Monday, August 23, 2010
The Bathtub or Weibull curve
The Bathtub or Weibull curve is a device used in Reliability Engineering to evaluate when it is time to replace a system, rather than repair it. It applies to all types of systems from cars to space shuttles, to office buildings to the Hoover Dam. Eventually, in any system, it is time to call it quits and start over.
For inexpensive consumer goods, this "time to call it quits" 0r design life may be relatively short - about 15 years or so. Some consumer advocates call this "planned obsolescence" but in reality, it is merely part of effective Engineering. There is little point in designing some consumer goods to "last a lifetime" when they will be outmoded within a few years. Alternately, there is little point in making a consumer good "last a lifetime" if such Engineering makes the product prohibitively expensive.
So Engineers have to balance a number of factors when designing a product, with price usually being the almighty design constraint. For things like cars, weight is another factor. You can make a car last forever, or you can make it affordable. You can make it lightweight and get good gas mileage, but that works against longevity. You can't have all design criteria optimized - you have to compromise.
So your typical consumer appliance, including the automobile, is designed to last about 15 years or so. As the bathtub curve illustrates, at the beginning of service life, a product will be most likely to fail - which is why we have warranties. After that point, most consumer products are quite reliable for many years, which is why extended warranties are a rip-off. But eventually, the product starts to fail, usually in multiple modes, at which point, repair is an expensive option, particularly given the cost of labor and the inevitability of later repairs.
When you reach the end of the Weibull curve, it is time to cash it in and move on.
As I noted in my BMW FRIGHT PIG and BMW FRIGHT PIG PART DEUX posts, it is common that many older BMWs end up at the end of this Weibull curve still looking pretty - and many young people buy them on the mistaken impression that all they need is a "little" repair. But the reality is, they are near that steep part of the curve and repair costs will quickly escalate to the point where you can buy a newer (or even brand new) BMW for less than the cost of repairing an older one.
In other words, there comes a time when you have to cash it in and move on. While it may be technically possible to rebuild such a car, the headaches and unreliability of an older car will make life difficult for the owner.
When I was young, I used to buy a lot of "junker" cars, near the end of the Weibull curve. These cars could be bought for very little, but they were worth even less. I was able, in some instances, to coax them into running for 10,000 miles or more. But eventually, something major would go wrong - a rear main seal, a blown transmission, a dropped valve, and it was time to move on, sell the car to the scrapper and find another heap to ride into the ground. If approached with the right attitude, you can buy such "junkers" and drive them inexpensively, but it is a difficult game and you have to be very handy with tools.
Consumer electronics are particularly characterized by the Weibull curve. Consumer electronics either work out of the box, or fail right away or within the first few hours of use. If the latter, you take it back and get a new one. Like a light bulb, they work for a good long time and then basically burn out. In most cases, the device is outdated or outmoded by the time it dies, so no one cares. Old cell phones, computers, analog televisions, and the like, are all outdated today, and no one uses them, even though they "work". One could argue that the ones still working were over-engineered.
When consumer electronics break, it generally is prohibitive to fix them. Most stereo repair places charge $75 just to look at an item to be repaired. It ain't worth it, when a new device can be had for not a lot more. So most electronics are junked when they break.
There are a few tricks the average handy man can do to make a piece of electronics last a few more years, but for the most part, it is cheaper to simply move on, once they break. Usually the power supply fails (the battery or internal power supply). Most electronics today use touch-membrane switches that break - and usually the "on off" button is the one that breaks first, being used the most. Avoid the temptation to "mash" this if you can.
But for the most part, an electronic device is outdated and outmoded long before it fails. 8mm Video cameras, analog cell phones, analog tube televisions, older computers, dial phones, VHS VCRs, cassette decks - you name it. Either the formats or systems are no longer supported or we just plain don't use them anymore.
Many consumers fall into the bad habit of fishing too far downstream on the Weibull curve - always buying broken or outdated electronics, cars, and other devices, on the premise that they are a "bargain". However, as the curve illustrates, machinery and systems at this stage of the curve are anything but a bargain, but rather are more costly than buying a brand new (or lightly used) car or other appliance.
The real bargains, of course, are for equipment in the flat part of the Weibull curve. A late model used car, about 1-3 years old, still under warranty, with 30,000 miles or less on the clock, is going to be very reliable for many years to come, and half to three-quarters the cost of a new one. Household appliances that are only a year or two old can be a good deal - I bought a lightly used dishwasher from a homeowner who "had" to upgrade to all stainless-steel. A $300 washer - for $75.
A bad bargain, on the other hand, is a car that is 15 years old, with 200,000 miles on the clock, needing nearly everything replaced. Such cars can cost only a few hundred dollars and "look good" but are a costly nightmares. Similarly, older consumer electronics are worth little, if anything, as they will be quickly outdated and their operational life is near the end.
Machinery and electronics are like rolls of toilet paper or paper towels. The more you use them, the less there is left on the roll. When you get down to the "core" the remaining value is nearly zilch, even if there still appears to be paper on the roll. And by the way, car tires work exactly like this - unwinding themselves in a thin band of rubber as you drive down the road. This is one reason used tires are hardly a bargain. There may be "half the tread left" on a tire, but it is worth far less than half the value of a new one, as there is a minimum legal tread depth that is basically the "core".
Fishing Further Upstream is a good idea and a good habit to get into. It may be tempting to buy older equipment and think you can "fix it up" - but even with your own "free" labor, the cost of repair can be staggering.
The trick, of course, is knowing where the "bend" in the Weibull curve is, and unloading the product before it hits that expensive mark. For a car, I think around 10 years and 150,000 miles is a "safe" marking point where you should think about unloading. Most cars can go that far on original struts, shocks, radiator, water pump, oxygen sensors, and other components. After that, all of these components (as well as a host of others) are slated for replacement or repair, and things like transmissions, CV joints, and clutches start to go South and need repair.
For consumer electronics, it is not usually an issue - the device is usually obsolete long before it "wears out". But for appliances, the same law applies. They are designed for 15 years of service, and even one service call ($100 to $200) can be a huge dent in the price of a new appliance. If your dishwasher is leaking and it is 15 years old, it is probably a smarter bet to buy a new one than to try to "fix" the old one. Ditto for refrigerators, washers, dryers, stoves, furnaces, hot water heaters, and all the other fun things you own.
For example, we have a boiler that is 15 years old. It has created a lot of service problems in the last two years, requiring numerous service calls (fortunately covered by our Service Club). But the time has come and it is time for a new boiler. There is little point in trying to "repair" the old boiler, which is now leaking. Technically, it would be possible to do, but the cost would far exceed that of a new boiler. We reached the end of the Weibull curve - time to move on.
We have an old pickup truck facing the same problem. It overheats under load, so I removed the thermostat. It runs, but for how long? A new head gasket is surely in its future. Similarly, it needs a valve adjustment desperately. And the transmission is missing part of a roller clutch. The cost of installing a rebuilt engine and transmission would exceed the resale value of the truck. So, we will use it for the time being, perhaps torque the head bolts down and adjust the valves. But when the time comes, it is time to move on. While replacing the engine and transmission might fix some problems, there are still a host of others that could crop up - including the all-original suspension.
Understanding the Bathtub or Weibull curve is the first step in controlling costs of ownership of systems and machinery. As a typical American, you may end up owning dozens of pieces of machinery in your daily lives. Uses these effectively and cost-effectively is an important part of your overall financial well-being.