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Making the Ca$e for SPCBy: Steven Ouellette for DataNetRead the article as published in Quality Magazine I am sometimes faced with the task of "selling" the implementation of statistical process control (SPC) to companies. There are a number of ways to do this, each way tailored to the person you need to convince. Let's focus on one. Implementing SPC will take energy and resources, so you had better be able to show a financial benefit for having done it. But how do you show this benefit before implementation? And how do you do that without hearing the coconut-like sounds of heads hitting desks? Managers speak the language of money, so you need to phrase these potential savings in their favorite metric: "S-bar" ($). One barrier you run into during these discussions is that there are a number of managers who have been trained by their own company to think of "quality" as "in-spec." I know, absurd though it is, there are some people who actually think that they are being "practical" when they say such a thing, when in fact this way of thinking loses lots of businesses lots of money. I have heard it put this way, "If it is in-spec it is good. If it is out of spec, it is bad. So why do I need to do SPC?" So how do you explain to someone that "in-spec" can mean unnecessary financial costs, and that SPC is a way to begin recovering those costs? One way that I have found useful is to explain the benefits using Taguchi's Loss Function. This is the only way I have found of convincing battle-hardened front-line managers that "in-spec and out the door" is tossing money in the trash.
Click here to read how Trane Corporation uses the Taguchi Loss Function (TLF) to calculate savings from implementing real-time SPC .
The way I introduce the Loss Function is to start with a thought experiment. Let's say that you are running a simple business making parts. (Change the terms to match your industry - nothing annoys managers more than a "widgets" example when they don't make widgets!) If we start from the premise that in spec = good, out of spec = bad (as in Figure 1) then what is the cost incurred by your business and that of your customers if a part is pretty far outside of the specification limit? Figure 1 - Traditional Quality Thinking  It should be easy to figure out what these costs are - you might have to scrap it losing all the expense you have put into it up to that point, or perhaps perform a lot of rework with the associated costs in time, personnel, and material. Maybe you can call the customer to get approval to send it on deviation, and they might have to do a custom setup to handle the out-of-spec material. As a part is further out from the spec, the costs associated with trying to make it work increase rapidly, and you probably don't have to get too far out before the costs outweigh any benefit. Now ask your manager if a part that is barely outside spec incurs the same costs. Probably the answer is no, though it still incurs cost. You might be able to lightly rework the part, and you still might have to call your customer to send it on deviation, and they might have to tweak their setup a bit to handle it. So we have shown that there is a continuum of incurred costs so that the further outside the spec the more loss is associated with it. Now consider a part that is barely in spec. Does that perform much differently than the part that was barely out of spec? Probably not, and so your customer will likely have some lesser difficulty in getting this to work. There may be long-term consequences to having a part that is barely inside the lower spec one day and a part that is barely inside the upper spec the next. As far as internal costs, if you charge by the part, you may be giving away material you bought by the pound if the part is on the high side, or maybe due to measurement variability there is some probability that you are likely to find a borderline in-spec part as out of spec and try to rework it. The ideal is if we can get the part where the customer needs it - right on target time after time. So we can easily see a part that is on target is one that has the lowest cost to us and our customers. We know the target is the minimum cost, and that once we approach and go beyond the spec limit we see an increasing cost to that part. But what costs do we experience further inside the specification? As the variability increases, so does the need for an infrastructure to catch out-of-specification parts. For example, as the variability approaches the spec limits, we find that we need to increase the sampling rate, and so need an ever-increasing number of non-value adding inspection overhead. We may find that in-process part variation causes us greater internal scrap rates or process costs as well. Therefore, a part that is in spec can incur cost on a continuum as well - as the variability increases, so do the costs at an ever increasing rate. One way of displaying this is shown visually in Figure 2, where costs can be seen increasing from the target out as indicated by color. This shows that quality is not conformance to specification. If you make something that is out of spec, it has no quality, or the characteristic of "un-quality" since you have not done what you promised the customer you would. Poor quality starts at the spec limits and quality gets better the closer you are to target. Figure 2 - Continuum of Quality within Specification  This is the essence of the Taguchi Loss Function. Taguchi concluded that these costs can be modeled by a parabolic curve, as shown by curve A in Figure 3. Figure 3 - The Taguchi Loss Function and Process Variability  How does variation even within the specification affect the cost of the process? We can use the Taguchi Loss Function to give us an answer. The general form of the Loss Function is: Loss = k(x - Target)2 Where k is the constant that makes the loss numbers match the loss from a particular process. If we use k = 1, then Table 1 gives the losses for our example graph above. (I have added $1 loss to everything to indicate that the loss may not be zero even at target.) Note that the specifications do not even come into the calculation. Specifications are the allowable variation about a target that your customer can tolerate, and ideally were generated by thinking through these costs. Table 1 - Process Loss and Capability for LSL = 97, Target = 100, USL = 103, k = 1, normal distribution, Loss = 1 + k(x - Target)2
*A uniform distribution is the result of using a lot of inspection to filter out a lot of nonconforming output, so the actual relative costs are likely much higher Using this table, it is clear that these processes have different quality (measured by the total process loss). Perhaps surprisingly, the uniform distribution indeed has the highest cost, even discounting the other hidden inspection costs that a uniform distribution might have. So the engineer or manager looking to sell their boss on investing the time and money into implementing SPC has a number of arguments.
Conclusion In management's eyes, the purpose of SPC should be to save money. The Taguchi Loss Function is an easy way to communicate to managers the true cost of variation - costs that do not show up as a line item on any balance sheet - and is useful to justifying the investment in implementing SPC. SPC tells you when to leave the process alone and when it is time to react. By using SPC, you can minimize the variation of your process by identifying, reacting to, and eliminating extra sources of variation. Minimizing variation around the customer's target makes you (and your customer) more money - a statistic that is near and dear to those who hold the purse strings. |
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