-2-1.png)
</center>
Formal Hypothesis Testing (3/4)
========================================================
**Hypothesis testing** re-defined:
- It is a process of determining a likelihood of surprise for a given sample result.
- How likely it is that we can obtain a sample mean of this size, given the claim is true?
Formal hypothesis: <br>
- $H_o: \mu = 12.5$ and $H_\alpha: \mu \neq 12.5$
Determination of the Likelihood (Excel Formula):
- $p-value = norm.dist(12.22, 12.5, 0.016, TRUE) = 7.16E-69 \approx 0$
**Verdict: It is very unlikely that the true mean is 12.5**
Any idea about the ture mean:
- All we know is, it is very unlikely 12.5. With a 95% confidence, it could be said it is within [12.19, 12.25]
Another Example - Two Group Mean Testing (Exercise)
========================================================
**Case**: Please determine whether the following two hospitals have the same quality rating.
- Data URL: [Download Data](https://blackboard.utdl.edu/bbcswebdav/pid-7699937-dt-content-rid-63616690_1/xid-63616690_1) <small>(*UTAD ID/PW Needed for Access*) </small>
<center>
<img src="Confidence Interval PowerPoint-figure/unnamed-chunk-5-1.png" title="plot of chunk unnamed-chunk-5" alt="plot of chunk unnamed-chunk-5" width="1000" height="600" />
</center>
Formalizing Two Group Mean Test
========================================================
A visual inspection of the confidence interval seems to be arguing that the means are not the same. Now, we formalize the test.
- The mean difference of $d = \bar{x}_A - \bar{x}_B$ are known to follow a **T distribution** when the both $\sigma_A$ and $\sigma_B$ are not known.
- T distribution gives a more liberal estimate than Z distribution as long as the degree of freem (*formula omitted*) is less than 120.
- A **formal hypothesis**: $H_0: \mu_A - \mu_B = 0$ and $H_\alpha: \mu_A - \mu_B \neq 0$
- Construct a hypothesized distribution with the mean of $0$ and the standard error of $\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}$
- Then draw samples from each group and calculate the mean difference $d$ to determine how likely (through $p-value$) it is that one can obtain such results when there are assumed to have no difference.
[Tool from ArtofStat (Two Mean Test)](https://istats.shinyapps.io/2sample_mean/)
Excel Solution for Two Group T-Test
========================================================
**Excel Data Analysis ToolPak**
![Analysis ToolPak in Excel](https://www.excel-easy.com/examples/images/t-test/select-t-test-two-sample-assuming-unequal-variances.png)
Also as Excel Formulae
$=T.DIST(X, DF, TRUE)$
$=T.DIST.2T(X, DF)$
$=T.DIST.RT(X, DF)$
***
**Side of the Test**
![Which side are you testing?](https://ars.els-cdn.com/content/image/3-s2.0-B9780128008522000092-f09-06-9780128008522.jpg)
How would you define a surprise?
- Too big is a surprise (Right-Tail)
- Too small is a surprise (Left-Tail)
- Too big or too small both (Two Tail)
Overview of Distributions and Their Usages
========================================================
Different test statistics assume different statistical distributions. Here are what is relevant to our current context.
<center>
| | Testing for One Group | Comparing Two Groups |
|------------------------------|-----------------------|----------------------|
| Mean | Z distribution | Z distribution |
| Mean (When $\sigma$ unknown) | T distribution | T distribution |
| Variance | $\chi^2$ distribution | F distribution |
</center>
In the quality context, we wish to know
- Whether the machine needs alignment? (Parts are even, but missing the target)
- Whether the machine needs re-calibration? (Generating uneven parts, but meets the target)
Overview of Distributions and Their Usages (cont.)
========================================================
Other types of distributions and their potential usage:
<center>
| Use Case | Distributions | Variable Type |
|---------------------------------------|-----------------|---------------|
| Number of defective units per x units | Poisson | Discrete |
| Time factor | Exponential | Continuous |
| Number of success per x trials | Binomial | Discrete |
| Sampling without replacement | Hyper-geometric | Discrete |
</center>
Many times, statistical distribution can be used to establish important baselines for the estimation.
**Now, resumed to the test of Variance**
Test of Variance
========================================================
Detecting whether the variance (or $\sigma^2$) of the process has changed provide important information
- About the machine condition
- About the accuracy of of the mean estimate
<center>
![Variance](https://www.qualitydigest.com/june08/Images/SimplifyingSPC/SimplifyingSPCFig7.gif)
</center>
***
<center>
<img src="Confidence Interval PowerPoint-figure/unnamed-chunk-6-1.png" title="plot of chunk unnamed-chunk-6" alt="plot of chunk unnamed-chunk-6" height="700" />
</center>
Test of Variance - Formalization (1/2)
========================================================
**One group variance testing statistics**
$$ \chi^2 = \frac{(n-1)s^2}{\sigma_0^2}$$
It follows a $\chi^2$ distribution with $n-1$ degree of freedom.
***
<center>
Shape of $\chi^2$ Distribution
![chi-sq](https://saylordotorg.github.io/text_introductory-statistics/section_15/5a0c7bbacb4242555e8a85c9767c03ee.jpg)
$\chi^2$ distribution is useful when determining whether an observed pattern follows the expected pattern.
</center>
Test of Variance - Formalization (2/2)
========================================================
**Two group variance testing statistics**
$$F = \frac{s_1^2}{s_1^2}$$
It follows a $F$ distribution with $n_1 - 1$ degree of freedom of numerator and $n_2 - 1$ degree of freedom of denominator.
$F$ distribution is a distribution of ratio.
***
<center>
Shape of $F$ Distribution
![F](https://upload.wikimedia.org/wikipedia/commons/thumb/7/74/F-distribution_pdf.svg/1200px-F-distribution_pdf.svg.png)
</center>
Test of Variance - Excel Solutions
========================================================
![F](https://www.teststeststests.com/microsoft-office/excel-2016/tutorials/13-excel-data-analysis-toolpak/1-t-test-F-test-z-test/6-F-Test-inExcel.gif)
***
Excel Formulae:
$=F.Dist(F, DF1, DF2, TRUE)$
$=F.Dist.RT(F, DF1, DF2)$
$=F.Test(Range1, Range2)$
One More Application of Confidence Interval
========================================================
Sometimes, for budgetary reason, we need to calculate the size of the sample befor we conduct a sampling. See if you can answer these two questions.
**Example:** <br>
A manager wants to ensure that whenever he rejects a shipment, he does not want to make more than 5% of mistake. Historically, the supplier's process had a very stable standard deviation of .5 mm. He believes 0.02 mm could serve as a meaningful margin of error size. What would be his choice of sample size? That is,
$$ 0.02 = 1.96 * \frac{.5}{\sqrt{n}}$$
Q: What is this n?
<br><br>
**Solution:** To get the sample size:
$$ 0.02 = 1.96 * \frac{.5}{\sqrt{n}}$$
$$ \sqrt{n}= (\frac{1.96 * .5}{.02})^2 = 2401$$
Sample Size Solution
========================================================

Price Break models are used where the price of inventory varies with the order size. In these models the economic order quantity is calculated for each price and compared to the amount of inventory that will be available at that price.