A New Method of Estimating the Process Capability Index with Exponential Distribution Using Interval Estimate of the Parameter

Abstract

Abstract This paper deals with a new method of deriving the Process Capability Index (PCI) when the quality characteristic X follows a positively skewed distribution. The focus of the paper is to derive a new estimate of PCI by taking into account the 100 ⁢ ( 1 - α ) {100(1-{\alpha})}   Confidence Intervals (CI) of the parameter (s) and arriving at a new expression. The formula C s {{C}_{{s}}} , proposed by Wright (1995) which contains a component for skewness, is reexamined and a new estimate is constructed by utilizing the lower, middle and upper values of the CI of the parameter. The weighted average of the three possible estimates of C s {{C}_{{s}}} is proposed as the new estimate by taking the weights inversely proportional to the squared deviation from the hypothetical value of C s {{C}_{{s}}} . The properties of the estimate are studied by simulation using one parameter exponential distribution.