Tolerance Limits which Control Percentages in Both Tails: Sampling from Mixtures of Normal Distributions

Abstract A study is made of the effects of nonnormality on the tolerance limits which control percentages in both tails. The type of nonnormality considered here is the mixtures of normal populations. The conclusions we have arrived at are that the effect of sampling from such a population is essentially to raise the value of γ. For the prescribed level of γ to be achieved, in the equal percentage case, the value of k is smaller than that of the normal case. However, the loss incurred as a result of using Owen's normal values of k is more than offset by the cost of determining k appropriate to this situation. Also, the deviation in the values of γ from the prescribed levels is extremely small.