Process control in contract manufacturing is frequently perplexed by the scale of subcontractor operations. As the number of product groups within a business grows, the number of input and quality characteristics that must be monitored and evaluated grows as well. As a result, stratification is used to avoid the proliferation of monitored parameters. The mixture structure (Y, X) is used to model parametric monitoring, where X represents the product group and Y represents the monitored feature. The purpose of this study was to determine a single feature of a bivariate mixture according to Olkin and Tate (1961). A new Cpk, say, was formulated using the above unconditional bivariate mixture. It was noted that was an erroneous estimator of. Likewise, was a skewed estimator of. Given that and estimate their respective parameters, the asymptotic variance of is also a biased estimator. However, when n is big, the bias approaches zero. When the efficiency of and is compared using asymptotic variances, i.e., Var and Var(), it is observed that Var is less efficient than Var ( ). This means that the generated variance is the most appropriate measure of variance for data derived from an unconditional bivariate mixture.