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Problem 1:

The diameter of the casting is an important quality characteristic. A coordinate measuring machine is used to measure the diameter of each casting at five different locations. Data for 20 castings are shown below. Perform a process capability study using x-bar and R charts. The specification limits are: Lower specification limit: 11.7; Upper specification limit: 11.8

Note: Provide your answer under each bullet

Measurements
Casting12345
111.762911.740311.751111.747411.7374
211.812211.750611.778711.773611.8412
311.774211.711411.75311.753211.7773
411.783311.731111.777711.810811.7804
511.713411.68711.730511.741911.6642
611.792511.761111.758811.701211.7611
711.691611.720511.695811.74411.7062
811.710911.783211.749611.749611.7318
911.798411.888711.772911.848511.8416
1011.791411.761311.735611.762811.707
1111.72611.732911.742411.764511.7571
1211.720211.753711.732811.758211.7265
1311.835611.797111.802311.780211.7903
1411.706911.711211.749211.732911.7289
1511.711611.797811.798211.742911.7154
1611.716511.728411.757111.759711.7317
1711.802211.812711.786411.791711.8167
1811.777511.737211.724111.777311.7543
1911.775311.78711.757411.76211.7673
2011.757211.762611.752311.739511.7884

a) Set up the x-bar and r-charts for this process, assuming the measurements on each casting form a rational subgroup. Show the xbar and r-charts for the stable process. Ensure you have a stable process.

b) Calculate the Cp and Cpk indices based on the stable process.

c) Do your capability analysis using Minitab and show Minitab output.

d) Is the process capable?

e) Is the process centered?

Problem 2:

A paper mill uses a control chart to monitor the imperfections in finished rolls of paper. Production output is inspected for twenty days, and the resulting data are shown below. Set up a control chart for nonconformities per roll of paper. Remove any out of control points, and re-calculate the control limits and center line. Provide the final control chart center line and limits below. Show your equations

DayNumber of Rolls ProducedTotal Number of ImperfectionsDayNumber of Rolls ProducedTotal Number of Imperfections
11812111818
21814121814
3242013198
42218142010
52215152014
62212162013
72011172416
82013182418
92012192220
102010202117

Problem 3:

The number of nonconforming switches in samples of size 150 is shown below. Create an np-chart with the following data and then remove the out of control points and provide the revised control charts. What are the final center lines, upper and lower control limits? Show your equations

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