Control Charts for Manufactured Parts Done by the Quality Control Inspector at Each Production Operation Control Charts are used inside a factory at each manufacturing operation. One type of control chart is a Proportion Defective Control Chart. It is based on the proportion defective of the manufacturing process. The equations for a Proportion Defective Control Chart are as follows: Center Line = p = (total number of defectives) / (total sample size) = D / N Upper Control Limit = p + (3) Square Root [ (p) (1p) / n ] Lower Control Limit = p (3) Square Root [ (p) (1p) / n ] Example of a Proportion Defective Control Chart For twenty consecutive days three hundred parts were inspected each day. The parts were produced on one machine inside a factory. After all twenty days a total of 120 defective parts were found and a total of 6,000 parts were inspected (20 days times 300 per day). Create a Proportion Defective Control Chart and round your upper and lower control limits to three decimal places. n = 300 parts per sample g = 20 groups of data (or samples or days) D = 120 defective parts for all 20 days N = 6,000 total parts for all 20 days p = D / N = 120 / 6,000 = 0.02 Upper Control Limit = p + (3) Square Root [ (p) (1p) / n ] Upper Control Limit = 0.02 + (3) Square Root [ (0.02) (1 0.02) / 300 ] Upper Control Limit = 0.02 + (3) Square Root [ 0.0000653 ] Upper Control Limit = 0.02 + (3) 0.008 Upper Control Limit = 0.044 Lower Control Limit = p (3) Square Root [ (p) (1p) / n ] Lower Control Limit = 0.02 (3) Square Root [ (0.02) (1 0.02) / 300 ] Lower Control Limit = 0.02 (3) Square Root [ 0.0000653 ] Lower Control Limit = 0.02 (3) 0.008 Lower Control Limit = 0.004 = 0 (A negative number is always rounded to zero) Explanation of the Above Control Chart: Select a random sample of 300 parts that have been produced by the machine. Inspect all 300 parts and keep track of the total number of defective parts. Divide the total number of defective parts found by 300 to yield the new "p" value. If the new "p" value is between 0.000 and 0.044 then the process is doing okay and no action needs to be taken at this time. If the new "p" value is less than 0.000 (not possible) or more than 0.044 then closely examine the process to determine the reason for the unusual variation. Assignment * YOU MUST EXPLAIN HOW YOU SOLVED EACH PROBLEM AND EXPLAIN WHAT MATHEMATICAL DECISION YOU MADE TO GET EACH ANSWER OR THE SOLUTION WILL BE DECLINED* Sampling Plans for the Leather Belt (Statistical Quality Control) Problem 1: Determine all the values for an ANSI/ASQ Z1.4 Normal Inspection Single Sampling Plan for some purchased cardboard boxes using the following information. The cardboard boxes will be used to ship the finished belts to the company's customers. The lot size (or shipment) is 300 cardboard boxes and the specified AQL is 2.5 percent. Therefore the Code Letter is = The Sample Size is = The Acceptance Number is = The Rejection Number is = Type your explanation of the above Acceptance Sampling Plan below: Problem 2: Determine all the values for a Proportion Defective Control Chart for the hole punch operation immediately after the die cutting operation and before the belt buckle operation using the following information. Round your upper and lower control limits to three decimal places. For thirty consecutive days 200 leather belts were inspected each day. After all thirty days a total of 90 defective leather belts were found and a total of 6,000 belts were inspected (30 days times 200 per day). n= g= D= N= p=D/N= Upper Control Limit = p + (3) Square Root [ (p) (1-p) / n ] Lower Control Limit = p - (3) Square Root [ (p) (1-p) / n ] Type your explanation of the above Proportion Defective Control Chart below