Winners of last month’s quiz and a copy of *Practical Tools for Continuous Improvement: Volume 1* are Nate Riker (RPM Carbide Die Inc. of Arcadia, OH); Dan Shope (Standard Aero of Cincinnati, OH); and Jill Savoie (Quick Turn Precision Machining of Ogden, UT). Congratulations! For this month’s quiz, and a chance to win a copy of *Practical Tools for Continuous Improvement: Volume 1*, submit your response by **February 28. **

Sam Francisco, a technician, wants to be named quality manager in his organization when the current quality manager, Les Angeles, retires. Sam’s strategy includes calling attention to his knowledge of SPC whenever he can, in spite of his own limitations in this area.

One of the quality teams has been addressing a problem associated with the percentage of defects on line #2, a process that makes a lighter component for installation in a dashboard assembly. The outer dimension of the lighter is checked by a go/no go gage. The team has been taking a sample of one hundred every hour, and creating p-charts to illustrate the data.

To ascertain whether the process is in control, Sam imports the data into *SQCpack*, and finds that it is indeed stable, but that p-bar is equal to .10. He has been asked to present this data to the plant manager and his staff, but this would mean revealing that the percentage of defects in this process is 10.

Sam may not be smart about statistics, but he knows something about covering his tracks. The first thing to do, he knows, is to prepare a flashy PowerPoint presentation outlining the many steps that have been taken to improve quality in his area. If the presentation is complex enough, he will never have to reveal the actual data.

Using * Practical Tools for Continuous Improvement* (p. 131), Sam outlines an extensive prologue that introduces the steps involved in creating p-charts. Formulas are always helpful when it comes to dodging the issue, so he includes the formula for calculating upper control limits for p-charts:

Unfortunately, a member of the audience asks the meaning of the 3 in the formula–a question for which Sam has no accurate response. But to Sam, accuracy is not the issue; he simply needs an answer that will have the appearance of accuracy. Hardly missing a beat, Sam says confidently that this means that the upper control limit is 3 standard deviations above the mean .

The truth of the matter, if one were to analyze the response to this question is that:

C) The standard deviation is often 3.

D) Three is a culturally significant number (e.g., 3 bears, 3 stooges)

Sam is correct

Sam is not correct. Upper limit cannot be 3 SD but to me the no of defects is 10, qne 10-1 ( pbar-p) /n-1 should be correct for which 3 is taken out of the root. and hence answer b) is correct.

The meaning of “3” in the formula is used because the Upper Control Limit (UCL) should be set at the mean (p-bar) + (3 x standard deviation). In this example, the formula then becomes 0.10 + 3 * [Square root ((0.10 (1 – 0.10)) / n-bar)].

Dear Sir,

Honestly I am not in theproduction line or quality assurance dept to answer this question with confidence. I am a retired person gathering knowledge only by reading books, journals and listening to seminar papers when I get an occassion. I just thought this may be correct answer, though not very good at Statistic at all.

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