We looked at two important ways in which the consumer price index  overstates inflation -- substitution bias and quality change bias. How do these problems affect the way that inflation is calculated?
The problem of substitution bias is that the consumer price index has historically measured the change in the cost of buying a fixed basket of goods. What we would really like is a measure of the change in the cost of making us as well off as before.
These are distinct questions. If relative prices change, I can increase my wellbeing by changing the product mix that I consumer. Put another way, the basket of goods I consume is not fixed. Let's imagine that one average prices rise by 10 percent -- some by less, some by more. Calculating the change in the CPI with a fixed basket of goods would lead us to say inflation was 10 percent. But I can change the basket of goods I consume and make myself just as well off as before with less than a 10 percent increase in income. Perhaps, allowing for this subsitution in the basket, the cost of living has only risen by 8 percent.
The government is tackling this problem by updating the basket of goods it uses to calculate inflation more frequently.
Quality change bias results from the difficulty of measuring changes in product specifications over time. The price of a car has risen modestly over the last ten years, so we would conclude that there has been positive but modest inflation in car prices. However, the quality of cars has risen dramatically - they are safer, faster, and not as ugly. 
If we are interested in the change in price of a car of constant quality, our problem is that the old cars are no longer being produced and we cannot see what prices they would sell for. So, what we have to do is try to measure how much of the increase in the price of cars is due to inflation, and how much is due to quality improvement. This demands that we are able to measure the quality change and work out what it is worth to people. Doing so is a costly and time-consuming task. The government has so far only decided it is worth doing for a small number of goods, most notably computers.