Six Sigma Exercise(Problems) Question – Training Class?
Hello:
I am currently reading the book Implementing Six Sigma: Smarter Solutions Using Statistical Methods and have made it to Chapter 7…
There are a few exercises I am struggling with and thought perhaps someone could lend a hand. This is for a training class so I want to understand the answers…
3. The diameter of a shaft has µ = 75mm with a standard deviation of ợ = 8mm. Determine the proportion of the population of bushings that has a diameter of less than 65 mm.
4. Determine the proportion of the population described in the previous exercise that has a diameter between 55 mm and 95 mm.
5. An electronic manufacturer observed a mean of 0.20 defects per board. Assuming a Poisson distribution, determine the probability of three defects occurring on the same board.
20. A complete software system averages 7 errors per 5,000 lines of code. Determine the probability of exactly 2 errors in 5,000 lines of randomly selected lines of code. (Six Sigma Study Guide 2002.)
Any assistance is greatly appreciated.
In each case, these are in the grouping of descriptive statistics and are using probability around the bell shaped curve. So, the best place to start in figuring these out is to draw the curve!
So:
3. The diameter of a shaft has µ = 75mm with a standard deviation of ợ = 8mm. Determine the proportion of the population of bushings that has a diameter of less than 65 mm.
u stands for the mean or center of the population – this should be the center of the curve.
The standard deviation is 8 so start drawing in +/- standard deviation dashed lines for plus/minus 1 standard deviation (75+/- 8 = 83 & 68), 2 standard deviations (75+/- 16 = 91 & 59) and 3 standard deviations (75+/- 24 = 99 & 51). You can now use the probabilities of 68%, 95% & 99% (use the exact numbers from your book) to calculate the percentage of values within each area of the curve.
Now, since this question asks for the population below a value of 65, you can look at your graph and get a very good approximation – 65 is just below the –1 standard deviation so you know that you can subtract the 68% (the plus/minus 1 standard deviation) and half of the other two values from your answer. So you will have something just below 17% of your population below a value of 65 mm.
Use this picture and the definitions in the book to calculate the exact value for the number of parts that will be found for this and the other questions that you pose.
If you still have trouble with the understanding of the concept, pick up a descriptive statistics book and look under probabilities.