Process capability indices and product reliability

doi:10.1016/S0026-2714(01)00227-X

Microelectronics Reliability

Volume 41, Issue 12, December 2001, Pages 2067-2070

https://doi.org/10.1016/S0026-2714(01)00227-X Get rights and content

Abstract

This paper discusses process capability indices—C_p and C_pk, their underlying assumptions, and the relationships between process capability indices and product reliability. An actual case is presented to demonstrate this relationship.

Introduction

A process is a unique combination of machines, tools, methods, and personnel engaged in providing a product or service. The output of a process can be product characteristic or process output parameter.

Process capability indices provide a common metric to evaluate and predict the performance of processes. There are two commonly used process capability indices, potential process capability index (C_p) and process capability index (C_pk).

These indices can be used for quality control. They can also be used be used as a communication tool for management as well as between the customer and producer [3], but not necessarily for reliability.

C_p is defined as the ratio of specification width over the process spread. The specification width represents customer and/or product requirements. The process spread represents the process variations. When the process variation is large (more variation), the C_p value is small, indicating a low process capability [5]. $C_{p} = Spec width Process spread = HSL − LSL 6σ$

As indicated by Eq. (1) and illustrated in Fig. 1, C_p indicates how well the process fits within the two specification limits, but does not consider any process shift. If the process average is not centered relative to the specification limits, the C_p index will give misleading results.

The process capability index C_pk is used to provide an indication of the variability associated with a process and how a process has conformed to its specifications. The index is usually used to relate the `natural tolerance' (3σ), to the specification limits [7]. Different from C_p, C_pk describes how well the process fits within the specification limits, taking into account the location of the process mean.

In different situations such as processes with or without a target, the equations for C_pk calculations are different. Process target is a point within the specification width reflecting customer's best interest as shown in Fig. 2. When the process characteristic reaches the target, the customers should be best satisfied. C_pk is the index to measure this real capability when the off-target variation is taken into consideration. The variation factor `k' is defined as: $k= | Target −μ| 0.5(HSL − LSL)$ C_pk is defined as: C_pk=C_p(1−k). When the process is perfectly on target, k=0 and C_pk=C_p. From Eq. (2), we can also see the maximum value for C_pk is C_p.

Eq. (2) is for double-sided specifications with process target specified. , is used for single-sided specifications with process target specified [4]. Eq. (3) is used when only one of the limits, the LSL exists; Eq. (4) is used when only HSL exists. $C_{pk} = Target − LSL 3σ 1− | Target −μ| (T − LSL)$ $C_{pk} = HSL − Target 3σ 1− | Target −μ| (HSL − T)$

When the process target is not specified, C_pk should be calculated based on , , . Eq. (5) is used for double-sided specifications, and can also be used when the target is in the center of the two specification limits. Eq. (6) is used when only HSL exists; Eq. (7) is used when only LSL exists. $C_{pk} = min (HSL −μ,μ− LSL) 3σ$ $C_{pk} = HSL −μ 3σ$ $C_{pk} = μ− LSL 3σ$

Section snippets

Assumptions and limitations

The definitions of C_p and C_pk are only applicable for normal distributions. C_p and C_pk calculated from a non-normal distribution, using conventional methods, will have completely different statistical meaning. For example, the percentage of non-conforming products from a non-normal distribution may be very different than from a normal distribution that has the same C_pk value. As illustrated in Fig. 3, curve 1 is a normal distribution; curve 2 is a rectangular distribution. Both of them have the

Case study: process capability indices and reliability

As a discussion example, we consider the process capability and process yield study conducted by Warrior [6]. This study involved assessments of actual C_p data and process yields for solder bumps associated with the flip-chip semiconductor devices.

Fig. 4 shows how the capability index value C_p of the solder bumping process was increased over a period of time. Fig. 4 also shows the bump failures in the assembly process and also the fact that there was an increase in failures after a process

Summary

Process capability indices, C_p and C_pk, are useful, so long as the fundamental underlying assumptions, such as normal distribution, stable process and variable data, are known. If two processes are identical except one with higher C_pk than another, then the process yield with higher C_pk will be higher than the process with lower C_pk. Since C_p does not take the process mean into account and reflect the non-conformance rejects, the conclusion does not apply to C_p. However C_pk cannot replace

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Defects tail off with six-sigma manufacturing
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S. Kotz et al.
Process capability indices in theory and practice
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There are more references available in the full text version of this article.

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Research noteProcess capability indices and product reliability

Abstract

Introduction

Section snippets

Assumptions and limitations

Case study: process capability indices and reliability

Summary

Measuring process capability: techniques and calculations for quality and manufacturing engineers

Defects tail off with six-sigma manufacturing

IEEE Circ Dev Mag

Process capability indices in theory and practice

Research note
Process capability indices and product reliability