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- Attribute Sampling Plans and Demonstrations

**LIGHTNING CALCULATOR**Statistical Quality Control Training Aids

P.O. Box 611

Troy, MI 48099-0611

Phone (248) 641-7030

Fax: (248) 641-7031

http://www.qualitytng.com

email: sales@qualitytng.com or lightningcalculator@comcast.net

Congratulations on purchasing your Lightning Calculator Sampling Box or Bowl. Now your wondering how your going to use this device. The real value of these training aids is to give the student or employee a practical feel and understanding for the laws of probability with out the labor of mathematical proofs. For this reason we recommend that demonstrations be performed early on in the teaching sessions to give the student a basic understanding and confidence in the power of statistics.

**Demonstration Number 1 - The Common Sense Sampling Plan **

The objective of this demonstration is to prove the futility of what people term common sense sampling or better known as we look at 10% of all the parts". The first objective is to get the class to commit to what they feel is an unacceptable percent defective (1%, 5%, 10% defective, etc.). Many will respond that zero percent is the only acceptable rate. Utilize the proper combination of colored beads to represent the selected percent defective and then begin sampling. If the selection was zero percent defective then approach the defective colored beads from the standpoint of assuming some arbitrary percent are defective, say 2 % for example, and see if the sampling procedures can catch the problem.

Make a table with five headings on the blackboard.

Lot |
Sample |
Sample |
Total |
Pass or |

Size |
Size |
Defects |
Defects |
Fail |

Next select lot sizes of let's say 30, 50, 100, and 150. If the sampling plan is that old common sense 10% then the sample sizes are 3, 5,10, and 15. Using the appropriate sampling hole pattern in the sampling boxes, or sampling bowl paddle begin the production process. Each sample represents a lot, for the 50 hole pattern it is a lot of fifty. Now before the sampling begins you have a person randomly pick a number from one to ten to represent which row in the sampling pattern is going to be the 10% sample. After drawing the sample go the predetermined row, count the number of bad parts and make the decision of pass or fail. (Pass if no parts are defective and reject on one or more) For the sample of 50, and a randomly selected row number of 6, go to the sixth row and count the number of defective beads in the sample of five. Before disposing of the sample count the total number defective on the entire paddle, or the entire lot. Now by repeating this process say 20 times you can easily demonstrate how many times the 10% decision rule caught defective products versus the true percent defective in each lot. This demonstration will show that the common sense 10% sampling plan that so many people think is a good number is in fact a terrible sampling plan regardless of whether the lot size is 25 or 150. Now statistically if the lots were say 5,000 or 10,000 pieces in size then the 10% rule does make sense but then the 10% rule is too expensive.

**Demonstration Number 2 - Sampling Plans **

Once students are convinced that the 10% rule is not reliable then they are ready to accept a statistically valid sampling plan. The specifics of such a plan are left up to the instructor. Mil Std 105D, Dodge Romig, or any other statistically valid plan can be demonstrated by proper selection of beads and sampling patterns.

Remember that different color combinations of beads can be combined to reach any specific percentage. Each sampling device has a list of the quantities of each color. So if the blue is 0.5% the pink is 0.1 %, and green is 5%, you could represent a 5.6% defective lot by counting all the blue, pink, and green beads that appear in a sample.

The results of the statistically valid sampling plan can then be compared to the 10% sampling plan.

For the advanced technical probability students remember to replace the samples. If you do, you can predetermine probabilities with the binomial distribution formulas. If you do not replace the samples then you are dealing with a hypergeometric distribution. More advanced students may appreciate calculating binomial probabilities of various sampling schemes and then verifying them with the sampling device.

**Demonstration Number 3 - Attribute Control Chart **

Attribute Control Charts can be effectively demonstrated by with a sampling bowl. Set up the sampling bowl as described below and create a p chart on the blackboard to record the readings.

Set up the bowl with 15% green, 20% yellow, and 7% red beads with the balance in white beads. Use a total of 2000 beads.

Sample beads 50 at a time for 25 samples and count and plot the number of green beads. (Remember to replace the beads after each sample)

Based on the initial 25 readings calculate the upper and lower control limits. (Refer to any SQC text book or Lightning Calculator Poster for the formulas)

Begin sampling again and this time count the yellow beads and note how the sample plot points now exceed the UCL.

Repeat the sampling process again and this time count the red beads which will show plot points below the LCL.

This demonstration is particularly effective due to the sampling variability. After you tell the student the real percentages he can get a feeling that if he follows the control chart he will have the laws of probability on his side in making a correct decision. With a little ingenuity this demonstration can be adopted for a U or C chart.

**Demonstration No 4 - The Pareto Chart **

You can use the sampling box to illustrate what a pareto chart is and how to construct one. Assume that the different colored beads represent different types of defects. If you wanted to know where to start in fixing the problems what would you do? Naturally, you would get data and categorize it according to type of defect. Continue by allowing the students to create a pareto chart of different colors of beads. The long run average should coincide with the bead distribution on the box, right?