a factory that produces a small number of items per day. In about 30% of working days the factory produces 7 units of the product, in 45% of working days it produces 8 units, and the rest of working days it produces 9 units. After production is completed, each unit is thoroughly inspected. Each unit fails inspection with probability ??. If two or more units fail inspection on the same day, the factory closes for a week to re-calibrate equipment. Say the factory opens today after being closed for a week, write a mathematical expression to calculate the probability that the factory will remain open at least 30 days before closing again.

28. A local contractor manufactures the speakers used in telephones. The phone com- pany requires the speakers to ring at a specified noise level (in decibels). An X chart is being designed to monitor this variable. The process of sampling speakers from the line requires hitting the speakers with a fixed-force clapper and measur- ing the decibel level on a meter designed for that purpose. The cost of sampling is $1.25 per speaker. When the process goes out of control, the thickness of the speakers is incorrect. The cost of searching for an assignable cause is estimated to be $50. The cost of operating the process in an out-of-control state is estimated to be $180 per hour. Out of control corresponds to a shift of 2ơ in the decibel level, and the probability that the process shifts out of control in any hour is .03. a. The company uses an X chart based on 3ơ limits and subgroups of size 4. What is its hourly cost? b. What are the optimal values of n and k for this process and the…

Yelp Dog Food produces specialized dog foods in 1-pound packages. The amount of dog food in each package should be 1 pound, and Yelp has determined that the standard deviation of the machine filling these packages is half an ounce, and the confidence interval is 14.85% (2= 1872). In order to confirm that the machine is operating properly, Yelp takes 16 sample bags every hour and weighs them. The means of these 16 bags for an 8-hr shift is given below. 1. 2. 3. 4 5. 6. 8 0.98 1.01 0.97 1.03 1.01 0.94 1.02 1.02 13. For this one day's worth of filling bags, what would be the upper control limit? A. 1.0000 B. 1.0209 C. 1.0324 D. 1.0913 14. What would be the lower control limit? A. .9038 B. 9567 C.9741 D..9892 15. How many, if any, of the hours were out of control? A.O B. 2 C.3 D. 7

match each variable types with its description: variables: Process input variable, Process output variable, Critical to quality, Key process output variable, Key process intput variable, description (a) a product or process requirement that is no matter to the customer (b) a product or process knob or control that affects characteristics of importance to the customer (c) a product or process knob or control that has no impact on the process (d) a product or process requirement that must be present to make the customer happy but that the customer does not know to explicitly specify (e)  a product or process requirement specifically requested by the customer