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Process Capability Six Sigma

Measure Process Health With Pp and Ppk

Are you telling the whole story with your metrics?  If your metrics are not considering measures of data dispersion, you are not missing half, but rather most of the picture.  So often people focus on the average (measure of central tendency) and leave off dispersion (measure of data tightness) altogether.

Imagine trading in your Toyota Camry for a Suburban or a Humvee.  You come up the driveway, open the garage door and jam the new, much wider vehicle into a garage built for a compact.  It doesn’t matter how well you center on the tennis ball hanging from the ceiling, at best, you’re hitting trash cans, ladders and golf clubs and probably can’t open the door.

Think of your customer specifications (Voice of the Customer or VOC) as the walls of the garage, and the process measurements of centering and dispersion (Voice or the Process) as the position and size of the vehicle you are trying to park.  If you are parking a motorcycle, centering becomes virtually irrelevant, whereas, pulling the new Suburban in becomes a feat of carefully calculated maneuvers.

Pp and Ppk Indices

The process capability indices Pp and Ppk measure how well your data vehicle fits inside your customer specification garage.  Pp is a measurement of how well the process data fits within the customer specifications (the difference between the width of the vehicle and the width of the garage).  Ppk measures the distance to the nearest specification limit (how close the vehicle is to one wall or another).

One of the great things about using Pp and Ppk is, because they are indices, they allow you to compare one process’ performance against another regardless of unit of measure.  A process with a Pp index of 1.43 is performing better relative to customer specifications than a process with a Pp index of 1.21…every time.  So, all else being equal, Pp and Ppk can help a team decide which process requires attention first.

Calculating Pp and Ppk

You need a few bits of information to calculate Pp and Ppk.  Sorry, but a little light-weight statistics are involved but fortunately, Excel can do all the heavy lifting.

  • Mean (Excel: =average(X1, X2, X3, X4…)
  • Standard Deviation (Excel: =stdev.s(X1, X2, X3, X4…)
  • Upper Specification Limit (USL provided by customer)
  • Lower Specification Limit (LSL provided by customer)

Pp (Fit)

Pp = (USL – LSL)/(6 * Standard Deviation)

So, lets break this down a tad starting with the numerator (USL-LSL).  This is the distance between the upper specification limit and the lower specification limit or, the width of the garage.

The denominator, (6 * Standard Deviation) is almost the full range of all of your data (99.7%).  This is based on the empirical rule which states that normally distributed data will fall within +/- 1, 2 and 3 standard deviations of the mean as follows:

  • 68% within +/-1 standard deviation
  • 95% within +/-2 standard deviations
  • 99.7% within +/-3 standard deviations

So, for our purposes, the vehicle we are parking in the garage is 6 standard deviations wide (provided you don’t have a 2×4 sticking out the window).  A Pp index of 1.5 and above means the data fits well within the specification limits with room to spare.  In other words, the garage is 1.5 times the size of the car, so we’re good.  Any lower and you have to take your groceries out of the back seat before parking in the garage.

Ppk (Centering)

Ppk (upper) = (USL – Mean)/(3 * Standard Deviation)

Ppk (lower) = (Mean – LSL)/(3 * Standard Deviation)

Because Ppk measures the distance to the closest limit, there are 2 formulas.  Since the closest wall of the garage is the one that is going to scratch the paint of our new car, that is the only one we are concerned with.  The numerators, (USL – Mean) and (Mean – LSL) tell use how far the specification limit is from the center of the data (distance between the “H” emblem on the hood of the Humvee and the closest wall).

Since we are only talking about measuring from the midpoint of the data for Ppk, we are only concerned with half of the distribution curve (so 3 standard deviations instead of 6).  If the Pp index is good (>1.5) but the Ppk is low, say 1.2, that tells us that the data could fit within the specification limits but the data is not centered and is therefore in danger of exceeding one of the specification limits.  Grandpa parked too close to one side of the garage.

Pp and Ppk are really valuable metrics to gauge process performance.  They are often misunderstood and so get ignored despite their obvious value.  Dust them off and give ’em shot in your process metrics.  You may never park a car the same way again.

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Lean Six Sigma Uncategorized

Understanding Variables

"outtake from the historic business life,"

In Six Sigma we talk a lot about X and Y variables.  We have to talk this way because, after all, Six Sigma is statistics.  Then you hear about ‘lead’ and ‘lag’ measures.  What are these and how do they relate to X and Y variables.  And what about ‘dependent’ and ‘independent’ variables.  Where do they fit in?  How do I know what to measure and when?  Relax.  It’s really not that complicated so lets step away and pull the covers back a little on some of the mystery.

X and Y and Independent and Dependent Variables

Ok…maybe you already knew this but these are the same thing.  X is the algebraic representation for the independent variable and Y represents the dependent variable.  Dependent or independent of what?  Well…of each other.  Let’s use a simple example to illustrate:

Let’s say it’s the New Year and you just made a resolution to loose weight (the most common of all resolutions and the one least likely to be kept by the way).  But your weight loss or gain doesn’t just happen in a vacuum. There are things that you decide to do to help you loose weight.  You work out, control your calories and your eating patterns for instance.  I have just described one dependent variable (Y) and three independent variables (X’s).

  • Dependent (Y) Variable – Your weight.  It is dependent on the other variables of how often and long you work out, how many calories you consume and whether you eat half a pint of Ben and Jerry’s Urban Bourbon ice cream at 11pm like I just did (I feel shameful but it was really gooood).
  • Independent (X) Variables – These are the variables that drive the Y variable.  The more you work out, the more you control your calories and the less you eat a large meal right before bed, the more you move the needle on the scale.

What is Y=f(X)

Do you suffer from algebraphobia?  Same here but this is really easy.  This equation is used commonly in Six Sigma to represent the relationship between the X and Y variables.  Read ‘Y=f(X)’ as ‘Y equals f of X’ or ‘Y is a function of X’.  Think of a function as a process.  X’s go into your function and a Y comes out.  The type, magnitude or other characteristic of X, determines the output of the function Y.  My weight loss (Y) is a function of my exercise habits (X1) or the extent to which I control my calories (X2) or how often I eat a big dinner late at night (X3).  Got it?  Cool.

Lead Versus Lag Measures

Ok…so we went from algebra to this lead and lag thing.  Again this is easy peasy.  ITS THE SAME THING!  Lead measures are the X values and lag measures are the Y values.  The reason we use lead and lag in this way is to describe their temporal relationship.  A lead measure is something you measure that is predictive of what will come after, or, the measurement that lags behind.  If I track my calories and keep them under a certain threshold everyday, I can reasonably expect the effect that lags behind will be weight loss.  The lag measure (weight loss) depends on the extent to which the lead measure (controlling calories daily) is met .

Think of lead measures as the lever that moves a big rock.  Consistent pressure on the lead measure, will eventually lead to the desired lag measure.  We act on and measure the lead measures as we are trying to affect change.  Measuring the lag measure doesn’t have any effect.  It only tells us at the end if we met our goal or not.  If I woke up everyday and all I did was weigh myself and say: “Boy, I’m really going to loose some weight today”, I probably would not be very successful.  But if I woke up every day and focused on the things in my control, my three X variables, it’s likely I’ll drop some lbs.

When to Measure What

In your improvement efforts, there are a lot of things that you will find that can be measured.  The key is to find the primary Y that you want to affect first and then find the levers to pull that are most likely to affect it…the X’s.  Once you have identified these key relationships, you first measure the Y (185lbs) before making any changes to the X’s.  This is your baseline measurement taken in the…yep…you guessed it…Measure phase of the DMAIC process.  Once you establish the baseline, then measure the X’s.

  • How many calories am I currently consuming daily? (3,000…yikes)
  • How often do I exercise each week? (2 times…er…ok 1 time)
  • How often do I eat after 9:00pm each week? (4 times…not including Ben & Jerry’s)

These are your X baselines; your levers for changing the Y.  Adjust them up or down to affect a change from the baseline in the target Y variable.  Then, measure the Y again to see the effect.

These concepts are cornerstones of process improvement and quality management principles.  Try to think of some other examples in every day life of lead and lag measures, X and Y variables and instances where Y=f(X).  Once you start to play with these concepts a bit they get easier and easier to see.  You begin to see causal relationships as levers to be pushed and pulled to deliver an outcome.

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Uncategorized

You Can’t Understand Traffic Flow by Just Counting Cars

If you counted the number of cars on a stretch of road every morning at the same time, and found that the number of cars was the same every day, would you draw the conclusion that none of the cars are moving?  Probably not.  Yet that is exactly what we do when we make inferences about the health of a process by only looking at the process’ inventory over time.  To understand how well a process is functioning, we must consider all three legs of the process measurement stool; Average Inventory, Throughput Rate and Cost.  The goal is always to increase throughput while decreasing inventory and cost.

I often see people make the mistake of looking at month over month counts of process inventory (e.g. number of in process work orders, expense reports, recruiting orders, sales orders etc.) and drawing conclusion from the change in count.  To carry forward the traffic analogy, in order to understand the flow efficiency, we need to know how many cars are entering and exiting the stretch of road and an average time between entry and exit.  These additional measures paint a picture of the flow of traffic (throughput) not just a static snap shot.

To really understand the efficiency of this stretch of road, there is one more measure to consider; Cost.  Capturing the cost to maintain the road now gets at the heart of the matter; the cost to move a car from one end of the road to the other.

With these three measures now in place, we can watch this stretch of road for variation in performance.  Significant changes in any of these three measures triggers research to determine cause.  Consider this scenario:

Number of cars on the road (inventory) decreases, and number of cars exiting the road (throughput) decreases and the maintenance costs increase – While a decrease in inventory is good, it comes at the expense of decreased throughput and increased cost.  After investigating the cause of these changes, we find that significant roadwork is being performed to build an additional lane.  This work closed one of the three existing lanes.  The lane closure reduced the capacity of the road meaning fewer cars can be on the road at any one time.  The reduced capacity also meant that cars were closer together and drivers were reducing their speed which compounded to result in a significant reduction in the number of cars exiting the road.  The work being performed was increasing the current costs, and, because there would now be another lane to maintain, increased the future maintenance costs as well.

Can you think of similar lane closures in your business processes?  What about when a key team member resigns?  Or the disruption caused by a change to a new tool or process.  What about organizational changes?  These are examples of temporary lane closures that impact business process health.  Armed with the right measures of Average Inventory, Throughput Rate and Cost, you have an early warning system that will alert you to problems sooner and improve your ability to assess the impact of changes on the overall health of your processes.

See also Three Process Metrics that Matter and Theory of Constraints

 

Categories
Lean Waste

The 3 Rules to Recognizing Waste

Have you ever gotten to the end of hectic day full of back to back meetings and deadlines and wondered, “what did I really accomplish today?”  I think we’ve all experienced this right?  The fact is that activity is not synonymous with productivity.  The vast majority of our lives is spent performing actions that do not really add value.  Some of the leanest processes in the world are still 80% waste.  Often, when we first start really analyzing processes, we find that less than 1% of our activities actually are really adding value.

Time and energy spent eliminating waste has a far greater ROI to the overall process efficiency than does working to increase the speed at which a wasteful activity is carried out.  But before we can begin to eliminate waste, we must first learn to see it.  Use these three criteria for evaluating your business process activities as value add or waste:

  1. The activity must physically change the object.
    Remember that lean has its roots in manufacturing so this rule was developed around processes that produce physical products like cars, shovels or squeegees.  So this means that an action that turns raw material into a part that can be used in the end product passes this value rule.  Think cutting a shape out of a piece of metal or painting a car body.  But for those of us not living in the world of manufacturing, this principle still applies.  Think about a business process like preparing a report.  You add information or maybe some charts and graphs which have now physically (or virtually) changed the report.  Then you send the report to your manager who reviews it and sends it back for revision.  The review does not change the report and therefore does not satisfy this first rule and leads us to the second rule.
  2. The activity must be done right the first time.
    Keeping in line with the above manufacturing example after the piece is cut out it is sent to the next station that files off burrs and saw marks after cutting.  De-burring and filing both physically change the piece.  Lean thinking teaches us though to ask, “why is deburring and filing necessary”.  The answer is that the cutting activity is not “done right” the first time requiring more downstream work.  Could burrs and saw marks be reduced or eliminated by using a sharper blade or changing the speed or pressure of the saw?  Instead of focusing on how to improve the filing and de-burring step, lean encourages us to think about what we can do to eliminate it altogether.  In business, we see this kind of refinement and rework all the time.  A project plan that needs an adjustment to scope or schedule.  A sales order that has to go back to the sales rep multiple times for clarification.  An expense report that is rejected for insufficient documentation or violation of policy.  Instead of focusing on improving the corrective or refinement activity, we need to ask, how can we eliminate the need for it altogether.
  3. The activity must be something the customer is willing to pay for.
    The problem many people have in applying this rule in business processes is understanding who the process customer is and what that customer values.  We must think of the customer in specific terms relative to the process in question.  The customer of the expense reporting process for instance is the employee getting reimbursed.  While the employee does not “pay” for this service, if he or she did, what parts of the process would be seen as valuable?  Certainly the actual reimbursement would be seen as valuable.  But what about filling out the report?  Scanning receipts?  Reviewing and approving?  Required to be reimbursed because the process requires it but the steps themselves are likely not things the employee would view as valuable.

When you begin to look at your business processes through the lens of these rules, you will be shocked at just how much action is really waste.  But don’t despair.  This is the beginning of every lean journey.  Learning to see the waste around us is the first step to improvement.  First we see waste, then we look deeper to analyze how to reduce or eliminate it and only then can we take actions that truly improve the way we work and live.

Read on here:

Value Add vs Non-Value Adding Processes

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Uncategorized

A Little Process Math

Rear view of man in suit staring at whiteboard with formulas in confusion. Classroom with concrete wall and wooden floor. Concept of exact sciences and studying.

In an earlier post, I talked about the Three Process Metrics that Matter; process inventory, throughput and cost.  These three metrics are the cornerstone to understanding how a particular process is performing. But, sometimes it can be difficult to find the average inventory of a system. Taking periodic sampling is one way to do it. Simply count the units in the process at several intervals and take the average to get average inventory. There are a few problems with this method however. For one thing, it is time consuming. It can also lead to inaccuracies caused by natural ebbs and flows of a process. For instance, say you decide to take the sampling of a trouble ticketing system every morning. Because the night shift is lightly staffed, the system naturally has a higher volume of tickets than later in the day after the fully staffed shifts have worked down the list. In this case, your average inventory will be artificially high. You could randomize your sampling schedule to take samples at different times throughout the day, but this can start to get rather complex and laborious. A better way is to use Little’s Law to calculate the average inventory over time.

In 1954, John Little published a paper on queuing theory in which he postulated that the average number of units in a stable system is equal to the average arrival rate of new units multiplied by the average time to process a single unit. This is the algebraic expression of Little’s Law:

Or, putting it a bit more simply:

Inventory = Throughput * Time

While the original description refers to “arrival” rate (as in, the arrival of customers to a store), the formula works equally as well to use the “exit” rate (as in, the rate at which sales orders are completed). Therefore, if we know for instance that we completed 50 sales orders in 10 days, our rate is 5 orders per day (throughput). And, assume we know that the average amount of time to process a single order is 2 days, then we can solve for the average inventory in the system.

Inventory (L units) = Throughput (5 orders per day) * Time (2 days)

Average Inventory = 10

Rearrange the formula to find any one of the missing three variables.

Time = Inventory / Throughput

OR

Throughput = Inventory / Time

A couple points of caution when using Little’s Law. First, be sure to keep your units of measure the same. If you are measuring throughput in days and process time in hours, you will need to convert hours to a portion of a day (or vice versa). The other thing to be aware of is Little’s Law does not account for units already present in a system at the start of the testing interval or units that have not yet completed when the testing interval is stopped. Using a longer testing interval tends to decrease the mathematical effects of these two conditions. If you need to keep your testing intervals short, you may need to find a way to estimate the leading and lagging units.

Little’s Law can save a great deal of time and produce more consistent results when measuring process performance. Try it out next time your measuring a process and amaze your friends and coworkers.

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Uncategorized

Three Process Metrics That Matter

Steam and chemical sampling panel in sampling room of power plant

Measuring process performance is the cornerstone of continual improvement. This may seem simple and obvious but like so many things, while it may be simple, it is often not easy. Sometimes it is difficult to capture the data necessary to maintain valuable measurements but I find this is not usually the problem. The more common problem is measuring too much of the wrong things. The technology that supports and enables business processes provide almost any data we want. Like Sherlock Holmes we think “Data, data, data; I can not make bricks without clay.” But, unlike fiction, more data often creates doubt and obscurity instead of leading us straight to the villain. There are only a critical three metrics that matter when gauging the health of any process. All other metrics are valuable as further forensics only after a problem is detected.

So, why not measure anything we can? I mean, we capture all this data, isn’t it a waste if we don’t use it? Consider Segal’s law; “a person with 2 watches is never sure of the time”.   Segal’s law is a cautionary postulation against the pitfalls of using too much information in decision making. If a person is wearing two watches, there are three potential states of those watches:

  1. Both watches are accurate and showing the same time. In this case, the wearer is confident because there is validation between instrumentation.
  2. One or both watches are inaccurate and displaying different times. In this case, the wearer is doubtful of the correct time because instrumentation is conflicting.
  3. Both watches are displaying the same inaccurate time. In this case, the wearer is just as confident of the correct time as if both watches are working putting trust in validated inaccuracy. Uh oh, then, if both watches are telling the same time, then that casts doubt on condition one.

So there is never a case where the wearer of 2 watches is truly confident of the correct time. Then the focus becomes on keeping instrumentation in synch. One well maintained high quality metric is far more useful than any combination of lower quality and often conflicting measurements.

The Theory of Constraints tells us there are only three key metrics to worry about when measuring the health of any given process; inventory, throughput and cost.

Inventory is all of the units in the process at any given time. Units are what the process acts on to produce an output. Some examples of business process units might include a sales order, trouble ticket, invoice, expense report or change order as example.

Throughput is the rate (expressed as # units over time period) at which a process produces output that is usable by all downstream processes. The last part of this is critical because it answers the common question “What about quality metrics?”. Quality is embedded in the throughput metric because only outputs that meet quality standards for all downstream processes are counted as throughput. If you apply this rule ruthlessly, it is not uncommon to find processes that, when first measured, have a throughput of zero because every output requires some level of rework, or does not meet service level’s or contains defects that are corrected by a downstream process.

Costs include all the money used to produce process throughput. Actual costs of a single process can be very difficult to capture. Most of the time, you’re looking at a single process acted on part time by many people for instance. Don’t get too wrapped up in this. If you can’t get to actual dollars, find a viable surrogate. In business processes, this is usually some variation of a human capital measurement.

When used together, these three metrics paint a valuable picture of the health of a single process. The objective is to reduce inventory and control or reduce costs while increasing throughput. Statistically relevant variations in the patterns of these three measures direct us to specific problems and areas requiring attention. Additionally, since each process is measured in a similar way, we can now make better decisions where to focus our improvement efforts. Given the choice between working on only one of two different processes, we can now compare relative changes in inventory, throughput and cost. Assuming both processes are valid candidates for improvement efforts, the one with the greatest deviation should get the most focus (all other things being equal).

Think of process measurement like a trip to the doctor. The first measures are simple indicators of health like weight, temperature and blood pressure. The results of these basic measures may drive further analysis but you’d never get wheeled in for a CAT scan or a full panel blood work up as a first step.

Don’t get seduced by the “more is better” mantra when it comes to process measurement. Reports that show a wall of data are rarely effective at driving action. Look for the key measures that are the best representation of inventory, throughput and cost and use those as your bellwether for action. Additional data may be required to select and direct specific actions. Use supporting data for forensic purposes not to measure top level process health. Start simple and use deeper level data to analyze once a problem is detected.