This chapter discusses a set of methods for monitoring process characteristics over time called control charts and places these tools in the wider perspective of quality improvement. The time series chapter, Chapter 14, deals more generally with changes in a variable over time. Control charts deal with a very specialized type of problem which we introduce in the ﬁrst subsection. The discussion draws on the ideas about Normally distributed data and about variability from Chapter 6, about the sampling distributions of means and proportions from Chapter 7, hypothesis tests from Chapter 9 and about plotting techniques from Chapters 2 and 3.
13.1.1 The Setting The data given in Table 13.1.1, from Gunter , was produced by a process that was manufacturing integrated circuits (ICs). The observations are coded measures of the thickness of the resistance layer on the IC for successive ICs produced. The design of the product speciﬁes a particular thickness, here 205 units. Thus, 205 is the target value. If the thickness of the layer strays too far from 205 the performance of the IC will be degraded in various ways. Other manufacturers who buy the ICs to incorporate in their own products may well impose some limits on the range of thicknesses that they will accept. Such limits are called speciﬁcation limits. Any ICs that fall outside this range are unacceptable to these customers. So the manufacturer is trying to manufacture ICs with the target resistancelayer thickness of 205, but despite the company’s best eﬀorts, the actual thicknesses vary appreciably. This is typical of the products of any process. No two products are ever absolutely identical. There are diﬀerences due to variation in raw materials, environmental changes (e.g. humidity and temperature), variations in the way machines are operating, variations in the way that people do
Control Charts things. In addition to...