Six Sigma

You may have struggled to get through my rather lengthy (I didn’t name the blog Hot Air Buffoon for nothing), and technical explanation of the sigma rating system yesterday but I felt it was a relevant bit of background for today’s, less maths-heavy, post.

In the mid 80s Motorola developed a new management strategy designed to elevate all of their production processes to a 6 sigma rating and, through this, six sigma became a term used to describe this management strategy. Since it’s inception the Six Sigma management strategy has been adopted by many companies across the world, including those outside of manufacturing. Companies that have successfully implemented Six Sigma include Amazon.com, Boeing, DELL, Ford, Pepsi, and essentially the entire US armed forces. And those are just the companies that I imagine most people have heard of; there are many more companies with insanely huge outputs that also use Six Sigma. This, however, isn’t to say the system isn’t without its faults.

As I mentioned above, Six Sigma is a management strategy with the aim of achieving a rating of 6 sigma in all of a manufacturer’s processes. This target is achieved through the use of two methods: DMAIC (pronounced duh-may-ick) is designed for improving current processes, and DMADV (pronounced duh-mad-vee) also sometimes referred to as Design For Six Sigma or DFSS (not to be confused with the furniture retailer) which is used to create new processes. Here is a fairly quick breakdown of DMAIC and DMADV, using the old toast example

DMADV stands for Define, Measure, Analyse, Design, and Verify; which, funnily enough, are also the five steps involved in the method. Rememeber: this is the method used to create new processes.

The first step is to specifically Define all aspects of the process such as the customer's requirements, and the project boundaries. This is a little like when my picky little princess asks me to make her some toast before work in the morning and tells me she wants it well toasted (not burnt) with just a very thin layer of butter (because she doesn’t want to get fat), and for it to be warm, with the butter all lovely and melted (because she’s a fussy little git). And she needs it quick because her train is at eight fifteen. From this I have a well defined specification and timeframe in which to produce the product.

The second step is to accurately Measure the customer’s needs and specifications. This would be where I ask her highness exactly how hot she’d like her toast to be, how much butter she would like, and how quickly she needs it.

The third step is to Analyse the different options for the production stage. Should I try and eyeball the butter for the sake of speed or should I use something to measure it precisely. Should I put the bread into the toaster on a medium setting, or blast it with the blowtorch from the shed.

The fourth step is to Design the process to meet the customer’s needs. So it’s a blast with the blowtorch to get the toast to the required forty five degrees Celsius followed by three grams of butter, which has been weighed out on the scales, thinly spread over the top.

The fifth and final step is to Verify the process. Hmm, it only took me thirty seconds to do this toast but it tastes a little too paraffiny, and footy. The bathroom scale may be sensitive but isn’t hugely accurate, or beneficial to the overall flavour. The blowtorch could need rethinking too. I think we need to move on to DMAIC

DMAIC stands for Define, Measure, Analyse, Improve, and Control; and is used to improve current processes.

The first step is to specifically Define all aspects of the process such as the customers requirements, and the project boundaries. This would be: hot toast at fourty five degrees Celsius, with three grams of melted butter, in three minutes.

The second step is to accurately Measure all the key aspects of the process and collect any relevant data. Given time, the process I’d use to produce toast for her highness could be monitored and I would make detailed notes on things such as the performance of the blowtorch in getting the toast to the correct toastyness, the accuracy of the scale, time taken, and so on.

The third step is to Analyse the data collected and determine the primary causes of any defects as well as identify areas for improvement. I might be burning the toast a bit and the amounts of butter might be a little inconsistent.

The fourth step is to Improve the process by finding ways to fix or prevent problems. Perhaps I could buy some kitchen scales to measure the exact amount of butter, or just use the toaster to stop burning the toast. It might take longer but, as long as it toasts in less than three minutes, we’re still ok.

The fifth and final step is to Control the improvements and make sure that the new process is maintained. In other words, keep using the toaster and don’t do stupid things like weighing food on the bathroom scales. After a bit of faffing around, my little bunnykins might even stop hitting me for trying to feed her blowtorched toast.

So that’s a quick rundown of the basic Six Sigma method, but I did say it has its faults. Some people claim that Six Sigma has negative effects such as stifling creativity and limiting the levels of innovation within a company. Another feature of Six Sigma is that it creates a hierarchy of roles based on martial arts rankings, with green belts and black belts being examples of terms used to describe people at different levels of Six Sigma proficiency within a company. The use of black belts as consultants travelling to different companies has aided the growth of training and certification, leading some people to claim that many consulting firms will oversell Six Sigma as an area of expertise for them when they only really have a basic understanding of the process.

Perhaps the biggest question about Six Sigma comes from its primary aim of achieving a process quality rank of 6 sigma. It may be ok for some processes to produce 3.4 defects per million opportunities, it might not make sense for others. Only 3.4 out of a million laptops failing might be great but would you want to be on a life support machine with the same chance of defect. It is also accepted that the quality of a process will deteriorate over time and so a sigma shift of 1.5 over time is considered acceptable. This means that a process with a long term sigma rating of 4.5 could still count as a 6 sigma process. That life support machine isn’t looking so life supporting now is it.

Well, I have once again managed to skip though a fairly deep subject with reckless abandon, and now I must compose some kind of dry and witty remark with which to sign off.

Bye!

The Sigma Rating System

Despite what this highly informative entry on Urban Dictionary might have you believe, the sigma rating system is not a way of rating the relative attractiveness of another person, but a way of rating the quality of a manufacturing process. The sigma rating system is based on the idea that the number of defects that could potentially occur in a production process is statistically predictable. That means that by observing the number of times, and how severely someone botches the production of an item during a relatively short sample period; you can predict how many, out of a million units, he’s going to totally bugger up.

The sigma scale ranges from one to six. 1 sigma is at the bottom of the scale with about 69%, or 687,672 units per million, of units produced being defective. This is probably about equivalent to a Tesco shopping bag which, roughly seven times out of ten, will fail to hold the wait of your shopping, causing it to liberate its contents all over the pavement. In contrast, six sigma signifies a DPMO (defects per million opportunities) of 3.4, which I have kindly illustrated below.

Every white pixel in this image represents non-defective output, and every black pixel represents defective output. You might need to click on the image and enlarge it to see the black pixels.

Assuming you understand what I’ve said so far, you might be wondering how they come up with this figure; it’s not as if a manufacturer can just do something a million times and then count the how often they balls it up. This is where the maths comes in. I wouldn’t normally bore you with this level of detail, but the graphs I found whilst researching this stuff were so mesmerising I just had to find out what they meant, and after a good few hours trying to get my head around it, I think I’ve earned the right to try and explain it to you.

Let’s say you want to go into manufacturing cups of tea from your kitchen. God knows why you’d want to do that but for the sake of argument let’s say I’ve come to visit with my chai chugging girlfriend. She needs a constant supply of tea, and you need to supply it. She’s fussy about her tea but more than that, she doesn’t want to have to wait around all day to get it since she must drink them at a rate of about one every ten minutes (yeah, this is what I have to deal with). So you need to be producing tea at a set rate to a fairly specific standard. For this example we’ll use the amount of milk in the tea as the thing being measured. We’ll say that Tea Monster likes roughly 50ml of milk in her tea. Since it wouldn’t make much difference to be a few ml over or under, we’ll assume a buffer of about 3ml over or under 50ml; these are our upper and lower specification limits (USL, LSL). If, after closely monitoring the amount of milk being put into each cup of tea for a while, you find that the amount of milk being added is at a fairly consistent and predictable standard, we could make a good estimate of the mean amount of milk used, and the standard deviation from that amount. Put simply: add up the total amount of milk used so far and divide it by the number up cups of tea made (this is the mean); then work out how much, on average, you go over or under that amount (this is the standard deviation). Let’s pretend that these work out as 49.4ml for the mean and 0.5ml for the standard deviation. At this point, you can imagine a scale stretching between your upper and lower specification limits, with a range of -6 to 6. The middle of this scale is what you’re aiming for, a distance of six sigma from either specification limit. Check out this graph for where we’re up to.

OK, so it’s a little squiffy but what you should be able to see on the graph is this:

• The black scale along the bottom represents the amount of milk in the tea ranging from 47ml to 53ml, and is divided up into twelve levels; six above the target 50ml and six below.
• The green line in the middle represents our target mean, the 50ml we want to be putting into each cup of tea.
• The red lines either side are our upper and lower specification limits of 47ml and 53ml of milk.
• The blue curve represents the measurements taken so far with the mean being at the peak of this line.

In this graph you can see that the largest amount of measurements (the peak of the blue line) is in the dead centre of the scale at 0, and drops off at about 3.5 points from the centre. This means that on average the cups of tea are getting 50ml of milk each with roughly a 3.5 point margin of error on each side. On this particular scale 1 point is about half an ml of milk. The maths all gets very complex here and there are certain formulas to work out the specific values, but basically this graph is translated into what is called a process capability index, with measurements of Cp and Cpk. A six sigma rating requires a Cp of 2 and a Cpk of 1.5 so with a bit of quick mathalizing, I can work out work out the sigma rating of our tea production process using the mean of 49.4ml and the standard deviation of 0.5ml. Check out my working below.

Assuming these chicken scratchings are correct, we can see that we have a Cp of 2 and a Cpk of 1.6. We could push our standard deviation to .75ml and it would still be a six sigma process as this would only change the Cpk to 1.5, which is within the formal definition of six sigma.

So there you have it, a rather thorough run-down of the sigma rating system. You might be wondering why stop at six sigma? Why not keep pushing and go to seven or eight sigma (whatever that would be)? Why not aim to eliminate all defects completely? Well those are very good questions that I will have to cover in a future blog post, but for now, I’m going to go and do something very dumb to make up for all the smart stuff I’ve just offloaded. Maybe I’ll stick a fork in the toaster.