Process capability index

Process Capability Indices Also known as process capability ratios, these provide a measure of w hether an in-control process is meeting its product specifications. Suppose that a quality variable x must have a volume between an upper specification limit (USL) and a lower specification limit (LSL) in order for product to satisfy customer requirements. The capability index Cp is defined as 

The CUSUM control chart was originally developed using a graphical approach based on V masks. However, for computer calculations, it is more convenient to use an equivalent algebraic version that consists of two recursive equations 

The selection of the threshold H can be based on considerations of average run length (ARL), the average number of samples required to detect a disturbance of specified magnitude. For example, suppose that the objective is to be able to detect if the sample mean x has shifted from the target by a small amount 8. The slack parameter K is usually specified as K = 0.58. For the ideal situation (e.g., normally distributed, uncorrelated disturbances), ARL values have been tabulated for different values of 8, K, and H. Table 8-7 summarizes ARL 

TABLE 8-7 Average Run Lengths for CUSUM Control Charts 

Adapted from Ryan, Statistical Methods for Quality Improvement, 2d ed., Wiley, New York, 2000. 

A second ciipability index C is based on average process performance X as well as process variability a. It is defined as 

Although both Cp and C are used, we consider Cp. to be superior to Cp for the following reason. l(x = T, the process is said to be centered and Cpt = Cp. But for xi T.Cp does not change, even though the process performance is worse, while Cpt does decrease. For this reason, Cpt is preferred. 

If the standard deviation a is not known, it is replaced by an estimate a in Eqs. (8-76) and (8-77). For situations where there is onfy a single specification limit, either USL or LSL, the definitions of Cp and Cpk can be modified accordingly. 

In practical plications, a common objective is to have a capability index of 2.0 while a value greater than 15 is considered to be acceptable. If the Cpk value is too low, it can be improved by making a change that either reduces process variability or causes x to move closer to the target. These improvements can be achieved in a number of ways that include better process control, better process maintenance, reduced variability in raw materials, improved operator training, and process changes. 

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Variation is an obvious measure for quality of conformance, but it must be associated with the requirements set by the specification to be of value at the design stage. Unfortunately, difficulty exists in finding the exact relationship between product tolerance and variability. Approximate relationships can be found by using process capability indices, quality metrics which are interrelated with manufacturing cost and tolerance (Lin et al., 1997). ... 

The critical characteristic on each component was analysed, calculated from the analysis and the value obtained was plotted against the process capability indices, Cpk and Cp, for the characteristic in question. See Appendix V for descriptions of the 21 components analysed, including the values of Cp and Cp from the SPC data supplied. Note that some components studied have a zero process capability index. This is a default value given if the process capability index calculated from the SPC data had a mean outside either one of the tolerance limits, which was the case for some of the components submitted. Although it is recognized that negative process capability indices are used for the aim of process improvement, they have little use in the analyses here. A correlation between positive values (or values which are at least within the tolerance limits) will yield a more deterministic relationship between design capability and estimated process capability. 

The way of measuring capability is to carry out a capability study and calculate a capability index. There are two commonly used process capability indices, Cp and Cpk. In both cases, it is assumed the data is adequately represented by the Normal distribution (see Appendix I). 

Kotz, S. and Lovelace, C. R. 1998 Process Capability Indices in Theory and Practice. London Arnold. 

Process capability indices [49], histograms, statistical analysis of system variation, legislation [4]... 

Metrics for this might include number of excursions from statistical process control, but one very useful metric for controllability is process capability, or more accurately, process capability indices. Process capability compares the output of an in-control process to the specification limits by using capability indices. The comparison is made by forming the ratio of the spread between the process specifications (the specification width ) to the spread of the process values. In a six-sigma environment, this is measured by six standard deviation units for the process (the process width ). A process under control is one where almost all the measurements fall inside the specification limits. The general formula for process capability index is ... 

Process Capability Indices Process capability indices provide a quantitative measure to assess the ability of a process to produce products that meet the specifications. A commonly used process capability index, denoted as Cp, can be calculated as... 

Arguably, the most important aspects of quality management for PAT are the concepts of quantitative process performance characterization using process capability indices as universal descriptors, which form the basis of the measure and analyze portions of the DMAIC model. Process capability indices consider simultaneously both process variability and process specifications to determine whether... 

One can use statistical software packages to calculate the level of control the process is under, and one may, for example, use process capability indices that compare the output of an in-control process to the specification limits. Indirect proxies for controllability metrics could also be the amount of materials and/or energy consumed per kg of product caused by excursions outside the control zone. For example, a rejected batch will become waste, and additional mass and energy will be required to replace or rework the rejected batch. 

For each analytical property, the proportion of individual pellets lying outside specification may be tabulated. This level should be minimal if the capability of the process and of the lyophilizer is consistent with the specification limits. If the distribution of pellet contents obeys the normal or log-normal law, it is further possible to predict for the whole batch the proportion of samples that can be expected to be outside the specifications. Alternately, process capability indices can be calculated [15. ... 

Two process capability indices are in common use, and they are as follows ... 

To estimate process capability indices from data, the estimates replace the true process values in the following formulas as follows ... 

Obviously, this gyro design requires tightly controlled surface micromachining processes with respect to the thicknesses of the polysilicon and sacrificial layers and to stress gradients within the polysilicon rotor. However, the tolerance band widths and process capability indices available for these model parameters were not indicative of significant yield losses in a factorial analysis. 

Controllability metrics might be something as simple as recording the number of excursions from statistical process control, but process capability indices are probably... 

In order to understand the true process capability for the critical processes, it is important to compute process capability indices using proper statistical procedures. These indices estimate the process s ability to meet design and customer requirements. Two of the most common capability indices are Cp and Cpk, where ... 

A standard method for computing and reporting process capability indices for the critical designs and processes should be developed. Following are some of the key elements that should be considered for a process capability algorithm and report ... 

Estimation of process capability indices for nonnormal data... 

If this is indeed the case, process capabilities can be calculated. Process capabilities indicate the variability (precision) and centering (accuracy) of the process output against the target and as a consequence, the percentage production which does not or cannot meet the product specification. ... 

Figure 1. Overview of the approach for determination of Multivariate Process Capability Indices (MPCI).

The goal is the analysis of risks, determination of MP(2I and failure probabilities of manufacturing processes based on multivariate product characteristics. Subsequently, it is possible to ensure optimised manufacturing processes. This paper focuses on one method for the calculation of multidimensional process capability index with an analogy to the state-of-the-art PCI. An overview of the developed method regarding the estimation of Multivariate Process Capability Indices (MPCI) is shown in Figure 1. The method steps are theoretically explained and applied within the case study in the following sections. 

The continuously analysis and control of the manufacturing process is the precondition for the obtaining of excellent products. The two established methods are quality control charts and the relayed process capability indices. Quality Control Charts (QCC) can be used without an exact knowledge of the characteristic distribution model and are useful in the analysis of manufacturing risks. QCCs show the mean and scattering of each product characteristic in relation to the given tolerance areas. Furthermore, alert and intervention limits can be adapted inside QCC, if needed. This method is an industrial standard, further explanations can be found in (Timischl 2002). It is possible... 

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