#### Basic Notation for Cusum Charts

The following notation is used in this chapter:

 denotes the mean of the population, also referred to as the process mean or the process level. denotes the target mean (goal) for the population. Goel and Wu (1971) refer to as the “acceptable quality level” and use the symbol instead. The symbol is used for in Glossary and Tables for Statistical Quality Control. You can provide with the MU0= option or with the variable _MU0_ in a LIMITS= data set. denotes the population standard deviation. You can provide with the variable _STDDEV_ in a LIMITS= data set (where _TYPE_='STANDARD'). denotes a known standard deviation. You can provide with the SIGMA0= option or the variable _STDDEV_ in a LIMITS= data set. denotes an estimate of . You can provide with the SIGMA0= option or the variable _STDDEV_ in a LIMITS= data set. To identify this value as an estimate, specify TYPE=ESTIMATE or assign the value 'ESTIMATE' to the variable _TYPE_ in a LIMITS= data set. n denotes the nominal sample size for the cusum scheme. You can provide n with the LIMITN= option or the variable _LIMITN_ in a LIMITS= data set. denotes the shift in to be detected, expressed as a multiple of the standard deviation. You can provide with the DELTA= option or the variable _DELTA_ in a LIMITS= data set. denotes the shift in to be detected, expressed in data units. If the sample size n is constant across subgroups, then . Some authors use the symbol D instead of ; for example, refer to Johnson and Leone (1962, 1974) and Wadsworth, Stephens, and Godfrey (1986). You can provide with the SHIFT= option. Although it may be more natural to specify the shift in data units, it is preferable to specify the shift as , since this generalizes to data with unequal subgroup sample sizes.