The specification for a plastic liner for concrete highway projects calls for a thickness of 6.0 mm ± 0.1 mm. The standard deviation of the process is estimated to be 0.02 mm. The process is known to operate at a mean thickness of 6.03 mm. What is the Cp and Cpk for this process? Determine whether this process meet 3-sigma requirements, 6-sigma requirements, or doesn’t meet any requirements.

Refer to Table 56.1-Factors for Computing Control Chart Limits.(3.sigma) for this problem. Auto pistons at Wemming Chung's plant in Shanghai are produced in a forging process, and the diameter is a critical factor that must be controlled. From sample sizes of 10 pistons produced each day, the mean and the range of this diameter have been as follows: a) What is the value of x? mm (round your response to two decimal places). b) What is the value of R? R=mm (round your response to two decimal places). c) What are the UCL, and LCL; using 3-sigma? Day 1 2 3 4 5 Upper Control Limit (UCL;)mm (round your response to two decimal places) Lower Control Limit (LCL;)mm (round your response to two decimal places). d) What are the UCL and LCL using 3-sigma? Upper Control Limit (UCLR)-mm (round your response to two decimal places). Lower Control Limit (LCL)-mm (round your response to two decimal places) Mean x (mm) 154.9 151.2 155.6 155.5 154.6 Range R (mm) 4.4 4.8 4.3 5.0 4.7 Next

2- Quality Control Charts A local brewery and bottling plant wants to keep track of the bottling filling equipment's accuracy, Bottles are to be filled with exactly 16 ounces of the drink. The following is data from the bottling equipment where 5 samples of bottles filled were pulled every hour and measured for actual quantity filled. 1- Calculate the UCL, LCL and mean for the X-bar and R data 2- Draw an X-Bar chart and a R chart. 3- Is this filling process in control or out of control? Hour X-bar R 1 16.05 .20 2 16.03 3 15.96 4 15.97 16.03 16.06 15.98 16.09 15.94 16.01 5 6 7 8 9 10 @n-5: A2 = 0.58, D3 =0, D4 = 2.11 .25 .62 .58 .71 .37 .46 .21 .35 .29

concernedas to whether caulking tubes are being properly capped. Ifa significant proportion of the tubes are not being sealed,Webster is placing its customers in a messy situation.Tubes are packaged in large boxes of 144. Several boxes areinspected, and the following numbers of leaking tubes arefound: Calculate p-chart three-sigma control limits to assesswhether the capping process is in statistical control.