The upper and lower specification limits for a component are 5.20, and 5.30 ounces, respectively. The process standard deviation is .05, and the process average is 5.24 ounces.   a) Calculate Cpk. (Show formula and calculations)   b) Does the process posses six sigma capability? Why or Why not? Please explain.

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The output of a certain integrated-circuit productionline is checked daily by inspecting a sample of 100 units.Over a long period of time, the process has maintaineda yield of 80 percent, that is, a proportion defective of 20 percent, and the variation of the proportion defec-tive from day to day is measured by a standard devi-ation of 0.04. If on a certain day the sample contains 38 defectives, find the mean of the posterior distribu-tion of as an estimate of that day’s proportion defec-tive. Assume that the prior distribution of Θ is a beta distribution.

The measurement of 85 automotive cables gave an arithmetic mean of the inner diameters of 3.51 mm and a standard deviation of 0.02 mm.The value required by the manufacturer is 3.5 upper/lower tolerance +0.04/ -0.12It is requested : a. Calculate the capability coefficients Cp, Cpk and state whether or not the machine is capable of producing compliant parts, i.e. whether or not the data dispersion is well centred. If applicable, calculate the adjustment coefficient Cr.b. If scrap is obtained, state whether it is recoverable or non-recoverable and calculate the percentage of scrap.c. Plot the limits of the tolerance field and the distribution of the measured data (using mean and standard deviation).

Is a capable process a perfect process? That is, does acapable process generate only output that meets specifications? Explain.