Question

First Name Last Name Please put your name on this test and every page that you submit. Please answer the questions and solve the problem in the proper order [1, 2, 3...] 20 points each. tely precisely, and completely as possible 1. Explain Deming's Funnel Experiment. What did he use it for? 2. Differentiate between Pareto Chart and Cause-and-Effect Diagram. Which one should be used first? 3. Explain "The Central Limit Theorem." Why is it so important in SQC? 4. Differentiate between control limits and specification limits. following problems. Show all needed formulas and your relevant work. 1. Upon viewing the x-bar and R- charts related to the fill level of 12 ounce beverage containers, it became obvious that points 7 and 25, out of 25 samples taken, are out-of-control on the Range chart. Investigation into the causes of this much variation in the process revealed that the machine needed adjusting. The problem is not expected to reappear. Revise the control chart. Assume assignable causes have been found for point 7 and 25 and remove these points from the charts. Be sure to recalculate the limits. Here is the relevant information: Sum of Xbars 301.47 Sum of R's-7.85 n 5 for Point 7, X-bar 12.202, R 0.692 for Point 25, X-bar 12.173, R 0.747 ABC, INC. makes rubber balls. The current process is capable of producing balls that weigh 3 ounces on average, with a (population) standard deviation of 0.25 ounces. [a] What is the process capability ratio, assuming upper and lower tolerance limits of 3.5 and 2.5 ounces? Is ABC able to meet the tolerance limits 99.73% of the time? Explain. [b] What would the standard deviation have to be to exactly meet the tolerance limits 99.73% of the time? [c] Suppose ABC invests in process improvements that lower the standard 2. deviation to just 0.10 ounces. Is this enough for Leah's to achieve "six sigma" quality levels with regard to the weight of the balls? Explain.

Solve Part 2

Answer 1

As required, solution of Part 2 follows:

1.

After removing point 7 and 25,

Revised Sum of Xbar's = 301.47 - 12.202 - 12.173 = 277.095

Revised Sum of R's = 7.85 - 0.692 - 0.747 = 6.411

Xdblbar = 277.095/23 = 12.0476

Rbar = 6.411/23 = 0.2787

Step1: Calculate XandR 5% R.+R.+ R. 0.2787 = = Step 2: D3, D4, A2 corresponding to subgroup size N D3 D4 A2 0 = 2.1140 0.5770 Step 3 Determine Control limits for R-chart and X-Chart Control limits of R-chart UCLr-D4R 0.5893 LCLr=DA : 0.0000 Control limits of X-chart UCLx-T-AF 12.2084 LCLx-X-AF = 11.8868

2.

Mean, m = 3 ounces

Standard deviation, s = 0.25 unces

(a)

USL = 3.5

LSL = 2.5

Process capabilty ratio, Cp = (USL-LSL)/6s = (3.5-2.5)/(6*0.25) = 0.667

z-stat for 99.73% = 3 , which means 3 sigma level.

Cp is less than 1, therefore, process is not able to meet the tolerance limits.

(b) Standard deviation required to exactly meet the tolerance limits = (USL-LSL)/6 = (3.5-2.5)/6 = 0.167

(c) Sigma level = (USL-LSL)/2s = (3.5-2.5)/(2*0.10) = 5 sigma level

This is still not enough to achieve 6 sigma quality level.