IE 355 QUALITY and APPLIED Statistics I

IE 355 QUALITY AND APPLIED STATISTICS I

LAB ASSIGNMENT 6 Measurement Methods and Process Control for Precision Parts

Your company is producing a part that is low volume and high precision. Your company has recently acquired a new measuring machine, a digital height gage, to determine the position of a drilled hole in this part. The goal is to develop a process control system to monitor the production of these parts.

Week 1

Instructions  Work in groups of 5.

 Make sure you have read the pertinent parts of the digital height gage manual before coming to the lab. Two copies are on reserve in the IME office. The pages that you should pay particularly close attention to are “Program for Determining the Gage Constant”, pp 9-10 and “Measurement Mode 2 with a Gage Constant-Double Probe Contact”, pp13-14 (focus on how to obtain the reading of h4).

 Since we have only one digital height gage, in order to assure that everyone has enough time to complete all the necessary measurements, time spent in the lab with the digital height gage must be used for measuring the part feature. Reading gage operating manual (first time), doing analysis or calculations and report writing are to be done outside of your allotted time with the gage.

1 Procedure

1. Set up the digital height gage according to the manual you have read.

2. The teaching assistant will give you 3 parts that you need to measure. Record your measurements. Each student in the group has to do this individually.

Week 2

Instruction

 Work in groups of 2.

Procedure

1. Refresh your memory in using the height gage (read the manual again if needed).

2. Since this is a low volume, high precision part, each part produced will be measured. Obtain 20 parts from production and use the height gage to measure the location of the drilled hole in the part. Create initial individuals control charts: X, MR and EWMA. Be sure to use the iterative procedure for constructing the charts.

3. Analyze the charts. Perform a process capability study. Use at least two different indices and analyze the results. For this part the width of the specification interval (or tolerance zone) is 0.0028.

4. Next, assume that your control charts are adopted for everyday production. After implementing it, collect and plot an additional 5 measurements. Analyze results.

Measuring Position

The feature you measure in this assignment is the position of the center of a hole in a part. To determine if the hole has been drilled in the right spot we use a measurement of position error.

2 Consider the part as shown in Figure 1. The square represents the part. The dotted circle represents the true position of the hole, that is, where the hole was supposed to be positioned according to the specifications. The solid lined circle represents the actual position of the hole, that is, where the hole was actually drilled.

Position error, z , is the distance of the center of the actual hole to the center of the position of the true hole. This distance is calculated as z=( D x)2 +( D y) 2 . To find z , we have to know two things: the true position, i.e., the specifications for the hole and the actual position of the hole, i.e., where the hole was actually drilled.

Z Actual

Ytrue Xactual

Yactual

Figure 1. Part showing true and actual center of hole.

The true position of the hole is determined from the blueprint of the part. Figure 2 shows an example of a blueprint. From the blueprint we see that the true position (specification) of the hole is 0.7 inch in vertical distance (along Y-axis) from the reference point labeled A and 0.7 inch in horizontal distance (along X-axis) from the reference point labeled B. These reference points are called datum. The theoretical exact diameter of the hole is0.375. This value is called the basic dimension and is found on the blueprint in the upper right corner. It is preceded by the symbol Ø to indicate that this basic dimension is a diameter. 3 Ø 0.375 Ø .0028 M A B B 0.700

248816-5 Prepared per ANSI Y14.5M - 2002 DoRight Mfg. Co. Slide Block

Figure 2. Blueprint

Replace Fig. 2 blueprint with newest jpeg.

The box in the upper right hand corner of this blueprint is called the feature control frame. One of the items in the feature control is the width of the specification interval. For this part the width of the specification interval (or tolerance zone) is 0.0028. Since the specification interval is preceded by Ø , it means that this specification interval is a diameter therefore this specification interval is a circle. So, for this hole to be within specifications, the position of the actual center of the hole must be within the circular specification region. In other words, the value of the position error, z , must be less than the length of the radius of this circular specification region.

Figure 3 shows an example of a part in-spec and out-of-spec. The specification region is the area inside the heavy lined circle. The left part is within specs because the center of the actual hole is inside the specification region. The part on the right is nonconforming because the center of the actual hole is outside the specification region.

4 Legend

Actual

In Spec Out of Spec

Figure 3. Left part is within specifications, Right part is nonconforming

Here is a numerical example. Given the specifications on the blueprint in Figure 2, if the measurements of the coordinates of a drilled hole on a part are (x= 1.253, y = 2.196) , then Dx = 0.003 and Dy = 0.004 inches. The position error is

0.0028 z=( D x2 + D y 2 ) = (0.003 2 + 0.004 2 ) = 0.005 inches. Since 0.0050> = 0.0014 , the 2 hole is outside of the specification region.

Final Report

Executive summary: approximately 1/2 page, describe the goal and the result.

Introduction: Describe the problem.

Process control system: Show and explain results of recommended control charts; how you used the data to develop the charts; out-of-control points; and process capability indices.

5 Week 1 Worksheet for initial control charts

Worksheet for 3 trial measurements Part Measurements 1 Part Measurements 2 1 3 2 4 3 5 6 7 Week 2 8 9

Worksheet for measurements taken after 10 implementing process control 11 system 12 13 Part Measurements 14 1 15 2 16 3 17 4 18 5 19 20