Statistics of Projector Manufacturing

Bob Raikes brought to my attention the fact that BenQ makes two virtually identical projectors, the MU686 and the MU706. Both are single panel DLP projectors using a 240W lamp. The only difference between the two was the MU686 was specified at 3500 ANSI lumens and the MU706 was specified at 4000 ANSI lumens. Since my background is strongly in projector technology, he hoped I could suggest what was going on.

I looked for tell-tale signs for differences between the two projectors that would account for the lumen differences. These signs could have been lamp power, lamp life, total projector power, projector weight and size and projector colorimetry. I also read the marketing discussions for the two projectors and they were identical, too.

Finally, all I could suggest was it was an effect due to the statistics of projector manufacturing. Unfortunately, most people’s eye’s glaze over at the mention of statistics, but wake up!, this is important.

This is a topic I first thought about while working on the Talaria projectors at GE in the early 1990’s, first wrote about in an internal Philips memo in 1995 and wrote about for public consumption in the 1st Edition of Projection Displays in 1998. That discussion, virtually unchanged from my internal Philips memo, was carried forward to section 11.7 of the 2nd Edition of Projection Displays (John Wiley and Sons.) published in 2008.

The variation in light output comes from the fact that there are many components that affect the light output of a projector. Some, but not all components, affecting projector lumen output are listed in the table below.

Let’s assume component number i in the projector has an average value of ?i and a standard deviation of ?i. The ratio of these values is the relative standard deviation, si. For example, a polarizer in polarized light might have a transmission of 84% with a standard deviation of 1.0%. This would give a relative standard deviation of si = 1.0%/84% = 1.2%. For each polarizer in a 3LCD projector with this 1.0% specification, there would be about a 1.2% contribution to the total variation in the lumen output of the projector.

These component standard deviations are combined into a standard deviation of the projector lumens with the equation:

BenQ equation 1

If you have n components, all with the same relative standard deviation s, this reduces to:

BenQ equation 2

In other words, the variation of the lumen output of a projector increases with the number of components in the projector that affect the lumen output.

The table below gives examples of components that affect the lumen output. The variation assigned to each component is my best guess so I hope no component or projector vendors jump on me because I’m off some. Component and projector manufacturers don’t release these sort of numbers. They may not even have them in usable form. For example, a red dichroic filter with a cut-off wavelength of 600 nm is likely to have a variation in the cut-off wavelength of about ±6nm in high volume production. The dichroic manufacturer could certainly tell you what wavelength variation their production process can produce. What they can’t tell the projector manufacturer is how much this variation will affect the lumen throughput. That will depend on the light source used, the target white point, the target color gamut, variations in the other dichroics, etc.

Key components affecting the lumen throughput of a projector
Component Projectors Variation (si) Comment
Lamp All 5% Laser/phosphor is probably more
Lamp power supply All 1%
Mechanical alignment between lamp and integrator All Étendue limited projectors 2% Virtually all modern projectors are étendue limited
Tunnel integrator DLP 1%
Lenslet integrator 3LCD 2%
Relay lenses DLP 2%
Relay lenses 3LCD 3% Same per lens as DLP, but more relay lenses in a 3LCD projector
Fold mirrors All 2%
Color wheel DLP 2%
Splitting dichroics 3LCD 2%
DMD imager DLP 3% Micromirror size, tilt angle, Aluminum reflectivity, etc.
LCD imager 3LCD 4% Pre/post polarizer, LCD thickness, LCD alignment, etc.
TIR prism DLP 1%
Combining X-prism 3LCD 2%
Color balance to white All 3%
Projection lens All 5% AR coating quality on multiple surfaces.
Total variation DLP 9.3%
Total Variation 3LCD 10.4%

Looking at the numbers, you say 9.3% variation for DLP or 10.4% for 3LCD – that’s not so bad. Or is it? Lets take it one step further.

BenQ Normal Distribution 2 resizeNormal distribution of projector lumen outputs (Image: M. Brennesholtz)

Let’s say you have a DLP projector where the lumen output would be 3750 lumens, when each component in the projector exactly matches the average for all components of that type used in a production run of that projector. The numbers in the table above correspond to one standard deviation. In a DLP projector with one standard deviation of 9.3% about an average of 3750 lumens, projectors one standard deviation brighter than average would have 4100 lumens and one standard deviation below average would have 3400 lumens. One standard deviation includes 68% of all samples, so 16% of the projectors coming off of the production line would be brighter than 4100 lumens and 16% of the projectors would be dimmer than 3400 lumens. Marketing won’t like that!

If you look at two standard deviations, it gets worse, of course. Using two standard deviations as your limit, the brightest projectors will be 4450 lumens and the dimmest will be 3050 lumens. And this still only includes only 95% of the projectors you manufacture! And every component in every projector was in spec! You don’t even want to think about lumen output variation using a three standard deviation limit so 97.5% of your projectors are within the limits. But you have to think about it – some people use Six Sigma as a process control tool for manufacturing.

Help! What do we do now?


There are several possible solutions to this problem, none of them very palatable to the projector manufacturers.

  • Ignore the problem and let your marketing department lie to end users about projector lumen output. Not a good idea since you’ll wind up with unhappy customers.
  • Adjust the lamp power to make every projector the target lumen output. To make a 3050 lumen projector put out 3750 lumens you would need to increase the lamp power by 18.6%, which would mean running your 240W lamp at 285W. Your warranty people wouldn’t like this and your lamp supplier would probably void any lamp life guarantees in your supply contract.
  • Mix and match your components. If you have a color wheel that is above average, use it with a DLP imager that is below average so they cancel each other out. This is not possible on a modern production line for $799 MSRP projectors.
  • Reduce the standard deviation of each of the components that affect the lumen output, especially the ones that have a high contribution, such as the lamp. This can be done, but expect to pay higher prices to your component suppliers. Some components such as LEDs are typically binned for output. You might wind up binning every component in your projector.
  • Sort only your key components (e.g. lamps) into bins and make bright and dim projectors from high and low performing lamps. What happens when a high performing lamp reaches end of life and is replaced with a low performing lamp? More unhappy customers.
  • Sort the finished projectors into two or more lumen output bins and assign different product numbers. Sell the brighter ones for a higher price.

The last solution is, perhaps, the best and most practical. Besides, the marketing department perks up when they hear “higher price.” This can make it easier to justify having two different model numbers for the same projector. If everyone goes for the brighter version, then your “higher price” isn’t high enough to balance the demand for the two versions.

The luminance of direct view displays have a much less severe statistical issue, for two reasons. First there are fewer components in a direct view LCD than in a projector, so the cumulative standard deviation problem is less severe. Second, the power of the LEDs illuminating a LCD can be adjusted to give the desired brightness. No consumer is likely to notice if the LED lifetime goes from 40,000 hours to 30,000 hours due to the higher power on the LEDs.

BTW, Bob checked with his contact at BenQ and the company confirmed that the reason for two such similar projector models as the MU686 and the MU706 was a sorting issue. It’s not clear (to me) if they are sorting key components or sorting finished projectors. –Matthew Brennesholtz