Table 2 Comparison of different software packages for computing tolerance intervals of some commonly used distributions

Normal

(Krishnamoorthy and Mathew 2009)

(Hoew 1969), (Wald and Wolfowitz 1946), (Weissberg and Beatty 1969)

(Young 2010)

(Krishnamoorthy and Mathew 2009)

(Meeker et al. 2017)

(Hoew 1969)

One-sided:

(JMP, Minitab, NCSS, Python, R, SAS)

Two-sided:

(JMP, Minitab, R, SAS)

(NCSS, Python, R)

Nonparametric

(Faulkenberry and Daly 1970), (Wilks 1941b), (Robbins 1944), (Krishnamoorthy and Mathew 2009)

(Hahn and Meeker 1991), (Bury 1999), (Wald 1943), (Wilks 1941a), (Young and Mathew 2014)

(Hong et al. 2017) (Battelle Memorial Institute 2017)

(Krishnamoorthy and Mathew 2009)

(Meeker et al. 2017)

(Bury 1999)

(Minitab, NCSS, R, SAS)

(Continuous)

(JMP, Python, R)

Lognormal

(Krishnamoorthy and Mathew 2009)

(Hoew 1969), (Wald and Wolfowitz 1946), (Weissberg and Beatty 1969)

(Young 2010)

(Minitab, R)

(Python, R)

Gamma

(Krishnamoorthy et al. 2008)

(Krishnamoorthy et al. 2008)

Exponential

(Fernandez 2010)

(Blischke and Murthy 2000)

Smallest extreme value

(Lawless 1975)

(Bain and Engelhardt 1981), (Coles 2001)

Weibull

(Lawless 1975)

(Bain and Engelhardt 1981), (Coles 2001)

Largest extreme value

(Lawless 1975)

(Bain and Engelhardt 1981), (Coles 2001)

Logistic

(Bain and Englehardt 1991)

(Balakrishnan 1992), (Hall 1975)

Loglogistic

(Bain and Englehardt 1991)

(Balakrishnan 1992), (Hall 1975)