Category: R

I am sure you must have heard of Six Sigma quality standard or Six Sigma experts. But, what is Six Sigma?

Six Sigma is a set of techniques used by organizations to improve their processes and optimize operations. Six Sigma was popularized by manufacturing organizations and Jack Welch, former CEO of GE, was one of advocators of Six Sigma. At the heart of Six Sigma lies the core strategies to improve the quality of processes by identifying and removing the causes leading to defects and variability in product quality and business processes. Six Sigma uses empirical and statistical quality management methods to carry out operational improvement and excellence projects in organizations.

Six Sigma projects follow methodologies which are called as DMAIC and DMADV. DMAIC methodology is used for projects aimed at improving existing business processes; while, DMADV is used for projects which aims at creating new processes. Since this article talks about control charts, we will focus on DMAIC project methodology of which control charts is a part of. DMAIC methodology has five phases:

1. Define
2. Measure
3. Analyze
4. Improve
5. Control

Define

Defining the goals that you wish to achieve – basically, identifying the problem statement you are trying to solve. In this stage, everyone involved in the project understands his/her role and responsibilities. There should be clarity on ‘Why is the project being undertaken?’

Measure

Understanding the ‘As-Is’ state of the process. Based on the goal defined in the ‘Define’ phase, you understand the process in detail and collect relevant data which is to be used in subsequent phases.

Analyze

By this phase, you know the goal that are you trying to achieve and also, you understand the entire process and have the relevant data to diagnose and analyze the problem. In this phase, make sure that your biases don’t lead you to results. Instead, it should be a complete fact-based and data-driven exercise to identify the root cause.

Improve

Now, you are aware about the entire process and cause behind the problems. In this phase, you need to find out ways or methodologies to work on the problem and improve the current processes. You have to think of new ways using techniques such as design of experiments and set up pilot projects to test the idea.

Control

You have implemented new processes and now, you have to ensure that any deviations in the optimized processes are corrected before they result in any defects. One of the techniques that can be used in control phase is statistical process control. Statistical process control can be used to monitor the processes and ensure that the desired quality level is maintained.

Control chart is the primary statistical process control tool used to monitor the performance of processes and ensure that they are operating within the permissible limits. Let’s understand what are control charts and how are they used in process improvement.

According to Wikipedia, “The data from measurements of variations at points on the process map is monitored using control charts. Control charts attempt to differentiate “assignable” (“special”) sources of variation from “common” sources. “Common” sources, because they are an expected part of the process, are of much less concern to the manufacturer than “assignable” sources. Using control charts is a continuous activity, ongoing over time.”

Let’s take an example and understand it step by step using above definition. You leave for office from your home every day at 9:00 AM. The average time it takes you to reach office is 35 minutes; while in most of the cases it takes 30 to 40 minutes for you to reach office. There is a variation of 5 minutes less or more because of slight traffic or you get all the traffic signals red on your way. However, on one fine day you leave from your home and you reach office in 60 minutes because there was an accident on the way and the entire traffic was diverted which caused additional delay of around 20 minutes. Now, relating our example with the definition above:

Measurements: Time to reach office – the time taken on daily basis to reach office from home is measured to monitor the system/process.

Variations: Deviations from the average time of 35 minutes – these variations are due to inherent attributes in the system such as traffic or traffic signals on the route.

Common sources: Slight traffic or traffic signals on the route – these are usually part of the processes and are of much less concern while driving to office.

Excessive Variation: Accident – these are events which leads to variations in the processes, leading to defects in the outputs or delayed processes.

Summing up everything, control charts are graphical techniques to monitor the performance of a process over time. In the control chart, the performance of these processes is monitored visually to identify any anomalies or variations from the usual behavior. For every control chart, there are control limits or decision limits set which define the normal behavior of the process. Any movement outside those limits indicate variation in the process and needs to be corrected to prevent further damage.

In any control chart, there are three main attributes – Average Line, UCL and LCL. Average line is the mean of all the observations taken in the process. UCL and LCL are upper control limit and lower control limit, respectively. These limits define the control or decision limits within which a process should always fall for efficient and optimized operations. These three values are determined by the process. For a process where all the values lie within the control limits and there is no specific pattern in the values, the process is said to be “in-control.”

X-axis can have either time or sample sequence; while, the Y-axis can have individual values or deviations. There are different control charts based on the data you have, continuous or variable (height, weight, density, cost, temperature, age) and attribute (number of defective parts produced). Accordingly, you choose the control chart and control objective.

Following steps present the step-by-step approach to implement a control chart:

• What process needs to be controlled?

Answer to this question will come from the DMAIC process while implementing the entire project methodology.

• Which system will provide the data to monitor?

Identifying the systems that will provide the data based on which control charts will be prepared and monitored.

• Develop and monitor control charts

Develop the control charts by specifying the X-axis and Y-axis.

• What actions to take based on control charts?

Once you have developed control charts, you need to monitor the processes and check for any special or excessive variations which may lead to defects in the processes.

By now, we have understood what control charts are and what information do they provide. Let us understand further uses of control charts and what more information can be extracted from these charts. Apart from manufacturing, control charts find their applications in healthcare industry and a host of other industries.

• Control charts provide a very simple and easy to understand methodology to understand the performance of processes.
• It reduces the need for inspection – the need for inspection arises only when the process behavior is significantly different from the usual behavior.
• If changes have been made to the process, control charts can help in understanding the impact of those changes on desired results.
• The data collected in the process can be used for improvement in the subsequent of follow-up projects

Control Chart Rules

For a process ‘in-control’, most of the points should lie near the average line i.e. Zone A, followed by Zone B and Zone C. Very few points should lie close to control limits and none of the points should fall beyond the control limits. There are eight rules which are helpful in identifying if there are certain patterns or special causes of variation in the observations.

Rule 1: One or more points beyond the control limits

Rule 2: 8 out of 9 points on the same side of the center line (Average line)

Rule 3: 6 consecutive points increasing or decreasing (monotonic)

Rule 4: 14 consecutive points are alternating up and down

Rule 5: 2 out of 3 consecutive points in Zone C or beyond

Rule 6: 4 out of 5 consecutive points in Zone B or beyond

Rule 7: 15 consecutive points are in Zone A

Rule 8: 8 consecutive points on either side of the Average line but not in Zone A

Now, we have understood the control charts, attributes, applications and associated rules, let’s try to implement a small example in R.

Let’s assume that there is a company which manufactures cylindrical piston rings. For each of the rings manufactured, measurement of the diameter is taken 5 times and captured to examine the within piece variability. These five measurements for one-piece forms one sample or one sub-group. Similarly, measurements for 25 pieces is taken. Using rnorm function in R, let’s create the measurement values.

In R chart, we look for all rules that we have mentioned above. If any of the above rules is violated, then R chart is out of control and we don’t need to evaluate further. This indicates the presence of special cause variation. If the R chart appears to be in control, then we check the run rules against the X-Bar chart. In the above chart, R chart appears to be in control; hence, we move to check run rules against the X-Bar chart.

In the above chart, one of the points lie outside the UCL which implies that the process is out of control. The standard deviation in the above chart is the standard deviation of means of each of the samples. If we were to look at the sample 18, we see that the values in sample 18 are usually higher than values in other samples.

Now, let’s check process capability. By process capability, we can check if control limits and specification limits are in sync with each other. For instance, in the case we have taken, our client wanted piston rings with target diameter of 1.5 cm with a variation of +/- 0.1 cm. Process capability will help us in identifying whether our system is capable to meeting the specified requirements. It is measured by process capability index C_pk.

In the above plot, red lines indicate the target value, the lower and upper specified range. It can easily be inferred that the system is not capable to manufacture products within the specified range. Also, for a capable process, value of C_pk should be greater than or equal to 1.33. In the above chart, the value is 0.356 which is less than the required value. This shows that the above process is neither stable nor capable.

I am sure after going through this article, you will be able to use and create control charts in multiple other cases in your work. We would love to hear your experience with creating control charts in different settings.

Author Bio:

This article was contributed by Perceptive Analytics. Jyothirmayee Thondamallu, Chaitanya Sagar and Saneesh Veetil contributed to this article.

Perceptive Analytics is a marketing analytics company and it also provides Tableau Consulting, data analytics, business intelligence and reporting services to e-commerce, retail, healthcare and pharmaceutical industries. Our client roster includes Fortune 500 and NYSE listed companies in the USA and India.

I recently had the wonderful opportunity to chat with Hadley Wickham. He is an immensely prolific, yet humble guy who has not only contributed heavily to the advancement and development of R as a language and environment, but who also cares and has thought a lot about the process of doing data science the right way.

As a result, he has given many interviews on this “process” and his approach to data science and programming in R, mostly on the technical side of things. So, when I spoke with him, I wanted to frame the conversation for a broader audience, in large part due to the rapid expansion of people who are using R, most of whom engage very little with the programming wing of the community. Though this expansion of R users is a great thing on many dimensions, it has the potential to create a cohort of frustrated, self-taught programmers.

So, I am sharing Hadley’s responses to my questions in this blog for three main reasons: first and foremost, in an effort to offer a life-raft of sorts to people just getting started with (and frustrated by) R; second, to try and bridge the applied side of R users with the programming side of R users; and third, in the spirit of the open source foundation of R, to speak openly and plainly about the basics of approaching programming in R, and then how to keep going when you run into problems.

Importantly, though this conversation is intentionally non-technical and aimed at beginning programmers and R users, there are many great points and ideas for all programmers to consider, regardless of levels of proficiency and comfort with R. I have highlighted (via bold text) several of these particularly practical and valuable points throughout.

A final technical note: I edited a few places to make the conversation more amenable to reading and for the purpose of a blog post. I did not, however, change any of the substantive content of Hadley’s responses, as you will note from the conversational style of the responses, virtually all of which are verbatim. Enough of me. Here is some advice from Hadley Wickham to young (and old) programmers.

• First, what is your role at R-Studio?

I am the chief scientist at R-Studio. I don’t really know what that means, or what chief scientists do. But I basically lead the teams that look after the Tidyverse, which is a set of packages for doing data science in R. So, my teams have a mix of roles, but there is some research in thinking what we should be working on, a bunch of programming, and also a bunch of education, like helping people understand how things work, webinars, books, talks, and Tweets.

• Why R? How did you come to it and why should other people be convinced?

When I started learning R, the reason was simple: it was the only open source programming language for statistics. That’s obviously changed today, with programs and languages like Python, Java Script, and Scala.

So why R today? When you talk about choosing programming languages, I always say you shouldn’t pick them based on technical merits, but rather pick them based on the community. And I think the R community is like really, really strong, vibrant, free, welcoming, and embraces a wide range of domains. So, if there are like people like you using R, then your life is going to be much easier. That’s the first reason.

And the second reason, which is both a huge strength of R and a bit of a weakness, is that R is not just a programming language. It was designed from day 1 to be an environment that can do data analysis. So, compared to the other options like Python, you can get up and running in R doing data science, learning much, much less about programming to get started. And that generally makes it like easier to get up and running if you don’t have formal training in computer science or software engineering.

• Let’s transition to Tidyverse, as you just mentioned. First, could you explain a bit behind the approach of the Tidyverse, from processing and management, to analysis in R?

The Tidyverse is a collection of R packages with the goal being, once you’ve learned one package in the collection, learning the other packages should be much easier. And what that means is that there is a deep, underlying philosophy and unity where you can learn things in one package and apply the same ideas elsewhere. So, it just means that your naïve ideas about what a function is going to do or how to tackle a problem should be fairly good, because you can draw on your experiences. Things are designed consistently in such a way where your experiences with other functions apply to new functions. So, for example, one of the ideas that underlies many, many packages in the Tidyverse is this idea of “tidy data,” which is a really simple idea, where when you are dealing with data science-y kind of data, you want to make sure that every variable is in a column, and then naturally every observation or case becomes a row. And if you put your data in that format once when you are doing data tidying, then you don’t have to hassle with it multiple times throughout the process.

• In an interview in 2014 at UseR, you said one of your main goals was streamlining the process of getting from raw data to visualization quickly and efficiently, with “tidying” up the data being a key aspect of that. Presumably, you were talking about development of the Tidyverse. Do you think you’re there on that goal? Is there more to be expected? Did you meet it?

Yeah, we have made a lot of progress towards that goal. And 2014 was well before the idea of the Tidyverse existed. And the biggest change in my thinking since then is thinking of the Tidyverse as a thing and not just individual packages, and then being consistent across packages. That’s playing off one of the things my team has been focusing on this year, and that’s consistency within the Tidyverse; not adding a bunch of new features or creating new packages. But just thinking, “how can we make sure everything fits together as well as it possibly can?”

So, we are making good progress and there’s always more to do. And one of the things I find really rewarding is people sharing their experiences, like getting started with data and having the first really enjoyable experience when you go from a new dataset to some cool visualization with as little pain as possible. A neat illustration of that is the “TidyTuesday” hashtag [#tidytuesday] on Twitter. Every Tuesday they post a little data set and challenge, and then people tackle it with R and other tools and Tweet their results. Its really cool. [And anybody can do this, I guess?] Yeah exactly. Totally community run and driven.

• Let’s shift and talk a little more conceptually about R and programming. There seems to be a ton of resources out there for R programmers given that its open source. This is naturally a wonderful thing. But I am wondering about beginning R programmers. Given that there is so much out there, how would you counsel a beginning programmer to sift through the resources to distinguish the signal from the noise?

So, I’m obviously biased in this recommendation, but I would say start with my book, “R for Data Science,” just because this is what it was designed for. It’s not going to teach you everything about R, and it’s by no means perfect, but I think it’s a really good way to get started. And it focuses relentlessly on giving you useful tools to help you understand data. It seems to be pretty popular and people seem to like it. And it’s free. You can buy a book if you want, but it’s free online.

After that, the other thing I would say is to try and find an R learning community. It’s much easier to learn and stay motivated when you are working with other people. And I think there’s lots of ways of doing that: look for a local meet up, like an R meet up or an R Ladies meet up in your area. There’s also the R-Studio community site.

Just find some way to find people like you who also are learning, because you can share your successes and your trials and your failures. It makes it much more likely that you will stick it out to the point where you will do something really useful.

• I’ve noticed a theme in your work and how you approach package and resource development is addressing and fixing common problems in R. I’m curious how you hone in on these problems.

Yeah, I am curious too. I seem to be able to do it. I don’t really know exactly how. Part of it is I just talk to people and I travel a lot. I talk to people in different areas working on different problems, and I interact with a bunch of people on Twitter. And somehow that all feeds into my brain, and then ideas come out in a way I don’t fully understand. But it seems to work. I don’t want to break it. Also, I talk to people who are actually struggling with data analysis problems, and I also read a lot of other programming languages, computer science, and software engineering, because there’s basically nothing that I have done that’s not been done in some way, somewhere else before. So, it’s just finding a right idea that someone else has come up with and then applying it in a new domain; it’s tremendously valuable.

• The use of R has seemed to explode within the past decade or so, moving far beyond the smaller world of computer programmers, spilling into many applied fields such as medicine, engineering, and even my own, political science. Having learned mostly on my own, I feel like there are two conversations going on, with a big gap, leaving the beginners to try and sift through complex worlds and tradeoffs. Specifically, in applied data analysis, the debate or tradeoff seems to be over using R versus another package like Stata. But from what I have observed, in the programming world, the debate seems to be over R versus other languages, such as Python, like you mentioned. So how should an applied analyst, someone who is not a programmer by training, navigate this tradeoff?

I think the tradeoff between Stata and R is: do you want a point-and-click interface, or do you want a programming interface? Point-and-click interfaces are great, because they lay out all of your options in front of you, and you don’t have to remember anything. You can navigate through the set of pre-supplied options. And that’s also it’s greatest weakness, because first of all, you are constrained into what the developer thought you should be able to do. And secondly, because your primary interaction is with a mouse, it’s very difficult to record what you did. And I think that’s a problem for science, because ideally you want to say how you actually got these results. And then simply do that reliably and have other people critique you on that. But it’s also really hard when you are learning, because when you have a problem, how do you communicate that problem to someone else? You basically have to say, “I clicked here, then I clicked here, then I clicked here, and I did this.” Or you make a screen cast, and it’s just clunky.

So, the advantages of programming languages like R or Python, is that the primary mechanism for communicating with the computer is text. And that is scary because there’s nothing like this blinking cursory in front of you; it doesn’t tell you what to do next. But it means you are unconstrained, because you can do anything you can imagine. And you have all these advantages of text, where if you have a problem with your code, you can copy and paste it into an email, you can Google it, you can check it and put it on GitHub, or you can share it by Twitter. There’s just so many advantages to the fact that the primary way you relate with a programming language is through code, which is just text. And so, as long as you are doing data analysis fairly regularly, I think all the advantages outweigh a point and click interface like Stata.

For R and Python, Python is first and foremost a programming language. And that has a lot of good features, but it tends to mean, that if you are going to do data science in Python, you have to first learn how to program in Python. Whereas I think you are going to get up and running faster with R, than with Python because there’s just a bunch more stuff built in and you don’t have to learn as many programming concepts. You can focus on being a great political scientist or whatever you do and learning enough R that you don’t have to become an expert programmer as well to get stuff done.

• As people develop in programming, could you talk a little about the tradeoff between technical complexity and simplicity and usability?

That’s a big question. People naturally go through a few phases. When you start out, you don’t have many tips and techniques at your disposal. So, you are forced to do the simplest thing possible using the simplest ideas. And sometimes you face problems that are really hard to solve, because you don’t know quite the right techniques yet. So, the very earliest phase, you’ve got a few techniques that you understand really well, and you apply them everywhere because those are the techniques you know.

And the next stage that a lot of people go through, is that you learn more techniques, and more complex ways of solving problems, and then you get excited about them and start to apply them everywhere possible. So instead of using the simplest possible solution, you end up creating something that’s probably overly complex or uses some overly general formulation.

And then eventually you get past that and it’s about understanding, “what are the techniques at my disposal? Which techniques fit this problem most naturally? How can I express myself as clearly as possible, so I can understand what I am doing, and so other people can understand what I am doing?” I talk about this a lot but think explicitly about code as communication. You are obviously telling the computer what to do, but ideally you want to write code to express what it means or what it is trying to do as well, so when others read it and when you in the future reads it, you can understand some of the reasoning.

• Any parting words of wisdom for R programmers or the community?

It’s easy when you start out programming to get really frustrated and think, “Oh it’s me, I’m really stupid,” or, “I’m not made out to program.” But, that is absolutely not the case. Everyone gets frustrated. I still get frustrated occasionally when writing R code. It’s just a natural part of programming. So, it happens to everyone and gets less and less over time. Don’t blame yourself. Just take a break, do something fun, and then come back and try again later.

# initial parameters for simulating data
n_indiv <- 25
min_days <- 50
max_days <- 200
min_dose <- 10
max_dose <- 50

# list of ids
id_list <- str_c("i", 1:n_indiv)

# intializing empty table
my_data <- as.data.frame(matrix(NA, n_indiv, (max_days+1)))
colnames(my_data) <- c("id", str_c("d", 1:max_days))
my_data$id <- id_list

# daily simulated data
set.seed(113)
for(i in 1:nrow(my_data)){
# n days follow up
n_days <- round(runif(1, min_days, max_days))
# maximum dose
dose <- round(runif(1, min_dose, max_dose))
# random daily value
my_data[i,2:ncol(my_data)] <- c(runif(n_days, 0, max_dose), rep(NA,(max_days-n_days)))
}

# cumulative simulated data
my_cum_data <- my_data
for(i in 3:ncol(my_cum_data)){
my_cum_data[[i]] <- my_cum_data[[i]] + my_cum_data[[i-1]] 
}

 # Color legend on the top
long_heat_plot <- function(my_data, cutoff, xmax) {
# my_data: longitudinal data with one line per individual, 1st column with id, and then one column per unit of time
# cutoff: cutoff value for color plot, all values above cutoff are same color
# xmax: x axis max value
n_lines <- nrow(my_data)
line_count <- 1
# color scale
COLS <- rev(heat.colors(cutoff))
# plotting area
par(oma=c(1,1,4,1), mar=c(2, 2, 2, 4), xpd=TRUE)
# plot init
plot(1,1,xlim=c(0,xmax), ylim=c(1, n_lines), pch='.', ylab='Individual',xlab='Time unit',yaxt='n', cex.axis = 0.8)
# plot line for each woman one at a time
for (i in 1 : n_lines) { 
# get id
id1 <- my_data$id[i]
# get trajectory data maxed at max_val
id_traj <- my_data[my_data$id == id1, 2:ncol(my_data)]
# get last day
END <- max(which(!is.na(id_traj)))
# plot dotted line
x1 <- 1:xmax
y1 <- rep(i,xmax)
lines(x1, y1, lty=3)
for (j in 1 : (ncol(my_data) - 1)) {
# trim traj to max val
val <- min(id_traj[j], cutoff)
# plot traj
points(j, i, col=COLS[val], pch=20, cex=1)
}
# add limit line
points((END+1), i, pch="|", cex=0.9)
}
# add legend
legend.col(col = COLS, lev = 1:cutoff)
mtext(side=3, line = 3, 'unit of measurement')
opar <- par()
text_size <- opar$cex.main
}

 long_heat_plot(my_data, 50, 200) 

 long_heat_plot(my_cum_data, 5000, 200) 

Stencila launches the first version of its (open source) word processor and spreadsheet editor designed for researchers.

By Michael Aufreiter, Substance, and Aleksandra Pawlik and Nokome Bentley, Stencila

Stencila is an open source office suite designed for researchers. It allows the authoring of interactive, data-driven publications in visual interfaces, similar to those in conventional office suites, but is built from the ground up for reproducibility.

Stencila aims to make it easier for researchers with differing levels of computational skills to collaborate on the same research article. Researchers used to tools like Microsoft Word and Excel will find Stencila’s interfaces intuitive and familiar. And those who use tools such as Jupyter Notebook or R Markdown are still able to embed code for data analysis within their research articles. Once published, Stencila documents are self-contained, interactive and reusable, containing all the text, media, code and data needed to fully support the narrative of research discovery.


Source: https://stenci.la

The Stencila project aims to be part of the wider vision to enable the next generation of research article – all the way from authoring through to publication as a reproducible, self-contained webpage. A key limitation of the current research publishing process is that conventional document formats (e.g. Word, PDF and LaTeX) do not support the inclusion of reproducible research elements, nor do they produce content in the structured format used for science publishing and dissemination (XML). Stencila aims to remove the need for manual conversion of content from source documents to XML and web (HTML) publishing formats, whilst enabling the inclusion of source data and computational methods within the manuscript. We hope that establishing a digital-first, reproducible archive format for publications will facilitate research communication that is faster and more open, and which lowers the barrier for collaboration and reuse. The development of Stencila is driven by community needs and in coordination with the goals of the Reproducible Document Stack, an initiative started by eLife, Substance and Stencila.