Quality system Design

 1. The Industrial Engineering Department completed a work measurement study of the time required per unit production on adjacent production lines producing the same products over a 30-day period. Minutes per unit for Line 1 and Line 2 are in the following table. 

a) Examine descriptive statistics of the mean, median, standard deviation, first quartile, third quartile, minimum value, and maximum value. What do these statistics indicate about the shape of each population distributions? 

b) Create stem-and-leaf plots with stems = 10s and leaves = 1s. What does the shape and distributions of the stem-and-leaf plots indicate about the shape and distribution of each population? 

c) Create histograms. What does the shape of each histogram tell of about the shape of the population distributions? 

d) Construct a normal probability plot, a lognormal probability plot, gamma probability plot, and a Weibull probability plot of each data set. Estimate the best fit parameters for each distribution. Based on the plots and associated Anderson-Darling (AD) fit statistics, identify which distributions seems to be the best fit model at α = 0.05. 

e) Assess data independence by creating a time series plot by day of each distribution. Are the data randomly distributed, or do there appear to be patterns in the time ordered data? 

2. Test the time per unit data in Problem 1 for equality of production rates between the two lines. 

(a) State the correct hypothesis, or hypotheses, and conduct the hypothesis, or hypotheses, test(s) at  = 0.05. 

(b) Interpret the p-value for the test. 

7. The data represents the copper concentration in a plating process. Copper concentration in a plating pool is controlled by an automated colorimeter that takes readings and adjusts the concentration as required. To verify the correct functioning of a new colorimeter system, copper concentration is measured manually six times per shift. 

(a) Plot an x-bar and R control chart for this process. Perform runs tests to Western Electric. Is the process in control? Revise the control limits as necessary.

(b) Estimate the mean and standard deviation of the revised process. 

(c) Is the layer thickness of the revised process normally distributed?

(d) If the specifications are 9.0  2.0 ppm, estimate the process capability. 

 9. For the data in problem 7, the target copper concentration ppm is 9.0.

 (a) Estimate the process standard deviation from the control charts in problem 7. 

(b) Create a tabular CUSUM chart for this process, using standardized values h = 5 and k = ½. (c) Interpret the CUSUM chart. 

10. Create an EWMA control chart for the problem 7 copper concentration ppm data using λ = 0.1 and L = 2.7. Interpret the EWMA control chart in comparison to the CUSUM chart.