### Statistics in the Manufacturing World

Before, when production quantities only amounts to tens and hundreds and most of product manufacturing is done either manually or in a small shop using few machines, quality control is quite easy. All you need is to check all your finished products or parts if it meets all the required dimensions and its tolerances. But as manufacturing enters “mass production”, quality check was elevated to a superlative degree.

Before, 99% quality signifies a high quality production process. So if the total quantity produced is 100, only one is defective. Fairly acceptable, isn’t it? Today, however, 99% is just far from acceptable. Now that production quantities amounts to millions, 99% quality translates to 10,000 defective products in a 1 Million produced!

Also, the complexity of the manufacturing process has increased dramatically. Before, creating one finished product can only take up to 10, 20 or even 50 steps and the number of components only amounts to a maximum of a hundred. Now, there are products that take up to 100 or more steps and components up to 1000 in number! Imagine the outcome if each step or each part is 99% in quality!

(99%) 10=90% (100,000 defectives)

(99%) 100=37% (630,000 defectives)

This concern has been one of the greatest challenges facing the manufacturing industry today. Indeed, 99% is just not enough…even far from what is acceptable.

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Improvement is a continuous process the manufacturing world is taking. Many techniques on quality have been developed. Most of these quality concepts involve one branch of mathematics we sometimes take for granted-Statistics.

Yes, you cannot check all the 1 Million products, do you? The quality inspection group depends on samples or small portions to predict the quality of the entire amount. Also, various statistical approaches and techniques have been developed to aid in quality improvement. Among these are Six Sigma, Design of Experiments (DOE) and Taguchi Methods.

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Yes, never before had statistics played a vital role like these in the world of manufacturing. In the future articles of this blog, we will discuss some of these quality improvement techniques.

### PAST MECHANICAL BOARD EXAM QUESTION: Machine Design Set-1 (solutions and answers)

The following are the solutions and answers to MODIFIED PAST MECHANICAL BOARD EXAM QUESTION: Machine Design Set-1 posted on this blog last Saturday, November 14, 2009. Again, I want to stress out that most of the questions here are modified from its original form for the purpose of improving the question. Past Mechanical Engineering Board Exam Question Number 1 A 4 inches diameter short shaft carrying 2 pulleys close to the bearings transmits how much horsepower if the shaft makes 120 rpm. A.200HP               B. 199 HP C.198 HP               D. 202 HP P = (D3N )/38 -- for mula for short shafts from PSME code P = (4)3(120)/38 P= 202 HP Past Mechanical Engineering Board Exam Question Number 2 An instrument that measures the hardness of the work piece in terms of elasticity. a. Durometer b. Scleroscope c. Mohs's Scale d. Brinell Tester Source: Machinery’s Handbook

### SOLUTION TO MECHANICAL BOARD EXAM PROBLEMS: Power Set-1

Here are the solutions to board problems given at Power Subject Set-1. If you do not understand anything, feel free to write a comment voicing out your concern. I'm still looking for better ways to present my solution. I still don't know how to present equations and mathematical symbols with blogger. Please bear with me. 1. An automobile tire is inflated to 32psig pressure at 50 degree F. After being driven, the temperature rises to 75 degree F. Determine the final gage pressure assuming the volume remains constant. (Electrical Engineering Board Exam Problem) Solution: Since volume is constant, use Charles’ Law on constant volume processes. P1/T1=P2/T2 Note: P and T should be absolute. (32+14.7)/ (50+460) =P2/ (75+460) P2=48.99 psia Converting back to gage pressure, P2g=48.99-14.7 P2g=34.29 psig 2. Four hundred cubic centimeters of gas at a pressure of 740 mmHg absolute and temperature of 18 degree C undergoes a process until the pressure and temperature be

### BOARD EXAM TIP: Which Review Center?

First of all, I would like to apologize for a long time I haven't posted anything but introduction. The reason for that is I'm busy optimizing the design of this site. I'm hoping that the make over is good. Anyway, I would like to dedicate this article to those who are going to take/retake the board exam this coming October. My sincere wish that you bring out the best among yourselves and may the deserving ones pass the exam. Going back to the One-Million-Peso worth question: "Which review center should I enroll?" , I would like to answer that in the most unbiased way I can. Of course, I'm only human and I had also my preferences but I will try my best to hide it. To start with I will enumerate some of the prominent review centers that offer board exam reviews for mechanical engineering in the Philippines. 1. Alcorcon (Cebu & Manila) 2. Excel (Cebu & Manila) 3. Linx Engineering (Manila) 4. MERIT (Manila) 5. PRIME (Cebu) 6. RLB's