One-sided specification intervals are frequent in industry, but the process capability analysis is not well developed theoretically for this case. Most of the published articles about process capability focus on the case when the specification interval is two-sided. Furthermore, usually the assumption of normality is necessary. However, a common practical situation is process capability analysis when the studied characteristic has a skewed distribution with a long tail towards large values and an upper specification limit only exists. In such situations it is not uncommon that the smallest possible value of the characteristic is 0 and that this also is the best value to obtain. We propose a new class of indices for such a situation with an upper specification limit, a target value zero, and where the studied characteristic has a skewed, zero-bound distribution with a long tail towards large values. A confidence interval for an index in the proposed class, as well as a decision procedure for deeming a process as capable or not, is discussed. These results are based on large sample properties of the distribution of a suggested estimator of the index. A simulation study is performed, assuming the quality characteristic is Weibull distributed, to investigate the properties of the suggested decision procedure.

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A family of capability indices, containing the indices Cp, Cpk, Cpm, and Cpmk, has earlier been defined by Vännman for the case of two-sided specification intervals. By varying the parameters of the family various indices with suitable properties can be obtained. Under the assumption of normality the asymptotic expected value and mean square error are derived. The obtained asymptotic expressions provide a convenient tool for determining specific values of the parameters, which satisfy the suggested suitable criteria for the estimators. Numerical investigations are carried out and recommendations for the values of the parameters are provided based on these calculations.

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Under the assumption of normality, the distribution of estimators of a class of capability indices, containing the indices C p , C pk , C pm and C pmk , is derived when the process parameters are estimated from subsamples. The process mean is estimated using the grand average and the process variance is estimated using the pooled variance from subsamples collected over time for an in-control process. The derived theory is then applied to study the use of hypothesis testing to assess process capability. Numerical investigations are made to explore the effect of the size and number of subsamples on the efficiency of the hypothesis test for some indices in the studied class. The results for C pm and C pk indicate that, even when the total number of sampled observations remains constant, the power of the test decreases as the subsample size decreases. It is shown how the power of the test is dependent not only on the subsample size and the number of subsamples, but also on the relative location of the process mean from the target value. As part of this investigation, a simple form of the cumulative distribution function for the non-central χ 2 -distribution is also provided.