# Question: Suppose that we have p 3 quality characteristics and

Suppose that we have p = 3 quality characteristics, and in correlation form all three variables have variance unity and all pairwise correlation coefficients are 0.8. The in-control value of the process mean vector is μ′ = [0, 0, 0].

(a) Write out the covariance matrix ∑.

(b) What is the chi-square control limit for the chart, assuming that a = 0.05?

(c) Suppose that a sample of observations results in the standardized observation vector y’ = [1, 2, 0]. Calculate the value of the T2 statistic. Is an out-of-control signal generated?

(d) Calculate the diagnostic quantities di = 1, 2, 3, from equation 11.22. Does this information assist in identifying which process variables have shifted?

(e) Suppose that a sample of observations results in the standardized observation vector y’ = [2, 2, 1]. Calculate the value of the T2 statistic.

(f) For the case in (e), calculate the diagnostic quantities di, i = 1, 2, 3 from equation 11.22. Does this information assist in identifying which process variables have shifted?

(a) Write out the covariance matrix ∑.

(b) What is the chi-square control limit for the chart, assuming that a = 0.05?

(c) Suppose that a sample of observations results in the standardized observation vector y’ = [1, 2, 0]. Calculate the value of the T2 statistic. Is an out-of-control signal generated?

(d) Calculate the diagnostic quantities di = 1, 2, 3, from equation 11.22. Does this information assist in identifying which process variables have shifted?

(e) Suppose that a sample of observations results in the standardized observation vector y’ = [2, 2, 1]. Calculate the value of the T2 statistic.

(f) For the case in (e), calculate the diagnostic quantities di, i = 1, 2, 3 from equation 11.22. Does this information assist in identifying which process variables have shifted?

**View Solution:**## Answer to relevant Questions

Consider the first two process variables in Table 11.5. Calculate an estimate of the sample covariance matrix using both estimators S1 and S2 discussed in section 11.3.2. Suppose that there are p = 2 quality characteristics, and in correlation form both variables have variance unity and the correlation coefficient is 0.8. The in-control value of the process mean vector is μ′ = [0, 0], and ...Reconsider the situation in Exercise 11.1. Suppose that the sample mean vector and sample covariance matrix provided were the actual population parameters. What control limit would be appropriate for phase II for the control ...Use the data in Exercise 12.9 to construct a bounded adjustment chart. Use = 0.2 and set L = 4. How does the bounded adjustment chart perform relative to the integral control adjustment procedure in part (a) of Exercise ...The following output was obtained from a computer program that performed a two-factor ANOVA on a factorial experiment. (a) Fill in the blanks in the ANOVA table. You can use bounds on the P-values. (b) How many levels were ...Post your question