Estimation of σ and the process capability index based on subsamples

The International Journal of Advanced Manufacturing Technology

Shu²,

Hsu

2004

A multiprocess performance analysis chart (MPPAC), based on the process capability index C pm , called C pm MPPAC, is developed to analyse the manufacturing quality of a group of processes in a multiple process environment. The C pm MPPAC conveys critical information about multiple processes regarding the departure of the process and process variability on one single chart. Existing research on MPPAC has been restricted to obtaining quality information from one single sample of each process, ignoring sampling errors. The information provided from the existing MPPAC chart, therefore, is unreliable and misleading, resulting in incorrect decisions. In this paper, the natural estimator of C pm is considered based on multiple samples. Based on the natural estimator of C pm , sampling errors are considered by providing an explicit formula with Matlab to obtain the estimation accuracy of the C pm . The sampling accuracy of C pm is tablulated for sample size determination so that engineers/practitioners can use it for in-plant applications. An example of multiple PVR processes is presented to illustrate the applicability of C pm MPPAC for manufacturing quality control.

Section: Estimating C Pm Based On Multiple Samplesmentioning

confidence: 99%

C pm MPPAC for manufacturing quality control applied to precision voltage reference process

The International Journal of Advanced Manufacturing Technology

Shu²,

Hsu

2004

“…They also proposed an efficient test for C p based on one single sample, and showed that the test is the UMP (uniformly most powerful) test. Kirmani et al [5] considered the estimation of σ and the precision index C p for cases where the data are collected as multiple samples. Pearn and Yang [6] proposed an unbiased estimator of C p for multiple samples, and showed that the unbiased estimator is the UMVUE of C p , which is asymptotically efficient.…”

Section: Estimating C P Based On Control Chart Samplesmentioning

confidence: 99%

“…However, for the small sample sizes often employed on variables control charts (n = 4, 5, or 6), it is entirely satisfactory. If m samples each of size n from the (X, S ) control chart are available, Kirmani et al [5] considered measuring the process precision index C p , and the natural estimatorĈ p defined as the following:…”

Section: Estimating C P Based On (X R) Samplesmentioning

confidence: 99%

See 1 more Smart Citation

Procedures for testing manufacturing precision Cpbased on ( $\bar{x}$ ,R) or ( $\bar{x}$ ,S) control chart samples

Int J Adv Manuf Technol

Chuang

2004

Process precision index C p has been widely used in the manufacturing industry for measuring process potential and precision. Estimating and testing process precision based on one single sample have been investigated extensively. In this paper, we consider the problem of estimating and testing process precision based on multiple samples taken from (X, R)or (X, S )control chart. We first investigate the statistical properties of the natural estimator of C p and implement the hypothesis testing procedure. We then develop efficient MAPLE programs to calculate the lower confidence bounds, critical values, and p-values based on m samples of size n. Based on the test, we develop a step-by-step procedure for practitioners to use in determining whether their manufacturing processes are capable of reproducing products satisfying the preset precision requirement.

“…Kirmani et al [10] indicated that a common practice of the process capability estimation in the manufacturing industry is to first implement a routine-basis data collection program for monitoring/controlling the process stability, then to analyse the past ''in control'' data. For multiple samples of m s groups each of with sizes n are chosen randomly from a stable process which follows a normal distribution N(l,r 2 ).…”

Section: Estimating C Pm Based On Multiple Samplesmentioning

confidence: 99%

C pm MPPAC for manufacturing quality control applied to the precision voltage reference process

The International Journal of Advanced Manufacturing Technology

Shu²,

Hsu

2003

The multiprocess performance analysis chart (MPPAC) based on the process capability index C pm , called C pm MPPAC, is developed for analysing the manufacturing quality of a group of processes in a multiple process environment. The C pm MPPAC conveys critical information of multiple processes regarding the departure of the process and process variability from one single chart. Existing research works on MPPAC are restricted to obtaining quality information from one single sample of each process ignoring sampling errors. The information provided from existing MPPAC charts, therefore, is unreliable and misleading and results in incorrect decisions. In this paper, we consider the natural estimator of C pm based on multiple samples. Based on the natural estimator of C pm , we consider the sampling errors by providing an explicit formula with the Matlab program to obtain the estimation accuracy of the C pm . We tabulate the sampling accuracy of C pm for sample size determination so that the engineers/practitioners can use it for their in-plant applications. An example of multiple precision voltage reference (PVR) processes is presented to illustrate the applicability of C pm MPPAC for manufacturing quality control.