Bootstrap confidence interval estimates of c_pk: an introduction

Obtaining confidence intervals for Cpk using percentiles of the distribution of Ĉp

“…Chou and Polansky's [4] estimates are based on the non-central t-distribution, Kushler [6] are computer intensive. Additionally, most of these confidence intervals are inordinately long.…”

“…Their candidates for comparison to their AM were three nonparametric bootstrap confidence limits for C pk : the standard bootstrap (SB), the percentile bootstrap (PB) and the biased corrected percentile bootstrap (BCPB) reported by Franklin and Wasserman [6]. The simulations involve the following parameters: USL = 61, LSL = 40, m = 50.5.…”

“…They refer to the estimator as AM (approximate method). They then follow Kushler and Hurley's [5] suggestion that the optimum choice for an estimator would be one which is easy to compute and highly accurate so they restrict simulation comparisons of their AM estimator to those of Franklin and Wasserman [6]. In this paper we develop another confidence interval for C pk (called CPE, for estimate fromĈ p ).…”

“…Tang et al [3] state that a competing method developed by Kushler and Hurley [5] is computationally complex. Franklin and Wasserman [6] have developed three different bootstrap confidence intervals. Tang et al [3] develop a scheme to ascertain a confidence interval by graphically investigating the relationship between the process potential index C p , the process shift index k and the percentage of non-conforming items p. From their discoveries they are able to derive approximate confidence limits for C pk .…”

Confidence intervals and sample size determination for Cpm

“…Kotz and Johnson [1], Kotz and Lovelace [2], SAS/QC Software [3], and Minitab, Release 13 [4]). As the use of the indices grows more widespread, users are becoming educated and sensitive to the impact of the estimators and their sampling distribution on constructing confidence intervals and performing hypothesis tests (Kane [5], Chan et al [6], Chou et al [7], Li et al [8], Boyles [9], Nagata and Nagahata [10,11], Franklin and Wasserman [12][13][14][15], Kushler and Hurley [16], Luceno [17], Levinson [18], Zimmer and Hubele [19], Deleryd and Vannman [20], Franklin [21]). The challenge is to develop and implement relatively simple, and intuitively appealing, methods for decision making.…”