## Abstract

Comparison of quality for products (supplies and goods) is extremely important for manufacturers and consumers. Based on correct comparisons, manufacturers and consumers can find better suppliers to cooperate and better merchandise to purchase, respectively. Quality is often measured and compared by process capability indices, among which C_{p} is very efiective, simple to apply, and particularly useful for the first round of comparison. In practice, C_{p} is unknown and should be estimated from observations. Let dCpi denote the maximum likelihood estimator obtained from normal process, Xi, with index value C_{p}i; i = 1; 2. If dCp1 > (<)d C_{p2} is observed, we will conclude that C_{p}1 > (<) C_{p2} and decide that X1 is better (worse) than X2. Given a small and positive number, , there is no need to make comparison when (1-€) C_{p2} < C_{p}1 < (1+€) C_{p2} since C_{p}1 is close to C_{p}2. It is desirable to observe dCp1 <d C_{p2} with high probability when (1 + €) C_{p2} > C_{p}1 and with low probability when (1-€) C_{p2} < C_{p}1. Given 0 < 1, 2 < 1, based on the table constructed from P(dC_{p}1 >d C_{p2}), we demonstrate how to find the smallest sample size needed to ensure observing dCp1 d C_{p2} with probability greater than 1 €1 when (1 + €) C_{p2} < C_{p}1 and smaller than 2 when (1 €) C_{p2} < C_{p}1.

Original language | English |
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Pages (from-to) | 3072-3085 |

Number of pages | 14 |

Journal | Scientia Iranica |

Volume | 23 |

Issue number | 6 |

DOIs | |

State | Published - 2016 |

## Keywords

- Biased estimator
- C
- Maximum likelihood estimator
- Process capability Index
- Unbiased estimator

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